Question 1
If a simple interest on a sum of money at 6% p.a. for 7 years is equal to twice of simple interest on another sum for 9 years at 5% p.a., the ratio (of the two sums) will be:
A
2 : 15✓✗
B
7 : 15✓✗
C
15 : 7✓✗
D
1 : 7✓✗
Explanation
Let the two sums be P1 and P2.
SI1 = P1 × 6 × 7100 = 42P1100
SI2 = P2 × 5 × 9100 = 45P2100
Given SI1 = 2 × SI2:
42P1 = 90P2
P1 : P2 = 90 : 42 = 15 : 7
Question 2
If the difference between the compound interest compounded annually and simple interest on a certain amount at 10% per annum for two years is Rs. 372, then the principal amount is:
A
Rs. 37,000✓✗
B
Rs. 37,200✓✗
C
Rs. 37,500✓✗
D
None of the above✓✗
Explanation
For 2 years, CI − SI = P × (R/100)2
372 = P × (10/100)2 = P × 10010000 = P100
P = 372 × 100 = 37,200
Question 3
A sum of money, lent out at simple interest, doubles itself in 8 years. Find in how many years will the sum become triple (three times) of itself at the same rate per cent.
A
16 years✓✗
B
15 years✓✗
C
20 years✓✗
D
None✓✗
Explanation
Let the principal be P. Since it doubles in 8 years, SI for 8 years = P.
P = P × R × 8100, so R = 12.5% p.a.
For the sum to triple, SI required = 2P.
Time = 2P × 100P × 12.5 = 20012.5 = 16 years
Question 4
The annual rate of simple interest is 12.5%. In how many years does the principal double?
A
11 years✓✗
B
9 years✓✗
C
8 years✓✗
D
7 years✓✗
Explanation
For the principal to double, SI over T years = P.
P = P × 12.5 × T100
T = 10012.5 = 8 years
Question 5
A certain sum of money borrowed at simple interest amounts to Rs. 2688 in three years and to Rs. 2784 in four years. The rate per annum is:
A
4%✓✗
B
6%✓✗
C
5%✓✗
D
7%✓✗
Explanation
The increase from year 3 to year 4 is one year's interest:
SI for 1 year = 2784 - 2688 = 96
SI for 3 years = 3 × 96 = 288
Principal = 2688 - 288 = 2400
Rate = SI × 100P × T = 96 × 1002400 × 1 = 4%
Question 6
An investor is saving to pay off an obligation of Rs. 15,250 which is due in seven years. If the investor is earning 7.5% simple interest rate per annum, how much must be deposited now to meet the obligation?
A
Rs. 8,000✓✗
B
Rs. 9,000✓✗
C
Rs. 10,000✓✗
D
Rs. 11,000✓✗
Explanation
Let the deposit be P. After 7 years at 7.5% simple interest:
P × (1 + 0.075 × 7) = 15,250
P × 1.525 = 15,250
P = 15,2501.525 = 10,000
Question 7
A man invests an amount of Rs. 15,860 in the names of his three sons A, B and C in such a way that they get the same interest after 2, 3 and 4 years respectively. If the rate of interest is 5%, then the ratio of amount invested in the name of A, B and C is:
A
6 : 4 : 3✓✗
B
3 : 4 : 6✓✗
C
30 : 12 : 5✓✗
D
None of the above✓✗
Explanation
Same interest means PA × 2 = PB × 3 = PC × 4 = k (since SI = P × R × T / 100, with R constant)
PA = k/2, PB = k/3, PC = k/4
Ratio = 12 : 13 : 14 = (multiplying by 12) 6 : 4 : 3
Question 8
In what time will a sum of money double itself at 6.25% p.a. simple interest?
A
5 years✓✗
B
8 years✓✗
C
12 years✓✗
D
16 years✓✗
Explanation
For the sum to double, SI over T years = P.
T = 1006.25 = 16 years
Question 9
The sum required to earn a monthly interest of Rs. 1,200 at 18% p.a. simple interest is:
A
Rs. 50,000✓✗
B
Rs. 60,000✓✗
C
Rs. 80,000✓✗
D
None of these✓✗
Explanation
Annual interest required = 1,200 × 12 = 14,400
P = 14,400 × 10018 = 80,000
Question 10
Sachin deposited Rs. 1,00,000 in his bank for 2 years at simple interest of 6%. How much interest would he earn? What is the final value of the deposit?
A
Rs. 6,000, Rs. 1,06,000✓✗
B
Rs. 15,000, Rs. 1,15,000✓✗
C
Rs. 11,600, Rs. 1,11,600✓✗
D
Rs. 12,000, Rs. 1,12,000✓✗
Explanation
SI = 1,00,000 × 6 × 2100 = 12,000
Final value = 1,00,000 + 12,000 = 1,12,000
Question 11
The simple interest on a sum of money at 6% p.a. for 7 years is equal to twice of simple interest on another sum for 9 years at 5% p.a. The ratio will be:
A
2 : 15✓✗
B
7 : 15✓✗
C
15 : 7✓✗
D
1 : 7✓✗
Explanation
Let the two sums be P1 and P2.
SI1 = P1 × 6 × 7100 = 42P1100
SI2 = P2 × 5 × 9100 = 45P2100
Given SI1 = 2 × SI2:
42P1 = 90P2
P1 : P2 = 90 : 42 = 15 : 7
Question 12
The simple interest on a certain sum of money is 1/25 times of the principal. If the rate of interest and time (in years) are numerically equal, find the rate of interest.
A
2%✓✗
B
3%✓✗
C
4%✓✗
D
None✓✗
Explanation
SI = P25. Using SI = P × R × T100 with R = T:
P25 = P × R2100
R2 = 10025 = 4
R = 2%
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