Ratio & Proportion Mcqs - Set 4

1)   The sum of squares of three numbers is 280. If the numbers are in the ratio 3:5:6, find the greatest number.

a. 8
b. 6
c. 12
d. 18
Answer  Explanation 

ANSWER: 12

Explanation:
Let the numbers be 3x,5x and 6x. (3x)²+(5x)²+(6x)²=280 9x²+25x²+36x²=280 70x²=280 x²=4 x=2 The greatest number is 6x=12.


2)   If a flat costs Rs.4500 per sq. ft, and a commercial space costs Rs.9500 per sq. ft, then what is the ratio of their areas if the total cost of both are the same?

a. 9:19
b. 19:9
c. 15:28
d. 28:15
Answer  Explanation 

ANSWER: 19:9

Explanation:
Let A1 be the area of flat and A2 be that of the commercial space
Total cost = area * rate
Therefore, cost of flat = A1*4500 ; cost of commercial space = A2*9500
Both the above costs are same
A1*4500 = A2*9500
A1:A2 = 9500:4500 = 19:9


3)   The sum of three numbers is 172. The ratio of the first and second numbers is 8:11. The ratio of the second and third is 5:7. Find the second number.

a. 44
b. 55
c. 66
d. 77
Answer  Explanation 

ANSWER: 55

Explanation:
Let the numbers be a, b and c. a+b+c = 172 a:b = 8:11 b:c = 5:7 11a = 8b a = 8b/11 7b = 5c c = 7b/5 (8b/11)+b+(7b/5) = 172 40b+55b+77b = 172*55 172b = 172*55 b=55


4)   4 singers, 5 dancers and 3 comperes divide an amount of Rs.130000 among themselves such that 3 comperes get as much as 2 dancers and 3 dancers get as much as 2 singers. Find the amount received by a singer.

a. Rs.18000
b. Rs.13000
c. Rs.15000
d. Rs.10000
Answer  Explanation 

ANSWER: Rs.15000

Explanation:
4S+5D+3C=130000 3C=2D 3D=2S S=3D/2 [4*(3D/2)]+5D+2D = 130000 6D+5D+2D = 130000 13D = 130000 D = Rs.10000 S=3D/2 = Rs.15000


5)   The sum of cubes of two numbers is 280. If the numbers are in the ratio 2:3, find the smallest number.

a. 4
b. 6
c. 3
d. 2
Answer  Explanation 

ANSWER: 4

Explanation:
Let the numbers be 2x and 3x. (2x)³+(3x)³=280 8x³+27x³=280 35x³=280 x³=8 x=2 The numbers are 4 and 6.


6)   Find the value of x when y = 5, if x varies directly as 4y-1 and x = 14 when y = 2.

a. 38
b. 35
c. 10
d. 28
Answer  Explanation 

ANSWER: 38

Explanation:
Let z = 4y-1
When x = 14, y = 2, z = (4*2) – 1 = 7
Now, x varies directly as z = 4y-1
When y = 5, z = (4*5) – 1 = 19
x 14 7
y – 19
Therefore, x = (14*19)/7 = 38


7)   The number of seats available for Biology and Computer Science in a school is in the ratio 5:8. They are to be increased by 30% and 25% . Find the new ratio.

a. 6:10
b. 13:20
c. 3:4
d. 35:33
Answer  Explanation 

ANSWER: 13:20

Explanation:
Let the number of seats be 5x and 8x. New ratio
= (1.3*5x):(1.25*8x)
= 6.5x:10x
= 13:20


8)   A:B=2:3, B:C=3:4, A:D=4:5. Find C:D.

a. 2:5
b. 4:5
c. 6:5
d. 8:5
Answer  Explanation 

ANSWER: 8:5

Explanation:
A:C=(A:B)*(B:C) =(2/3)*(3/4)= 1/2 C:D=(C:A)*(A:D) =(2)*(4/5) = 8:5


9)   Find the fourth proportion to 3, 7 and 9.

a. 63
b. 31
c. 21
d. 27
Answer  Explanation 

ANSWER: 21

Explanation:
3:7::9:x 3x=7*9=63 x=21


10)   If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number ?

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

ANSWER: 5 : 3

Explanation:
No explanation is available for this question!


11)   Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats ?

a. 2 : 3 : 4
b. 6 : 7 : 8
c. 6 : 8 : 9
d. None of these
Answer  Explanation 

ANSWER: 2 : 3 : 4

Explanation:
5:7:8 = 50:70:80
50*140/100=70 ; 70*150/100=105 ; 80*175/100=140
70: 105: 140 or
14: 21: 28 or
2: 3: 4


12)   In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

a. 50
b. 100
c. 150
d. 200
Answer  Explanation 

ANSWER: 150

Explanation:
No explanation is available for this question!


13)   Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is :________?

a. 27
b. 33
c. 49
d. 55
Answer  Explanation 

ANSWER: 49

Explanation:
No explanation is available for this question!


14)   Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is :__________?

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

ANSWER: 4 : 5

Explanation:
Let the third number be x.
Then, first number = 120% of x = 120x/100 = 6x/5 second numbet = 150% of x = 150x/100 = 3x/2 Ratio of first two numbers = 6x/5 : 3x/2 =12x : 15x = 4 : 5.


15)   A surn of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share ?

a. Rs. 500
b. Rs. 1500
c. Rs. 2000
d. None of these
Answer  Explanation 

ANSWER: Rs. 2000

Explanation:
No explanation is available for this question!


16)   The ratio of the number of boys and girls in a college is 7 : 8. If the percentage iikcrease in the number of boys and girls be 20% and 10% respectively, what will be the new ratio ?

a. 8 : 9
b. 17 : 18
c. 21 : 22
d. Cannot be determined
Answer  Explanation 

ANSWER: 21 : 22

Explanation:
Originally, let the number of boys and girls in the college be 7x and 8x respectively. Their increased number is (120% of 7x) and (110% of 8x), i . e . ( 120/100 X 7x ) and ( 110/100 X 8x ) i . e . 42x/5 and 44x/5 Required ratio = 42x/5 : 44x/5 = 21 : 22


17)   The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is :__________?

a. 20
b. 30
c. 48
d. 58
Answer  Explanation 

ANSWER: 30

Explanation:
Let the three parts be A, B, C Then,
A : B = 2 : 3 and B : C = 5 : 8 (5 X 3/5 ) : (8 X 3/5 ) = 3 : 24/5
A:B:C= 2 : 3 : 24/5 10:15:24
B = (98 X 15/49 ) = 30.