Ratio MCQ’S

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#1. If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : c is equal to

Answer: Option A
Solution:
 a : b : c 
3 : 4 : 7 
3x:4x:7x14x
a b c=14x
c=7x
(a b c):c
=14x:7x
=2:1

#2. The number of students in 3 classes is in the ratio 2 : 3 : 4. If 12 students are increased in each class this ratio changes to 8 : 11 : 14. The total number of students in the three classes in the beginning was

Answer: Option A
Solution:

Let the number of students in the classes be 2x, 3x and 4x respectively;
Total students = 2x 3x 4x = 9x

According to the question,
(2x 12)/(3x 12)=8/11
or,24x 96=22x 132
or,2x=13296
or,x=36/2=18
Hence, Original number of students, 9x=9×18=162

#3. A box has 210 coins of denominations one-rupee and fifty paise only. The ratio of their respective values is 13 : 11. The number of one-rupee coin is

Answer: Option D
Solution:

Respective ratio of the number of coins;
= 13 : 11 × 2 = 13 : 22
Hence, Number of 1 rupee coins;
= 13×210/13 22
= 78

#4. If 2/3 of A=75% of B = 0.6 of C, then A : B : C is

Answer: Option D
Solution:
According to the question, (2A/3)=(75B/100)=(C×6/10);
Above relation gives;
A×2/3=B×3/4
A/B=9/8 And,
B×3/4=C×3/5
B/C=4:5B/C=8:10 (multiple by 2) 
Thus,
A:B:C=9:8:10

#5. If A and B are in the ratio 3 : 4, and B and C in the ratio 12 : 13, then A and C will be in the ratio

Answer: Option B
Solution:
(A/B)×(B/C)=(3/4)×(12/13)
Or,
A/C=36/52=9:13

#6. The salaries of A, B and C are in the ratio 1 : 3 : 4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio

Answer: Option C
Solution:

Let A’s Salary = Rs. 100
Then, B’s Salary = Rs. 300
And, C’s Salary = Rs. 400
Salary has given in 1 : 3 : 4 ratio
Now,
5% increase in A’s Salary,
A’s new Salary = (100 5% of 100) = Rs. 105
B’s Salary increases by 10%, Then,
B’s new Salary = (300 10% of 200) = Rs. 330
C’s Salary increases by 15%,
C’s new Salary = (400 15% of 400) = Rs. 460
Then, ratio of increased Salary,
A : B : C = 105 : 330 : 460 = 21 : 66 : 92

Alternative
100 (A’s salary) === 5%↑ ===> 105(A’s increased salary)
300 (B’s salary) === 10%↑ ===> 330 (B’s increased salary)
400 (C’s salary) === 15%↑ ===> 460 (C’s increased salary)
Ratio of their increased salary = 105 : 330 : 480 = 21 : 66 : 92

#7. If A : B = 2 : 3 and B : C = 4 : 5 then A : B : C is

Answer: Option C
Solution:
A/B=2/3
B/C=4/5

A : B : C = 2 × 4 : 3 × 4 : 3 × 5 = 8 : 12 : 15

#8. If two times A is equal to three times of B and also equal to four times of C, then A : B : C is

Answer: Option D
Solution:
2A=3B
Or,B=(2/3)A;
and 2A=4C
Or,C=(1/2)A;
Hence,
A:B:C =A:2A/3:A/2
=1:22:12
=6:4:3

#9. In a school having roll strength 286, the ratio of boys and girls is 8 : 5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes

Answer: Option D
Solution:

Boys : girls = 8 : 5 (let the boys = 8x, girl = 5x)
Total strength = 286
8x 5x = 286
13x = 286
Or, x =

286/13 = 22

Boys = 176 and girls = 110
22 more girls get admitted then number of girls become
(5x 22) = 110 22 = 132
Now, new ratio of boys and girls = 176 : 132 = 4 : 3

#10. Two numbers are in ratio 4 : 5 and their LCM is 180. The smaller number is

Answer: Option C
Solution:

Let two numbers be 4x and 5x
Their LCM = 180 and HCF = x
Now,
1st number × 2nd number = LCM × HCF
Or, 4x × 5x = 180 × x
Or, 20x = 180
Or, x = 9
Then, the smaller number = 4 × 9 = 36

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