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Home > Practice > Arithmetic Aptitude > Ratio and Proportion > Miscellaneous

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

A. 2 : 1

B. 14 : 3

C. 7 : 2

D. 1 : 2

Discuss

Solution:

\begin{aligned} a : b : c \\ 3 : 4 : 7 \\ 3 x : 4 x : 7 x \Rightarrow 14 x \\ ∴ a + b + c = 14 x \\ c = 7 x \\ ∴ (a + b + c) : c \\ = 14 x : 7 x \\ = 2 : 1 \end{aligned}

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

A. 162

B. 108

C. 96

D. 54

Discuss

Solution:

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

\begin{aligned} According to the question, \\ \frac{2 x + 12}{3 x + 12} = \frac{8}{11} \\ o r, 24 x + 96 = 22 x + 132 \\ o r, 2 x = 132 - 96 \\ o r, x = \frac{36}{2} = 18 \\ Hence, \\ Original number of students, \\ 9 x = 9 \times 18 \\ = 162 \end{aligned}

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

A. 65

B. 66

C. 77

D. 78

Discuss

Solution:

Respective ratio of the NUMBER of coins;
= 13 : 11 × 2 = 13 : 22
Hence, Number of 1 rupee coins;
=

\frac{13 \times 210}{13 + 22}

= 78

4. If $\frac{2}{3}$ of A=75% of B = 0.6 of C, then A : B : C is

A. 2 : 3 : 3

B. 3 : 4 : 5

C. 4 : 5 : 6

D. 9 : 8 : 10

Discuss

Solution:

\begin{aligned} According to thequestion, \\ \frac{2 A}{3} = \frac{75 B}{100} = \frac{C \times 6}{10} \\ Above relation gives; \\ \frac{A \times 2}{3} = \frac{B \times 3}{4} \\ \to \frac{A}{B} = \frac{9}{8} \\ And, \\ \frac{B \times 3}{4} = \frac{C \times 3}{5} \\ \to \frac{B}{C} = 4 : 5 \\ \to \frac{B}{C} = 8 : 10 (multiple by 2) \\ Thus, \\ A : B : C = 9 : 8 : 10 \end{aligned}

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

A. 3 : 13

B. 9 : 13

C. 36 : 13

D. 13 : 9

Discuss

Solution:

\begin{aligned} \frac{A}{B} \times \frac{B}{C} = \frac{3}{4} \times \frac{12}{13} \\ O r, \frac{A}{C} = \frac{36}{52} = 9 : 13 \end{aligned}

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

A. 20 : 66 : 95

B. 21 : 66 : 96

C. 21 : 66 : 92

D. 19 : 66 : 92

Discuss

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 300) = 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 : 460 = 21 : 66 : 92

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

A. 2 : 3 : 5

B. 5 : 4 : 6

C. 8 : 12 : 15

D. 6 : 4 : 5

Discuss

Solution:

\begin{aligned} \frac{A}{B} = \frac{2}{3} \\ \frac{B}{C} = \frac{4}{5} \end{aligned}

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

A. 2 : 3 : 4

B. 3 : 4 : 2

C. 4 : 6 : 3

D. 6 : 4 : 3

Discuss

Solution:

\begin{aligned} 2 A = 3 B \\ O r, B = (\frac{2}{3}) A; and \\ 2 A = 4 C \\ O r, C = (\frac{1}{2}) A; \\ Hence, \\ A : B : C = A : \frac{2 A}{3} : \frac{A}{2} \\ = 1 : \frac{2}{3} : \frac{1}{2} \\ = 6 : 4 : 3 \end{aligned}

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

A. 12 : 7

B. 10 : 7

C. 8 : 7

D. 4 : 3

Discuss

Solution:

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

\frac{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

A. 9

B. 15

C. 36

D. 45

Discuss

Solution:

Let two numbers be 4x and 5x
Their LCM = 180 and HCF = x
Now,
1^st number × 2^nd 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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