Ratio and Proportion - Quantitative Aptitude (MCQ) questions

1)   Two numbers are in the ratio of 6 : 8. If 10 is subtracted from each, the new numbers are in the ratio 16 : 32. Find the smaller number.
- Published on 22 Apr 16

a. 22
b. 12
c. 38
d. 15
Answer  Explanation 

ANSWER: 15

Explanation:
Let the number be 6x and 8x.
Then, (6x – 10) / (8x – 10) = 1 / 2
2 (6x – 10) = (8x – 10)
12x – 20 = 8x – 10
4x = 10
x = 2.5
The smaller number = (6 x 2.5) = 15


2)   It was intended that Rs. 585 be divided among P, Q and R in the ratio of 4 : 3 : 2, but by mistake the distribution was made in the proportion of 1/4 : 1/3 : 1/2. How much does 'R' gain by the error ?
- Published on 22 Apr 16

a. Rs. 99
b. Rs. 126
c. Rs. 140
d. Rs. 152
e. None of these
Answer  Explanation 

ANSWER: Rs. 140

Explanation:
Total amount = Rs. 585
on dividing it in the ratio of 4 : 3 : 2
Share of P = 4/9 * 585 = Rs. 260
Share of Q = 3/9 * 585 = Rs. 195
Share of R = 2/9 * 585 = Rs. 130
But the amount has been divided in the proportion of 1/4 : 1/3 : 1/2 i.e. 3 : 4 : 6
Share of P = 3/13 * 585 = Rs. 135
Share of Q = 4/13 * 585 = Rs. 180
Share of R = 6/13 * 585 = Rs. 270
Therefore, gain for R by virtue of error = Rs. 270 – Rs. 130 = Rs. 140


3)   If a : b : : 3 : 5, b : c : : 4 : 3 and c : d : : 4 : 5, a : d = ?
- Published on 19 Apr 16

a. 4 :5
b. 16 : 25
c. 64 : 25
d. 64 : 125
e. 16 : 125
Answer  Explanation 

ANSWER: 16 : 25

Explanation:
a/b * b/c * c/d = 3/5 * 4/3 * 4/5 = 42/52 = 16/25
a : d = 16 : 25


4)   By giving Rs. 50 to M, A would have the amount equal to what M had earlier. If the sum of the amounts with A and M is Rs. 650. What is the ratio of the amount with A to that with M earlier?
- Published on 15 Apr 16

a. 7 : 4
b. 5 : 3
c. 2 : 1
d. 7 : 6
Answer  Explanation 

ANSWER: 7 : 6

Explanation:
let the amounts with A and M be Rs. “X” and Rs. “Y” respectively.
Thus, we have, X + Y = 650 and
X – 50 = Y
X – Y = 50.
Hence, X = 350 & Y = 300
Thus the required ratio is 350 : 300 = 7 : 6


5)   By giving Rs. 50 to M, A would have the amount equal to what M had earlier. If the sum of the amounts with A and M is Rs. 650. What is the ratio of the amount with A to that with M earlier?
- Published on 05 Apr 16

a. 7 : 4
b. 5 : 3
c. 2 : 1
d. 7 : 6
e. 2 : 3
Answer  Explanation 

ANSWER: 7 : 6

Explanation:
Let the amounts with A and M be Rs. “X” and Rs. “Y” respectively.
Thus, we have, X + Y = 650 and
X – 50 = Y
X – Y = 50.
Hence, X = 350 & Y = 300
Thus the required ratio is 350 : 300 = 7 : 6


6)   A housewife wishes to purchase three articles A, B and C from a sum of Rs. 200. The unit prices of the articles A, B and C are Rs. 20, Rs. 35 and Rs. 25 respectively. If she spends the entire amount by purchasing 5 numbers of articles of type C, what is the ratio of the number of articles purchased of type A to that of, type B?
- Published on 01 Apr 16

a. 1 : 2
b. 2 : 1
c. 1 : 1
d. None of these
e. Cannot be determined
Answer  Explanation 

ANSWER: 2 : 1

Explanation:
After spending Rs. 125 (25 * 5) for articles of type C, the housewife is left with Rs. 75 (200 – 125). Since this amount has to be spent in totality, she must have purchased 2 articles of type A (equivalent to Rs. 40) and 1 article of type B (equivalent to Rs. 35). Thus, the required ratio is 2 : 1.


7)   Shruti purchased several number of three articles P, Q and R in the proportion 3 : 2 : 3. If the unit costs of the articles P, Q and R are 200, Rs. 90 and Rs. 60 respectively, how many articles of Q must have been purchased in the total purchases of Rs. 4800?
- Published on 31 Mar 16

a. 8
b. 10
c. 12
d. 14
e. None of these
Answer  Explanation 

ANSWER: 10

Explanation:
Let the number of articles of types P, Q and R be 3a, 2a and 3a respectively.
Thus, we get,
(200 x 3a) + (90 x 2a) + (60 x 3a) = 4800
960a = 4800
a = 5
Hence, the number of articles of type “Q” = 2x5 = 10


8)   If a : b = 2 : 3, find the value of (3a + 5b) : (3a – b)
- Published on 28 Mar 16

a. 2 : 7
b. 7 : 1
c. 2 : 5
d. 4 : 9
Answer  Explanation 

ANSWER: 7 : 1

Explanation:
Given: a/b = 2/3
(3a + 5b) / (3a – b)
= [3(a/b) +5] / [3(a/b) – 1]
= [3(2/3) +5] / [3(2/3) – 1]
= 7/1


9)   In what ratio should the profit of Rs.8000 be divided if X starts a business with an investment of Rs. 20000, Y invests Rs.7500 for 4 months and Z invests Rs.15000 after 3 months from the start of the business.
- Published on 06 Jul 15

a. 16 : 2 : 3
b. 8 : 3 : 6
c. 16 : 2 : 9
d. 6 : 9 : 1
Answer  Explanation 

ANSWER: 16 : 2 : 9

Explanation:
Let the profit of X be P1, that of Y be P2 and of Z be P3.
P1:P2:P3 = 20000*12 : 7500*4 : 15000*9 = 240 : 30 : 135 = 80 : 10 : 45
= 16 : 2 : 9


10)   In a partnership for a business, Jay invests Rs.6000 for complete year & Viru invests Rs.3000 for 6 months. What is Viru’s share if they earn Rs.240 as profit?
- Published on 06 Jul 15

a. 120
b. 80
c. 192
d. 48
Answer  Explanation 

ANSWER: 48

Explanation:
If A invests amount C1 for T1 time and his share of profit is P1, and B invests amount C2 for T2 time and his share of profit is P2, then, C1 * T1 / C2 * T2 = P1/P2
If P is the Viru’s share of profit, then Jay gets (240 – P)
Therefore, 6000 * 12 / 3000 * 6 = (240 - P) / P = 72/ 18 = 4
4P = (240 – P)
5P = 240
P = 48


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