Practice Quantitative Aptitude questions on Stocks and Shares, covering share prices, face value, market value, dividends, brokerage, investment returns, and profit or loss on share transactions. Takes about 20–25 minutes and is useful for placement tests, TCS NQT, SSC, banking and MBA entrance exams.
Question 1
Find the number of shares that can be bought for Rs.8200 if the market value is Rs.20 each with brokerage being 2.5%.
A
450✓✗
B
500✓✗
C
400✓✗
D
410✓✗
Explanation
Cost of each share = 20 + 2.5% of 20 = Rs.20.5. Number of shares = 820020.5 = 400.
Question 2
Find the market value of the stock if 6% yields 10%.
A
60✓✗
B
70✓✗
C
80✓✗
D
100✓✗
Explanation
For a desired yield of 10%, an investment of Rs.100 gives an income of Rs.10. So for the stock's income of Rs.6, the investment = 60010 = Rs.60.
Question 3
What is the investment made if one invests in 15% stock at 50 and earns Rs.1500?
A
8000✓✗
B
7000✓✗
C
5000✓✗
D
6000✓✗
Explanation
To earn Rs.15, the investment required is Rs.50. Hence, to earn Rs.1500, investment = 1500 × 5015 = Rs.5000.
Question 4
A company pays 12.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares?
A
6.25✓✗
B
25✓✗
C
50✓✗
D
12.5✓✗
Explanation
Dividend on 1 share = 12.5 × 50100 = Rs.6.25. Since Rs.25 income corresponds to an investment of Rs.100 (a 25% yield), Rs.6.25 income corresponds to an investment of 6.25 × 10025 = Rs.25.
Question 5
Which of the following is a better investment?
A
10% stock at 80✓✗
B
15% stock at 70✓✗
C
12% stock at 75✓✗
D
All of these✓✗
Explanation
Effective yield per Rs.100 invested: for 10% stock at 80, yield = 100 × 1080 = 12.5%. For 15% stock at 70, yield = 100 × 1570 = 21.43%. For 12% stock at 75, yield = 100 × 1275 = 16%. The 15% stock at 70 gives the highest yield, making it the better investment.
Question 6
Rs.7,50,000 are invested in Rs.100 shares which are quoted at Rs.1200. Find the income if 25% dividend is declared on the shares.
A
1560✓✗
B
15625✓✗
C
15600✓✗
D
16500✓✗
Explanation
Number of shares = 7500001200 = 625. Dividend per share = 25% of the face value Rs.100 = Rs.25. Income = 625 × 25 = Rs.15,625.
Question 7
Amit invests Rs.9000 partly in 5% Rs.100 shares at Rs.125, and partly in 3% Rs.100 shares at Rs.60. If his total income is Rs.400, how much has he invested in each?
A
Rs.3000 and Rs.6000✓✗
B
Rs.2000 and Rs.7000✓✗
C
Rs.6000 and Rs.3000✓✗
D
Rs.5000 and Rs.4000✓✗
Explanation
Income on the first shares = 5 on every Rs.125 invested, which is 4% of the investment. Income on the second shares = 3 on every Rs.60 invested, which is 5% of the investment.
Let x be invested in the first shares. 0.04x + 0.05(9000 - x) = 400, so 450 - 0.01x = 400 and x = 5000.
The investment is Rs.5000 in the first and Rs.4000 in the second.
Question 8
Rs. 6,00,000 are invested in Rs. 100 shares which are quoted at Rs. 120. Find the income if 20% dividend is declared on the shares.
A
Rs. 96,000✓✗
B
Rs. 1,00,000✓✗
C
Rs. 1,20,000✓✗
D
Rs. 1,25,000✓✗
Explanation
Number of shares bought = 600000 / 120 = 5000.
Face value total = 5000 × 100 = Rs. 5,00,000.
Dividend income = 20% of 5,00,000 = Rs. 1,00,000.
Question 9
X buys 200 shares at Rs.99.70, 300 at Rs.100.10, and 100 at Rs.100.50. Then the price settles at Rs.99.95. How many should he buy at this price, so that his average cost is Rs.100 per share?
A
600✓✗
B
400✓✗
C
250✓✗
D
500✓✗
Explanation
Cost so far = 200 × 99.70+300 × 100.10+100 × 100.50 = 60020 for 600 shares. For n more shares at 99.95, (60020+99.95n)/(600+n)=100 gives n=400.
Question 10
What is the CP of Rs 100 stock at 4 discount, with 15% brokerage?
A
99.6✓✗
B
96.2✓✗
C
97.5✓✗
D
98.25✓✗
Explanation
The cost price of Rs. 100 stock at a discount of 4 = 100 - 4 = Rs. 96.
The brokerage is 15% of 100 = Rs. 0.20.
Cost price = 96 + 0.20 = Rs. 96.2.
Question 11
What investment must be made to obtain Rs 650 income from 10% stock at Rs 96?
A
3100✓✗
B
6240✓✗
C
3500✓✗
D
6000✓✗
Explanation
The investment to get an income of Rs. 650 from a 10% stock at Rs. 96 = 650 × 9610 = Rs. 6240.
Question 12
The selling price of 3 shares is equal to the face value of 12 shares. Find the profit or loss percentage on selling a share. Profit or loss is reckoned on the face value.
A
75% profit✓✗
B
300% profit✓✗
C
400% profit✓✗
D
75% loss✓✗
Explanation
Let the face value of 1 share be Rs. x.
Selling price of 3 shares = face value of 12 shares = 12x, so the selling price of 1 share = 12x ÷ 3 = 4x.
Profit on 1 share = 4x − x = 3x.
Profit % = 3xx × 100 = 300%.
Shortcut Method
SP of 1 share = 12 ÷ 3 = 4 × FV
Profit = 4 − 1 = 3 × FV
∴ 300% profit ✓
Question 13
The face value of a share is 40% of its market value, and the share is sold at 150% of its market value. Find the profit percentage. Profit or loss is reckoned on the face value.
A
175%✓✗
B
225%✓✗
C
275%✓✗
D
375%✓✗
Explanation
Let the face value be Rs. 100.
Face value = 40% of the market value, so the market value = 100 × 10040 = Rs. 250.
Selling price = 150% of 250 = Rs. 375.
Profit = 375 − 100 = Rs. 275, so profit % = 275%.
Shortcut Method
FV = 100 → MV = 250 → SP = 375
∴ Profit = 275% ✓
Question 14
The face value of a share is Rs. 60 and it is sold at a profit of 30% on its face value. If the face value is raised to Rs. 65 while the selling price stays the same, what is the new profit percentage on the face value?
A
15%✓✗
B
18%✓✗
C
25%✓✗
D
20%✓✗
Explanation
Selling price = 60 + 30% of 60 = 60 + 18 = Rs. 78.
New face value = Rs. 65, so the new profit = 78 − 65 = Rs. 13.
New profit % = 1365 × 100 = 20%.
Shortcut Method
SP = 60 × 1.3 = 78
Profit = 78 − 65 = 13
∴ 1365 = 20% ✓
Question 15
The profit on selling 5 shares is Rs. 600. If the profit on each share is 25% of its market value, and the market value is 160% of the face value, find the face value of one share.
A
Rs. 240✓✗
B
Rs. 360✓✗
C
Rs. 300✓✗
D
Rs. 480✓✗
Explanation
Profit on 1 share = 600 ÷ 5 = Rs. 120.
120 = 25% of the market value, so the market value = 120 × 4 = Rs. 480.
480 = 160% of the face value, so the face value = 480 × 100160 = Rs. 300.
Shortcut Method
Profit/share = 120 → MV = 120 × 4 = 480
FV = 480 ÷ 1.6
∴ FV = Rs. 300 ✓
Question 16
The face value of a share is changed from Rs. 250 to Rs. 300. The market value is always 150% of the face value, and the profit on selling the share is always 20% of the market value. Find the change in the profit.
A
Rs. 15✓✗
B
Rs. 10✓✗
C
Rs. 20✓✗
D
Rs. 25✓✗
Explanation
Before: market value = 150% of 250 = Rs. 375, so profit = 20% of 375 = Rs. 75.
After: market value = 150% of 300 = Rs. 450, so profit = 20% of 450 = Rs. 90.
Change in profit = 90 − 75 = Rs. 15.
Shortcut Method
Profit = 20% × 150% × FV = 0.3 × FV
Change = 0.3 × (300 − 250) = 0.3 × 50
∴ Rs. 15 ✓
Question 17
The face value of a share is revalued from Rs. 40 per share to Rs. 90 for 2 shares. The market value is 180% of the face value and the profit on selling a share is 50% of its market value. Find the change in the profit on one share.
A
Rs. 3.60✓✗
B
Rs. 5.40✓✗
C
Rs. 9✓✗
D
Rs. 4.50✓✗
Explanation
Before: face value = Rs. 40, market value = 180% of 40 = Rs. 72, profit = 50% of 72 = Rs. 36.
After: face value = 90 ÷ 2 = Rs. 45 per share, market value = 180% of 45 = Rs. 81, profit = 50% of 81 = Rs. 40.50.
Change in profit = 40.50 − 36 = Rs. 4.50.
Shortcut Method
New FV = 90 ÷ 2 = 45 (per share)
Profit = 50% × 180% × FV = 0.9 × FV
Change = 0.9 × (45 − 40) = 0.9 × 5
∴ Rs. 4.50 ✓
Question 18
The market value of a share is 40% of its face value, and the face value is 25% of its selling price. If the profit on selling the share is Rs. 270, find the market value of the share. Profit or loss is reckoned on the face value.
A
Rs. 36✓✗
B
Rs. 90✓✗
C
Rs. 27✓✗
D
Rs. 360✓✗
Explanation
Let the face value be Rs. x. The face value is 25% of the selling price, so the selling price = 4x.
Profit = 4x − x = 3x = 270, so x = Rs. 90.
Market value = 40% of 90 = Rs. 36.
Shortcut Method
SP = 4 × FV → profit = 3 × FV = 270 → FV = 90
MV = 40% of 90
∴ MV = Rs. 36 ✓
Question 19
The face value of a share is 40% of its market value, and the market value is 80% of its selling price. If the face value is Rs. 160, find the selling price.
A
Rs. 400✓✗
B
Rs. 640✓✗
C
Rs. 500✓✗
D
Rs. 800✓✗
Explanation
Face value = 40% of the market value, so the market value = 160 × 10040 = Rs. 400.
Market value = 80% of the selling price, so the selling price = 400 × 10080 = Rs. 500.
Shortcut Method
MV = 160 ÷ 0.4 = 400
SP = 400 ÷ 0.8
∴ SP = Rs. 500 ✓
Question 20
The selling price of a share is 50% more than its market value, and the market value is 100% more than its face value. Find the profit percentage on selling the share. Profit or loss is reckoned on the face value.
A
150%✓✗
B
250%✓✗
C
300%✓✗
D
200%✓✗
Explanation
Let the face value be Rs. 100.
Market value = 100 + 100% of 100 = Rs. 200.
Selling price = 200 + 50% of 200 = Rs. 300.
Profit = 300 − 100 = Rs. 200, so profit % = 200%.
Shortcut Method
FV = 100 → MV = 200 → SP = 300
∴ Profit = 200% ✓
Question 21
The selling price of a share is 60% of its market value, and the market value is 50% of its face value. Find the loss percentage. Profit or loss is reckoned on the face value.
A
30%✓✗
B
70%✓✗
C
40%✓✗
D
80%✓✗
Explanation
Let the face value be Rs. 100.
Market value = 50% of 100 = Rs. 50.
Selling price = 60% of 50 = Rs. 30.
Loss = 100 − 30 = Rs. 70, so loss % = 70%.
Shortcut Method
SP = 60% × 50% = 30% of FV
∴ Loss = 100 − 30 = 70% ✓
Question 22
The market value of a share is 80% of its face value and 20% less than its selling price. Find the profit or loss percentage. Profit or loss is reckoned on the face value.
A
20% loss✓✗
B
20% profit✓✗
C
No profit, no loss✓✗
D
25% profit✓✗
Explanation
Let the face value be Rs. 100.
Market value = 80% of 100 = Rs. 80.
The market value is 20% less than the selling price, so 80 = 80% of the selling price, and the selling price = 80 × 10080 = Rs. 100.
Selling price = face value, so there is no profit and no loss.
Shortcut Method
MV = 80, MV = 0.8 × SP → SP = 100 = FV
∴ No profit, no loss ✓
Question 23
The selling price of a share is Rs. 210. If the market value is 60% of the face value and the loss on selling is 30%, find the market value. Profit or loss is reckoned on the face value.
A
Rs. 126✓✗
B
Rs. 210✓✗
C
Rs. 300✓✗
D
Rs. 180✓✗
Explanation
Loss = 30%, so the selling price = 70% of the face value.
70% of the face value = 210, so the face value = 210 × 10070 = Rs. 300.
Market value = 60% of 300 = Rs. 180.
Shortcut Method
SP = 0.7 × FV = 210 → FV = 300
MV = 60% of 300
∴ MV = Rs. 180 ✓
Question 24
The market value of a share is 32% more than its face value and 10% more than its selling price. Find the profit percentage on selling the share. Profit or loss is reckoned on the face value.
A
20%✓✗
B
10%✓✗
C
22%✓✗
D
32%✓✗
Explanation
Let the face value be Rs. 100.
Market value = 100 + 32% of 100 = Rs. 132.
The market value is 10% more than the selling price, so the selling price = 132 × 100110 = Rs. 120.
Profit = 120 − 100 = Rs. 20, so profit % = 20%.
Shortcut Method
MV = 132 → SP = 132 ÷ 1.1 = 120
∴ Profit = 20% ✓
Question 25
The market value of a share is 30% of its face value and 25% less than its selling price. Find the profit or loss percentage. Profit or loss is reckoned on the face value.
A
60% profit✓✗
B
40% loss✓✗
C
60% loss✓✗
D
70% loss✓✗
Explanation
Let the face value be Rs. 100.
Market value = 30% of 100 = Rs. 30.
The market value is 25% less than the selling price, so 30 = 75% of the selling price, and the selling price = 30 × 10075 = Rs. 40.
Loss = 100 − 40 = Rs. 60, so loss % = 60%.
Shortcut Method
MV = 30 = 0.75 × SP → SP = 40
∴ Loss = 100 − 40 = 60% ✓
Question 26
The selling price of a share is Rs. 336. If the market value is 45% of the face value and the loss on selling is 16%, find the market value. Profit or loss is reckoned on the face value.
A
Rs. 151.20✓✗
B
Rs. 180✓✗
C
Rs. 200✓✗
D
Rs. 400✓✗
Explanation
Loss = 16%, so the selling price = 84% of the face value.
84% of the face value = 336, so the face value = 336 × 10084 = Rs. 400.
Market value = 45% of 400 = Rs. 180.
Shortcut Method
SP = 0.84 × FV = 336 → FV = 400
MV = 45% of 400
∴ MV = Rs. 180 ✓
Question 27
The market value of a share is 52 times the profit made on selling it. If the face value is Rs. 640 and the profit is 25% of the face value, find the market value.
A
Rs. 160✓✗
B
Rs. 256✓✗
C
Rs. 480✓✗
D
Rs. 400✓✗
Explanation
Profit = 25% of 640 = Rs. 160.
Market value = 52 × 160 = Rs. 400.
Shortcut Method
Profit = 640 ÷ 4 = 160
MV = 52 × 160
∴ MV = Rs. 400 ✓
Question 28
The market value of a share is 60% more than its face value and 25% more than its selling price. Find the profit percentage on selling the share. Profit or loss is reckoned on the face value.
A
25%✓✗
B
35%✓✗
C
28%✓✗
D
60%✓✗
Explanation
Let the face value be Rs. 100.
Market value = 100 + 60% of 100 = Rs. 160.
The market value is 25% more than the selling price, so the selling price = 160 × 100125 = Rs. 128.
Profit = 128 − 100 = Rs. 28, so profit % = 28%.
Shortcut Method
MV = 160 → SP = 160 ÷ 1.25 = 128
∴ Profit = 28% ✓
Question 29
The market value of a share is 42% of its face value and 40% less than its selling price. Find the profit or loss percentage. Profit or loss is reckoned on the face value.
A
30% loss✓✗
B
30% profit✓✗
C
58% loss✓✗
D
70% loss✓✗
Explanation
Let the face value be Rs. 100.
Market value = 42% of 100 = Rs. 42.
The market value is 40% less than the selling price, so 42 = 60% of the selling price, and the selling price = 42 × 10060 = Rs. 70.
Loss = 100 − 70 = Rs. 30, so loss % = 30%.
Shortcut Method
MV = 42 = 0.6 × SP → SP = 70
∴ Loss = 100 − 70 = 30% ✓
Question 30
The selling price of a share is Rs. 1,176. If the market value is 96% of the face value and the loss on selling is 2%, find the market value. Profit or loss is reckoned on the face value.
A
Rs. 1,128.96✓✗
B
Rs. 1,200✓✗
C
Rs. 1,152✓✗
D
Rs. 1,176✓✗
Explanation
Loss = 2%, so the selling price = 98% of the face value.
98% of the face value = 1,176, so the face value = 1,176 × 10098 = Rs. 1,200.
Market value = 96% of 1,200 = Rs. 1,152.
Shortcut Method
SP = 0.98 × FV = 1,176 → FV = 1,200
MV = 96% of 1,200
∴ MV = Rs. 1,152 ✓
Question 31
The market value of a share is 80% more than its face value and 20% more than its selling price. Find the profit percentage on selling the share. Profit or loss is reckoned on the face value.
A
40%✓✗
B
80%✓✗
C
60%✓✗
D
50%✓✗
Explanation
Let the face value be Rs. 100.
Market value = 100 + 80% of 100 = Rs. 180.
The market value is 20% more than the selling price, so the selling price = 180 × 100120 = Rs. 150.
Profit = 150 − 100 = Rs. 50, so profit % = 50%.
Shortcut Method
MV = 180 → SP = 180 ÷ 1.2 = 150
∴ Profit = 50% ✓
Question 32
The market value of a share is 90% of its face value and 85% less than its selling price. Find the profit or loss percentage. Profit or loss is reckoned on the face value.
A
400% profit✓✗
B
500% profit✓✗
C
600% profit✓✗
D
No profit, no loss✓✗
Explanation
Let the face value be Rs. 100.
Market value = 90% of 100 = Rs. 90.
The market value is 85% less than the selling price, so 90 = 15% of the selling price, and the selling price = 90 × 10015 = Rs. 600.
Profit = 600 − 100 = Rs. 500, so profit % = 500%.
Shortcut Method
MV = 90 = 0.15 × SP → SP = 600
∴ Profit = 600 − 100 = 500% ✓
Question 33
The selling price of a share is Rs. 900. If the market value is 72% of the face value and the loss on selling is 64%, find the market value. Profit or loss is reckoned on the face value.
A
Rs. 648✓✗
B
Rs. 1,800✓✗
C
Rs. 1,250✓✗
D
Rs. 2,500✓✗
Explanation
Loss = 64%, so the selling price = 36% of the face value.
36% of the face value = 900, so the face value = 900 × 10036 = Rs. 2,500.
Market value = 72% of 2,500 = Rs. 1,800.
Shortcut Method
SP = 0.36 × FV = 900 → FV = 2,500
MV = 72% of 2,500
∴ MV = Rs. 1,800 ✓
Question 34
The face value of a share is revalued from Rs. 60 per share to Rs. 90 per share. If the market value is 80% of the face value and the selling price is 150% of the market value, find the change in the selling price.
A
Rs. 30✓✗
B
Rs. 36✓✗
C
Rs. 45✓✗
D
Rs. 54✓✗
Explanation
Before: market value = 80% of 60 = Rs. 48, selling price = 150% of 48 = Rs. 72.
After: market value = 80% of 90 = Rs. 72, selling price = 150% of 72 = Rs. 108.
Change in the selling price = 108 − 72 = Rs. 36.
Shortcut Method
SP = 150% × 80% × FV = 1.2 × FV
Change = 1.2 × 30
∴ Rs. 36 ✓
Question 35
The face value of a share is revalued from Rs. 200 per share to Rs. 120 per share. If the market value is 110% of the face value and the selling price is 60% of the market value, find the change in the selling price.
A
Rs. 48✓✗
B
Rs. 66✓✗
C
Rs. 52.8✓✗
D
Rs. 88✓✗
Explanation
Before: market value = 110% of 200 = Rs. 220, selling price = 60% of 220 = Rs. 132.
After: market value = 110% of 120 = Rs. 132, selling price = 60% of 132 = Rs. 79.2.
Change in the selling price = 132 − 79.2 = Rs. 52.8.
Shortcut Method
SP = 60% × 110% × FV = 0.66 × FV
Change = 0.66 × 80
∴ Rs. 52.8 ✓
Question 36
The face value of a share is revalued from Rs. 180 per share to Rs. 120 per share. If the market value is 75% of the face value and the selling price is 140% of the market value, find the change in the selling price.
A
Rs. 45✓✗
B
Rs. 84✓✗
C
Rs. 105✓✗
D
Rs. 63✓✗
Explanation
Before: market value = 75% of 180 = Rs. 135, selling price = 140% of 135 = Rs. 189.
After: market value = 75% of 120 = Rs. 90, selling price = 140% of 90 = Rs. 126.
Change in the selling price = 189 − 126 = Rs. 63.
Shortcut Method
SP = 140% × 75% × FV = 1.05 × FV
Change = 1.05 × 60
∴ Rs. 63 ✓
Question 37
The face value of a share is revalued from Rs. 1,440 per share to Rs. 1,500 per share. If the market value is 115% of the face value and the selling price is 160% of the market value, find the change in the selling price.
A
Rs. 110.4✓✗
B
Rs. 96✓✗
C
Rs. 115.2✓✗
D
Rs. 138✓✗
Explanation
Before: market value = 115% of 1,440 = Rs. 1,656, selling price = 160% of 1,656 = Rs. 2649.6.
After: market value = 115% of 1,500 = Rs. 1,725, selling price = 160% of 1,725 = Rs. 2,760.
Change in the selling price = 2,760 − 2649.6 = Rs. 110.4.
Shortcut Method
SP = 160% × 115% × FV = 1.84 × FV
Change = 1.84 × 60
∴ Rs. 110.4 ✓
Question 38
The face value of a share is revalued from Rs. 500 per share to Rs. 1,250 per share. If the market value is 40% of the face value and the selling price is 300% of the market value, find the change in the selling price.
A
Rs. 600✓✗
B
Rs. 1,200✓✗
C
Rs. 900✓✗
D
Rs. 1,500✓✗
Explanation
Before: market value = 40% of 500 = Rs. 200, selling price = 300% of 200 = Rs. 600.
After: market value = 40% of 1,250 = Rs. 500, selling price = 300% of 500 = Rs. 1,500.
Change in the selling price = 1,500 − 600 = Rs. 900.
Shortcut Method
SP = 300% × 40% × FV = 1.2 × FV
Change = 1.2 × 750
∴ Rs. 900 ✓
Question 39
A 7.5% stock yields 6%. The market value of the stock is:
A
Rs. 80✓✗
B
Rs. 100✓✗
C
Rs. 125✓✗
D
Rs. 150✓✗
Explanation
A 7.5% stock gives an income of Rs. 7.5 on every Rs. 100 of face value.
A yield of 6% means this income is 6% of the money invested.
Investment = 7.5 × 1006 = Rs. 125.
So the market value of the Rs. 100 stock = Rs. 125.
Shortcut Method
MV = rate × 100yield
7.5 × 1006
∴ MV = Rs. 125 ✓
Question 40
A 9% stock yields 7.5%. What is the market value of the stock?
A
Rs. 120✓✗
B
Rs. 83.33✓✗
C
Rs. 100✓✗
D
Rs. 150✓✗
Explanation
A 9% stock gives an income of Rs. 9 on every Rs. 100 of face value.
A yield of 7.5% means this income is 7.5% of the money invested.
Investment = 9 × 1007.5 = Rs. 120.
So the market value of the Rs. 100 stock = Rs. 120.
Shortcut Method
MV = rate × 100yield
9 × 1007.5
∴ MV = Rs. 120 ✓
Question 41
Money is worth 6%. At what price should a stock paying 9 percent be quoted?
A
Rs. 66.67✓✗
B
Rs. 100✓✗
C
Rs. 125✓✗
D
Rs. 150✓✗
Explanation
The 9% the investor earns should equal 6% of the amount invested.
To earn Rs. 6, one invests Rs. 100.
To earn Rs. 9, one invests 100 × 96 = Rs. 150.
So the stock should be quoted at Rs. 150.
Shortcut Method
6% of price = 9
price = 100 × 96
∴ Rs. 150 ✓
Question 42
If money is worth 5%, what should be the quoted price of a stock that pays 4 percent?
A
Rs. 80✓✗
B
Rs. 75✓✗
C
Rs. 90✓✗
D
Rs. 125✓✗
Explanation
The 4% the investor earns should equal 5% of the amount invested.
To earn Rs. 5, one invests Rs. 100.
To earn Rs. 4, one invests 100 × 45 = Rs. 80.
So the stock should be quoted at Rs. 80.
Shortcut Method
5% of price = 4
price = 100 × 45
∴ Rs. 80 ✓
Question 43
Money is worth 8%. At what price should the stock which pays 9 percent be quoted?
A
Rs. 88.89✓✗
B
Rs. 100✓✗
C
Rs. 112.50✓✗
D
Rs. 118.50✓✗
Explanation
The 9% the investor earns should equal 8% of the amount invested.
To earn Rs. 8, one invests Rs. 100.
To earn Rs. 9, one invests 100 × 98 = Rs. 112.50.
So the stock should be quoted at Rs. 112.50.
Shortcut Method
8% of price = 9
price = 100 × 98
∴ Rs. 112.50 ✓
Question 44
Money is worth 12.5%. At what price must a 15% stock be quoted?
A
Rs. 83.33✓✗
B
Rs. 100✓✗
C
Rs. 150✓✗
D
Rs. 120✓✗
Explanation
The 15% the investor earns should equal 12.5% of the amount invested.
To earn Rs. 12.5, one invests Rs. 100.
To earn Rs. 15, one invests 100 × 1512.5 = Rs. 120.
So the stock must be quoted at Rs. 120.
Shortcut Method
12.5% of price = 15
price = 100 × 1512.5
∴ Rs. 120 ✓
Question 45
The cost price of a Rs. 100 stock at 6 discount, when the brokerage is 12%, is:
A
Rs. 94.50✓✗
B
Rs. 93.50✓✗
C
Rs. 94✓✗
D
Rs. 106.50✓✗
Explanation
A stock at 6 discount is bought at 100 − 6 = Rs. 94.
The brokerage of 12% (Rs. 0.50) is added to the buying price.
Cost price = 94 + 0.50 = Rs. 94.50.
Shortcut Method
price = 100 − 6 = 94
buying: add brokerage
∴ CP = 94 + 0.50 = Rs. 94.50 ✓
Question 46
What is the cost of a Rs. 100 stock at 5 premium when the brokerage is 15%?
A
Rs. 104.80✓✗
B
Rs. 105✓✗
C
Rs. 105.50✓✗
D
Rs. 105.20✓✗
Explanation
A stock at 5 premium is quoted at 100 + 5 = Rs. 105.
The brokerage of 15% (Rs. 0.20) is added to the buying price.
Cost = 105 + 0.20 = Rs. 105.20.
Shortcut Method
price = 100 + 5 = 105
buying: add brokerage
∴ Cost = 105 + 0.20 = Rs. 105.20 ✓
Question 47
By investing Rs. 2,730 in 7% stock, Priya earns Rs. 210. The stock is then quoted at:
A
Rs. 13✓✗
B
Rs. 91✓✗
C
Rs. 84✓✗
D
Rs. 98✓✗
Explanation
To earn Rs. 210, the investment is Rs. 2,730.
To earn Rs. 7 (the income on Rs. 100 of 7% stock), the investment = 2,730 × 7210 = Rs. 91.
So the market value of the Rs. 100 stock = Rs. 91.
Shortcut Method
Rs. 210 income → Rs. 2,730
Rs. 7 income → 2,730 × 7210
∴ Quoted at Rs. 91 ✓
Question 48
Ravi invests Rs. 3,150 in 9% stock and earns Rs. 270. At what price is the stock quoted?
A
Rs. 105✓✗
B
Rs. 81✓✗
C
Rs. 95✓✗
D
Rs. 117✓✗
Explanation
To earn Rs. 270, the investment is Rs. 3,150.
To earn Rs. 9 (the income on Rs. 100 of 9% stock), the investment = 3,150 × 9270 = Rs. 105.
So the stock is quoted at Rs. 105.
Shortcut Method
Rs. 270 income → Rs. 3,150
Rs. 9 income → 3,150 × 9270
∴ Quoted at Rs. 105 ✓
Question 49
A man invests Rs. 5,040 in Rs. 10 shares quoted at Rs. 8.40. If the rate of dividend is 15%, his annual income is:
A
Rs. 90✓✗
B
Rs. 756✓✗
C
Rs. 900✓✗
D
Rs. 6,000✓✗
Explanation
Number of shares = 5,0408.40 = 600.
Face value of the shares = 600 × 10 = Rs. 6,000.
Annual income = 15% of Rs. 6,000 = Rs. 900.
Shortcut Method
shares = 5,040 ÷ 8.40 = 600
face value = 600 × 10 = 6,000
∴ Income = 15% of 6,000 = Rs. 900 ✓
Question 50
Rs. 7,800 is invested in Rs. 20 shares quoted at Rs. 26. If the dividend declared is 10%, the annual income is:
A
Rs. 60✓✗
B
Rs. 780✓✗
C
Rs. 1,000✓✗
D
Rs. 600✓✗
Explanation
Number of shares = 7,80026 = 300.
Face value of the shares = 300 × 20 = Rs. 6,000.
Annual income = 10% of Rs. 6,000 = Rs. 600.
Shortcut Method
shares = 7,800 ÷ 26 = 300
face value = 300 × 20 = 6,000
∴ Income = 10% of 6,000 = Rs. 600 ✓
Question 51
Find the annual income obtained by investing Rs. 4,800 in 6% debentures of face value Rs. 100 at Rs. 96.
A
Rs. 288✓✗
B
Rs. 300✓✗
C
Rs. 312✓✗
D
Rs. 360✓✗
Explanation
Number of debentures bought = 4,80096 = 50.
Each debenture earns 6% of Rs. 100 = Rs. 6.
Total annual income = 50 × 6 = Rs. 300.
Shortcut Method
debentures = 4,800 ÷ 96 = 50
income each = Rs. 6
∴ Income = 50 × 6 = Rs. 300 ✓
Question 52
What annual income is obtained by investing Rs. 9,000 in 7% debentures of face value Rs. 100 at Rs. 120?
A
Rs. 450✓✗
B
Rs. 560✓✗
C
Rs. 630✓✗
D
Rs. 525✓✗
Explanation
Number of debentures bought = 9,000120 = 75.
Each debenture earns 7% of Rs. 100 = Rs. 7.
Total annual income = 75 × 7 = Rs. 525.
Shortcut Method
debentures = 9,000 ÷ 120 = 75
income each = Rs. 7
∴ Income = 75 × 7 = Rs. 525 ✓
Question 53
How much money should be invested to purchase Rs. 7,200 of 5% stock at 9834, brokerage being 14%?
A
Rs. 7,092✓✗
B
Rs. 7,128✓✗
C
Rs. 7,164✓✗
D
Rs. 7,200✓✗
Explanation
Price of Rs. 100 stock = 9834 = Rs. 98.75.
Brokerage 14% = Rs. 0.25, which is added when buying.
Total paid for Rs. 100 stock = 98.75 + 0.25 = Rs. 99.
Investment = 7,200 × 99100 = Rs. 7,128.
Shortcut Method
per Rs. 100 stock: 98.75 + 0.25 = 99
7,200 × 99100
∴ Investment = Rs. 7,128 ✓
Question 54
What sum is needed to buy Rs. 4,500 of 6% stock at 11212, the brokerage being 12%?
A
Rs. 5,062.50✓✗
B
Rs. 5,107.50✓✗
C
Rs. 5,085✓✗
D
Rs. 5,130✓✗
Explanation
Price of Rs. 100 stock = 11212 = Rs. 112.50.
Brokerage 12% = Rs. 0.50, which is added when buying.
Total paid for Rs. 100 stock = 112.50 + 0.50 = Rs. 113.
Investment = 4,500 × 113100 = Rs. 5,085.
Shortcut Method
per Rs. 100 stock: 112.50 + 0.50 = 113
4,500 × 113100
∴ Investment = Rs. 5,085 ✓
Question 55
How much should a person invest in 6% stock at Rs. 96 to get a net income of Rs. 540 a year after paying income tax of 10 paise in a rupee?
A
Rs. 9,600✓✗
B
Rs. 8,640✓✗
C
Rs. 10,560✓✗
D
Rs. 10,800✓✗
Explanation
Gross income on Rs. 96 invested = Rs. 6.
Income tax = 10 paise in a rupee = 10% of Rs. 6 = Rs. 0.60, so net income = 6 − 0.60 = Rs. 5.40.
To get Rs. 5.40, one invests Rs. 96. To get Rs. 540, one invests 540 × 965.40 = Rs. 9,600.
Shortcut Method
gross 6, tax 10% → net = 5.40
Rs. 5.40 → invest Rs. 96
∴ Rs. 540 → 540 × 965.40 = Rs. 9,600 ✓
Question 56
A person wants a net annual income of Rs. 600 from 8% stock at Rs. 120 after paying income tax of 25 paise in a rupee. How much must be invested?
A
Rs. 9,000✓✗
B
Rs. 12,000✓✗
C
Rs. 14,400✓✗
D
Rs. 16,000✓✗
Explanation
Gross income on Rs. 120 invested = Rs. 8.
Income tax = 25 paise in a rupee = 25% of Rs. 8 = Rs. 2, so net income = 8 − 2 = Rs. 6.
To get Rs. 6, one invests Rs. 120. To get Rs. 600, one invests 600 × 1206 = Rs. 12,000.
Shortcut Method
gross 8, tax 25% → net = 6
Rs. 6 → invest Rs. 120
∴ Rs. 600 → 600 × 1206 = Rs. 12,000 ✓
Question 57
How much should be invested in 5% stock at Rs. 120 to get a net income of Rs. 450 a year after paying income tax of 40 paise in a rupee?
A
Rs. 10,800✓✗
B
Rs. 15,000✓✗
C
Rs. 18,000✓✗
D
Rs. 22,500✓✗
Explanation
Gross income on Rs. 120 invested = Rs. 5.
Income tax = 40 paise in a rupee = 40% of Rs. 5 = Rs. 2, so net income = 5 − 2 = Rs. 3.
To get Rs. 3, one invests Rs. 120. To get Rs. 450, one invests 450 × 1203 = Rs. 18,000.
Shortcut Method
gross 5, tax 40% → net = 3
Rs. 3 → invest Rs. 120
∴ Rs. 450 → 450 × 1203 = Rs. 18,000 ✓
Question 58
To earn a net income of Rs. 960 a year from 8% stock at Rs. 105, how much must be invested if income tax of 20 paise in a rupee is deducted?
A
Rs. 12,600✓✗
B
Rs. 14,000✓✗
C
Rs. 16,800✓✗
D
Rs. 15,750✓✗
Explanation
Gross income on Rs. 105 invested = Rs. 8.
Income tax = 20 paise in a rupee = 20% of Rs. 8 = Rs. 1.60, so net income = 8 − 1.60 = Rs. 6.40.
To get Rs. 6.40, one invests Rs. 105. To get Rs. 960, one invests 960 × 1056.40 = Rs. 15,750.
Shortcut Method
gross 8, tax 20% → net = 6.40
Rs. 6.40 → invest Rs. 105
∴ Rs. 960 → 960 × 1056.40 = Rs. 15,750 ✓
Question 59
The market value of a 9% stock, in which an income of Rs. 540 is derived by investing Rs. 8,100, brokerage being 12%, is:
A
Rs. 134.50✓✗
B
Rs. 133✓✗
C
Rs. 135✓✗
D
Rs. 135.50✓✗
Explanation
For an income of Rs. 540, investment = Rs. 8,100.
For an income of Rs. 9, investment = 8,100 × 9540 = Rs. 135.
So buying a Rs. 100 stock costs Rs. 135 in all, which includes the brokerage of Rs. 0.50.
Market value of Rs. 100 stock = 135 − 0.50 = Rs. 134.50.
Shortcut Method
Rs. 9 income → 8,100 × 9540 = 135 (cost incl. brokerage)
MV = 135 − 0.50
∴ MV = Rs. 134.50 ✓
Question 60
Find the market value of a 6% stock if an income of Rs. 360 is obtained by investing Rs. 7,800 and the brokerage is 14%.
A
Rs. 129.50✓✗
B
Rs. 129.75✓✗
C
Rs. 130✓✗
D
Rs. 130.25✓✗
Explanation
For an income of Rs. 360, investment = Rs. 7,800.
For an income of Rs. 6, investment = 7,800 × 6360 = Rs. 130.
So buying a Rs. 100 stock costs Rs. 130 in all, which includes the brokerage of Rs. 0.25.
Market value of Rs. 100 stock = 130 − 0.25 = Rs. 129.75.
Shortcut Method
Rs. 6 income → 7,800 × 6360 = 130 (cost incl. brokerage)
MV = 130 − 0.25
∴ MV = Rs. 129.75 ✓
Question 61
A man invests in 8% stock at 80 and in 12% stock at 90. To obtain equal incomes from both, the ratio of his investments must be:
A
8 : 9✓✗
B
2 : 3✓✗
C
4 : 3✓✗
D
3 : 4✓✗
Explanation
For an income of Rs. 1 from the 8% stock at 80, investment = 808 = Rs. 10.
For an income of Rs. 1 from the 12% stock at 90, investment = 9012 = Rs. 7.50.
Ratio of investments = 10 : 7.50 = 4 : 3.
Shortcut Method
Re 1 income: 80 ÷ 8 = 10; 90 ÷ 12 = 7.5
10 : 7.5
∴ 4 : 3 ✓
Question 62
A man invests partly in 5% stock at 75 and partly in 8% stock at 96 so that the incomes from the two are equal. In what ratio must the money be divided between them?
A
5 : 4✓✗
B
25 : 32✓✗
C
4 : 5✓✗
D
5 : 8✓✗
Explanation
For an income of Rs. 1 from the 5% stock at 75, investment = 755 = Rs. 15.
For an income of Rs. 1 from the 8% stock at 96, investment = 968 = Rs. 12.
Ratio of investments = 15 : 12 = 5 : 4.
Shortcut Method
Re 1 income: 75 ÷ 5 = 15; 96 ÷ 8 = 12
15 : 12
∴ 5 : 4 ✓
Question 63
Rs. 9,120 is invested partly in 6% stock at 75 and partly in 5% stock at 80 so that the incomes from both are equal. The investment in the 6% stock is:
A
Rs. 3,500✓✗
B
Rs. 4,000✓✗
C
Rs. 4,560✓✗
D
Rs. 5,120✓✗
Explanation
Let the investment in 6% stock be Rs. x, so the investment in 5% stock = Rs. (9,120 − x).
Income from the 6% stock = 675 × x = 225x.
Income from the 5% stock = 580 × (9,120 − x) = 116(9,120 − x).
Equal incomes: 225x = 116(9,120 − x), so 32x = 25(9,120 − x).
32x + 25x = 228,000, so 57x = 228,000 and x = Rs. 4,000.
Shortcut Method
income per Re: 675 = 0.08, 580 = 0.0625
investments in ratio 0.0625 : 0.08 = 25 : 32 (57 parts = 9,120)
∴ 6% stock: 25 × 160 = Rs. 4,000 ✓
Question 64
Rs. 11,900 is invested partly in 10% stock at 125 and partly in 9% stock at 100 to have equal incomes. The investment in the 10% stock is:
A
Rs. 5,600✓✗
B
Rs. 5,950✓✗
C
Rs. 6,300✓✗
D
Rs. 6,800✓✗
Explanation
Let the investment in 10% stock be Rs. x, so the investment in 9% stock = Rs. (11,900 − x).
Income from the 10% stock = 10125 × x = 225x.
Income from the 9% stock = 9100 × (11,900 − x).
Equal incomes: 225x = 9100(11,900 − x), so 8x = 9(11,900 − x).
8x + 9x = 107,100, so 17x = 107,100 and x = Rs. 6,300.
Shortcut Method
income per Re: 10125 = 0.08, 9100 = 0.09
investments in ratio 0.09 : 0.08 = 9 : 8 (17 parts = 11,900)
∴ 10% stock: 9 × 700 = Rs. 6,300 ✓
Question 65
Meera invests Rs. 15,000 partly in 8% stock at 80 and the rest in 10% stock at 125. Her total annual dividend is Rs. 1,360. How much does she invest in the 8% stock at 80?
A
Rs. 6,000✓✗
B
Rs. 7,000✓✗
C
Rs. 9,000✓✗
D
Rs. 8,000✓✗
Explanation
Let the investment in 8% stock at 80 be Rs. x, so the investment in 10% stock at 125 = Rs. (15,000 − x).
Income from the 8% stock = 880 × x = 0.10x.
Income from the 10% stock = 10125 × (15,000 − x) = 0.08(15,000 − x).
0.10x + 0.08(15,000 − x) = 1,360, so 0.10x + 1,200 − 0.08x = 1,360.
0.02x = 160, so x = Rs. 8,000.
Shortcut Method
yields: 880 = 0.10, 10125 = 0.08
all in 10%: income 1,200; need 160 more
each Rs. moved to 8% adds 0.02 → 160 ÷ 0.02
∴ 8% stock: Rs. 8,000 ✓
Question 66
Rohit invests Rs. 20,000 partly in 6% stock at 75 and the rest in 9% stock at 120. His total annual dividend is Rs. 1,560. How much does he invest in the 6% stock at 75?
A
Rs. 8,000✓✗
B
Rs. 10,000✓✗
C
Rs. 12,000✓✗
D
Rs. 15,000✓✗
Explanation
Let the investment in 6% stock at 75 be Rs. x, so the investment in 9% stock at 120 = Rs. (20,000 − x).
Income from the 6% stock = 675 × x = 0.08x.
Income from the 9% stock = 9120 × (20,000 − x) = 0.075(20,000 − x).
0.08x + 0.075(20,000 − x) = 1,560, so 0.08x + 1,500 − 0.075x = 1,560.
0.005x = 60, so x = Rs. 12,000.
Shortcut Method
yields: 675 = 0.08, 9120 = 0.075
all in 9%: income 1,500; need 60 more
each Rs. moved to 6% adds 0.005 → 60 ÷ 0.005
∴ 6% stock: Rs. 12,000 ✓
Question 67
A man sells Rs. 4,000, 6% stock at 125 and invests the proceeds partly in 5% stock at 100 and partly in 12% stock at 120. His income increases by Rs. 110. How much is invested in the 12% stock at 120?
A
Rs. 2,000✓✗
B
Rs. 1,500✓✗
C
Rs. 2,500✓✗
D
Rs. 3,000✓✗
Explanation
Sale proceeds = 4,000 × 125100 = Rs. 5,000.
Original income = 6% of 4,000 = Rs. 240, so new income = 240 + 110 = Rs. 350.
Let the investment in 12% stock at 120 be Rs. x. Income = 12120x = 0.10x.
Investment in 5% stock at 100 = Rs. (5,000 − x), income = 0.05(5,000 − x).
0.10x + 0.05(5,000 − x) = 350, so 0.05x + 250 = 350 and x = Rs. 2,000.
Shortcut Method
proceeds = 4,000 × 1.25 = 5,000; old income 240, new 350
yields 0.10 and 0.05; all at 5%: income 250
need 100 more, each Rs. moved adds 0.05 → 100 ÷ 0.05
∴ 12% stock: Rs. 2,000 ✓
Question 68
A man sells Rs. 8,000, 5% stock at 110 and invests the proceeds partly in 4% stock at 80 and partly in 10% stock at 125. His income rises by Rs. 160. How much does he invest in the 10% stock at 125?
A
Rs. 3,200✓✗
B
Rs. 4,000✓✗
C
Rs. 4,800✓✗
D
Rs. 5,000✓✗
Explanation
Sale proceeds = 8,000 × 110100 = Rs. 8,800.
Original income = 5% of 8,000 = Rs. 400, so new income = 400 + 160 = Rs. 560.
Let the investment in 10% stock at 125 be Rs. x. Income = 10125x = 0.08x.
Investment in 4% stock at 80 = Rs. (8,800 − x), income = 480(8,800 − x) = 0.05(8,800 − x).
0.08x + 0.05(8,800 − x) = 560, so 0.03x + 440 = 560 and x = Rs. 4,000.
Shortcut Method
proceeds = 8,000 × 1.10 = 8,800; old income 400, new 560
yields 0.08 and 0.05; all at 4%: income 440
need 120 more, each Rs. moved adds 0.03 → 120 ÷ 0.03
∴ 10% stock: Rs. 4,000 ✓
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