Practice MCQ Questions and Answer on Ratio

111.

What must be added to each term of the ratio 7 : 11, So as to make it equal to 3 : 4?

(A) 8
(B) 7.5
(C) 6.5
(D) 5

Solution: $\begin{aligned} Let x be added to each term . \\ According to question, \\ \frac{7 + x}{11 + x} = \frac{3}{4} \\ O r, 33 + 3 x = 28 + 4 x \\ O r, x = 5 \end{aligned}$

112.

The sum of two numbers is 40 and their difference is 4. The ratio of the numbers is = ?

(A) 21 : 19
(B) 22 : 9
(C) 11 : 9
(D) 11 : 18

113.

If a, b and c are positive numbers such that (a² + b²) : (b² + c²) : (c² + a²) = 34 : 61 : 45, then b - a : c - b : c - a = . . . . . . .

(A) 3 : 1 : 2
(B) 3 : 2 : 1
(C) 1 : 2 : 3
(D) 2 : 1 : 3

114.

If $\frac{x}{2} = \frac{y}{3} = \frac{z}{4} =$ ÃÂÃÂ $\frac{2 x - 3 y + 5 z}{k},$ ÃÂÃÂ ÃÂÃÂ then the value of k is -

(A) 12
(B) 15
(C) 16
(D) 18

Solution: $\begin{aligned} Let \frac{x}{2} = \frac{y}{3} = \frac{z}{4} = l \\ Then, \\ = x = 2 l, y = 3 l, z = 4 l \\ ∴ \frac{x}{2} = \frac{2 x - 3 y + 5 z}{k} \\ \Rightarrow \frac{2 l}{2} = \frac{2 \times 2 l - 3 \times 3 l + 5 \times 4 l}{k} \\ \Rightarrow k = 4 - 9 + 20 = 15 \end{aligned}$

115.

If a : b = 2 : 3 and b : c = 4 : 5, then (a + b) : (b + c) is equal to-

(A) 6 : 8
(B) 8 : 6
(C) 20 : 27
(D) 27 : 20

Solution: $\begin{aligned} a : b = 2 : 3, \\ b : c = 4 : 5 = 4 \times \frac{3}{4} : 5 \times \frac{3}{4} \\ = 3 : \frac{15}{4} \\ S o, a : b : c = 2 : 3 : \frac{15}{4} \\ = 8 : 12 : 15. \\ Let \\ a = 8 k, \\ b = 12 k, \\ c = 15 k . \\ Then, \\ \frac{(a + b)}{(b + c)} = \frac{(8 k + 12 k)}{(12 k + 15 k)} \\ = \frac{20 k}{27 k} \\ = \frac{20}{27} \end{aligned}$

116.

If A : B = 7 : 9 and B : C = 5 : 4, then A : B : C is -

(A) 7 : 45 : 36
(B) 28 :36 : 35
(C) 35 : 45 : 36
(D) None of these

Solution: $\begin{aligned} = A : B = 7 : 9 and \\ B : C = 5 : 4 \\ = (5 \times \frac{9}{5}) : (4 \times \frac{9}{5}) \\ = 9 : \frac{36}{5} . \\ \Rightarrow A : B : C = 7 : 9 : \frac{36}{5} \\ = 35 : 45 : 36. \end{aligned}$

117.

The ratio of the monthly incomes of X and Y is 5 : 4 and that of their monthly expenditures is 9 : 7. If the income of Y is equal to the expenditure of X, then what is the ratio of the saving of X and Y?

(A) 9 : 8
(B) 6 : 7
(C) 8 : 9
(D) 7 : 6

Solution: $\begin{matrix} X : Y \\ Income \to & 5_{\times 9} : 4_{\times 9} \\ Expenditure \to & 9_{\times 4} : 7_{\times 4} \\ Saving \to & \overset{―}{\underset{―}{9 : 8}} \end{matrix}$ Y's income = X's Expenditure Saving = 9 : 8

118.

If A : B = 7 : 9 and B : C = 3 : 5 then A : B : C is equal to = ?

(A) 7 : 9 : 5
(B) 21 : 35 : 45
(C) 7 : 9 : 15
(D) 7 : 3 : 15

119.

In a school, $\frac{5}{12}$ of the number of students are girls and the rest are boys. $\frac{4}{7}$ of the number of boys are below 14 years of age, and $\frac{2}{5}$ of the number of girls are 14 years or above 14 years of age. If the number of students below 14 years of age is 1120, then the total number of students in the school is:

(A) 1900
(B) 1820
(C) 1290
(D) 1920

Solution: Let total student = 12 unit B : G 7 : 5 B → $\frac{4}{7}$ (14 year less) B = 4 (14 year less) G → $\frac{2}{5}$ G = 3 (14 year less) Total student less than 14 year = 4 + 3 = 7 7 → 1120 1 → 160 12 → 1920 total student

120.

The ratio of incomes of two persons is 5 : 3 and that of their expenditures is 9 : 5. If they save Rs. 2600 and Rs.1800 respectively, their incomes are.

(A) Rs. 9000, Rs. 5400
(B) Rs. 10000, Rs. 6000
(C) Rs. 6000, Rs. 3600
(D) Rs. 8000, Rs. 4800

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Practice MCQ Questions and Answer on Ratio

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