Practice MCQ Questions and Answer on Ratio

If p : q : r = 1 : 2 : 4, then $\sqrt{5 p^{2} + q^{2} + r^{2}}$ ÃÂÃÂ ÃÂÃÂ is equal to -

(A) 5
(B) 2q
(C) 5p
(D) 4r

Solution: $\begin{aligned} p = k, q = 2 k, r = 4 k \\ Then, \\ \sqrt{5 p^{2} + q^{2} + r^{2}} \\ = \sqrt{5 k^{2} + {(2 k)}^{2} + {(4 k)}^{2}} \\ = \sqrt{5 k^{2} + 4 k^{2} + 16 k^{2}} \\ = \sqrt{25 k^{2}} \\ = 5 k \\ = 5 p . \end{aligned}$

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

Solution: Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x) $= (\frac{140}{100} \times 5 x),$ $(\frac{150}{100} \times 7 x)$ and $(\frac{175}{100} \times 8 x)$ $\begin{aligned} = 7 x, \frac{21 x}{2} and 14 x \\ ∴ The required ratio \\ = 7 x : \frac{21 x}{2} : 14 x \\ = 14 x : 21 x : 28 x \\ = 2 : 3 : 4 \end{aligned}$

The number to be added to each of the numbers 7, 16, 43, 79 to make the numbers in proportion is = ?

(A) 2
(B) 3
(C) 5
(D) 1

The ratio of the income of A and B as well as B and C is 3 : 2. If one - third of A's income exceeds one - fourth of C's income by Rs. 1000, what is B's income in Rs = ?

(A) Rs. 3000
(B) Rs. 2500
(C) Rs. 3500
(D) Rs. 4000

Solution: Given, A : B = 3 : 2 B : C = 3 : 2 Equal the value of B in both equation A : B = 3 : 2 (multiply with 3) and B : C = 3 : 2 (multiply with 2) i.e. A : B = 9 : 6 and B : C = 6 : 4 ∴ A : B : C = 9 : 6 : 4 Now $\frac{A}{3}$ - 1000 = $\frac{C}{4}$ i.e. $\frac{9 x}{3}$ - 1000 = $\frac{4 x}{4}$ ⇒ 3x - 1000 = x ⇒ x = 500 ∴ Income of B is = 6x = 6 × 500 = 3000

Of three positive numbers, the ratio of first and second is 8 : 9, that of second and third is 3 : 4. The product of first and third is 2400. The sum of the three number is = ?

(A) 145
(B) 185
(C) 295
(D) 155

Solution: $\begin{aligned} First : Second : Third \\ 8 : 9 \\ 3 : 4 \\ \frac{\overset{―}{24 : 27 : 36}}{\underset{―}{8 : 9 : 12}} \\ Let 8x : 9x : 12x \\ ∴ First \times Third \\ 8 x \times 12 x = 2400 \\ \Rightarrow 96 x^{2} = 2400 \\ \Rightarrow x^{2} = \frac{2400}{96} = 25 \\ \Rightarrow x = 5 \\ ∴ Sum of three numbers \\ First + Second + Third \\ 8 x + 9 x + 12 x = 29 x \\ ∴ 29 \times 5 = 145 \end{aligned}$

The ratio of age of two boys is 5 : 6. After two years the ratio will be 7 : 8. The ratio of their age after 12 years will be = ?

(A) $\frac{22}{24}$
(B) $\frac{15}{16}$
(C) $\frac{17}{18}$
(D) $\frac{11}{12}$

Solution: Ratio of ages of Boys A and B $\begin{aligned} A : B \\ Present age 5 x : 6 x \\ ∴ After two years \\ ∴ \frac{5 x + 2}{6 x + 2} = \frac{7}{8} \\ \Rightarrow 40 x + 16 = 42 x + 14 \\ \Rightarrow 2 x = 2 \\ \Rightarrow x = 1 \\ ∴ Present age \\ A = 5 \times 1 = 5 \\ B = 6 \times 1 = 6 \\ After 12 years \\ A = 5 + 12 = 17 \\ B = 6 + 12 = 18 \\ \frac{A}{B} = \frac{17}{18} \end{aligned}$

In two alloys A and B the ratio of Zinc and Tin is 5 : 2 and 3 : 4 respectively. 7 kg of the alloy A and 21 kg of the alloy B are mixed together to form a new alloy. What will be the ratio of Zinc and Tin tin the new alloy ?

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

Solution: Zinc : Tin A 5x : 2x = 7x B 3y : 4y = 7y ⇒ A ⇒ 7x = 7 kg x = 1 kg ∴ Zinc in alloy A ⇒ 5kg Tin in alloy A ⇒ 2 kg ⇒ B ⇒ 7y = 21 kg y = 3 kg Zinc in alloy B ⇒ 3 × 3 = 9 kg Tin in alloy B ⇒ 3 × 4 = 12 kg ∴ After mix - up the ratio of Zinc and Tin in new alloy $\begin{aligned} Zinc : Tin \\ A 5 : 2 \\ B 9 : 12 \\ \overset{―}{A + B : 14 14} \\ 1 : 1 \end{aligned}$

If the ratio of the ages of Maya and Chhaya is 6 : 5 at present, and fifteen years from now, the ratio will get changed to 9 : 8, then find Maya's present age.

(A) 24 years
(B) 30 years
(C) 18 years
(D) 33 years

Solution: Let Maya's and Chhaya's present age is 6x and 5x respectively And, $\frac{6 x + 15}{5 x + 15} = \frac{9}{8}$ Or, 48x + 120 = 45x = 135 Or, 3x = 15 Or, x = 5 Present age of Maya = 6x = 30

The ratio of monthly income of A and B is 6 : 5 and their expenditure are in the ratio of 4 : 3. If each of them saves Rs. 400 per month, find the sum of their monthly incomes ?

(A) Rs. 2300
(B) Rs. 2400
(C) Rs. 2200
(D) Rs. 2500

10.

Two alloys both are made up of copper and tin. The ratio of the copper and tin in the first alloy is 1 : 3 and in the second alloy is 2 : 5. In what ratio should the two alloys be mixed to obtain a new alloy in which the ratio of tin and copper be 8 : 3 ?

(A) 3 : 5
(B) 4 : 7
(C) 3 : 8
(D) 5 : 11

Solution: Given: ⇒ Let the alloys be mixed in the ratio of $x$ : $y$ (Assumption) ⇒ In 1st alloy, Copper = $\frac{x}{4}$ ⇒ In 1st alloy, Tin = $\frac{3 x}{4}$ ⇒ In 2nd alloy, Copper = $\frac{2 y}{7}$ ⇒ In 2nd alloy, Tin = $\frac{5 y}{7}$ To find: ⇒ The ratio in which 2 alloys must be mixed to get a new alloy with a ratio of copper and tin be 3 : 8 =? Now we have, $\begin{aligned} (\frac{x}{4} + \frac{2 y}{7}) : (\frac{3 x}{4} + \frac{5 y}{7}) = 3 : 8 \\ \Rightarrow \frac{(\frac{x}{4} + \frac{2 y}{7})}{(\frac{3 x}{4} + \frac{5 y}{7})} = \frac{3}{8} \\ \Rightarrow \frac{\frac{7 x + 14 y}{28}}{\frac{21 x + 20 y}{28}} = \frac{3}{8} \\ \Rightarrow \frac{7 x + 14 y}{21 x + 20 y} = \frac{3}{8} \\ \Rightarrow 56 x + 64 y = 63 x + 60 y \\ \Rightarrow 64 y - 60 y = 63 x - 56 x \\ \Rightarrow 4 y = 7 x \\ ∴ \frac{x}{y} = \frac{4}{7} \end{aligned}$ ⇒ Ratio in which 2 alloys must be mixed to get a new alloy with a ratio of copper and tin be 3 : 8 = 4 : 7

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Practice MCQ Questions and Answer on Ratio

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