Ratio and Proportion MCQs

1. A school has boys and girls in the ratio 3 : 4. If 18 more boys join, the new ratio becomes 4 : 5. Find the original number of boys and girls.

a) 54 boys, 72 girls b) 60 boys, 80 girls c) 48 boys, 64 girls d) 50 boys, 70 girls

Correct Answer: a) 54 boys, 72 girls

Explanation:
Let the original number of boys and girls be $3 x$ and $4 x$ respectively.
After 18 more boys join, the new ratio is: $\frac{3 x + 18}{4 x} = \frac{4}{5}$
Cross multiplying:
$5 (3 x + 18) = 4 (4 x)$
$15 x + 90 = 16 x$
$x = 18$
So, boys = $3 \times 18 = 54$ and girls = $4 \times 18 = 72$ .

2. If A : B = 2 : 3, B : C = 4 : 5, and C : D = 6 : 7, find A : D.

a) 16 : 35 b) 12 : 25 c) 8 : 15 d) 10 : 21

Correct Answer: a) 16 : 35

Explanation:
Convert the ratios to a common base:
A : B = $2 : 3$ , B : C = $4 : 5$ ⇒ Multiply to match B:
⇒ $(2 : 3)*4 < = (4 : 5)*3$
A : B : C = $8 : 12 : 15$ .
C : D = $6 : 7$ ⇒ Multiply to match C:
A : B : C : D = $16 : 24 : 30 : 35$ .
So, $A : D = 16 : 35$ .

3. Divide ₹ 720 among A, B, and C in the ratio 3 : 4 : 5.

a) ₹ 180, ₹ 240, ₹ 300 b) ₹ 200, ₹ 250, ₹ 270 c) ₹ 150, ₹ 300, ₹ 270 d) ₹ 210, ₹ 240, ₹ 270

Correct Answer: a) ₹ 180, ₹ 240, ₹ 300

Explanation:
Total ratio = $3 + 4 + 5 = 12$ .
A's share = $\frac{3}{12} \times 720 = 180$ .
B's share = $\frac{4}{12} \times 720 = 240$ .
C's share = $\frac{5}{12} \times 720 = 300$ .

4. If two numbers are in the ratio 5 : 7 and their difference is 24, find the two numbers.

a) 60, 84 b) 50, 70 c) 40, 56 d) 30, 42

Correct Answer: a) 60, 84

Explanation:
Let the numbers be $5 x$ and $7 x$ .
Difference: $7 x - 5 x = 2 x = 24$ .
Solving for x: $x = 12$ .
So, the numbers are $60$ and $84$ .

5. The ratio of present ages of A and B is 3 : 5. After 8 years, the ratio becomes 4 : 6. Find their present ages.

a) 24, 40 b) 18, 30 c) 30, 50 d) 12, 20

Correct Answer: a) 24, 40

Explanation:
Let the present ages be $3 x$ and $5 x$ .
After 8 years, the ratio is: $\frac{3 x + 8}{5 x + 8} = \frac{4}{6}$ .
Solving for x: $x = 8$ .
So, present ages are $24$ and $40$ .

6. The salaries of P, Q, R are in the ratio 3:4:6. If the increments of 12%, 15%, and 18% are allowed respectively in their salaries, then what will be the new ratio of their salaries?

a) 8:11:14 b) 9:10:12 c) 33:46:71 d) Can’t be determined

Correct Answer: c) 33:46:71

Explanation:
Let the salaries of P, Q, R be $3 x$ , $4 x$ , and $6 x$ respectively.
After increments:
P's new salary = $3.36 x$ .
Q's new salary = $4.60 x$ .
R's new salary = $7.08 x$ .
New ratio = $33 : 46 : 71$ (after simplifying).

7. In a class of 150 students, 25% students can dance, $\frac{3}{5}$ of the total students can sing, and $\frac{1}{3}$ of the remaining students are good at sports. What is the respective ratio of the students who can dance to students who are good at sports?

a) 4:3 b) 3:2 c) 5:7 d) 3:5

Correct Answer: b) 3:2

Explanation:
Total students = $150$ .
Students who can dance = $25 %$ of $150$ = $37.5$ ≈ $38$ .
Students who can sing = $\frac{3}{5}$ of $150$ = $90$ .
Remaining students = $150 - 90$ = $60$ .
Students good at sports = $\frac{1}{3}$ of $60$ = $20$ .
Ratio of dancers to sports students = $38 : 20$ = $19 : 10$ ≈ $3 : 2$ .

8. $A : B : C$ is in the ratio of $4 : 5 : 6$ . Then how much money will $C$ get out of $Rs 600$ ?

a) Rs. 240 b) Rs. 300 c) Rs. 360 d) Rs. 400

Correct Answer: c) Rs. 360

Explanation:
Total ratio = $4 + 5 + 6$ = $15$ .
$C$ 's share = $\frac{6}{15} \times 600$ = $Rs 360$ .

9. Rate of income tax is increased from $5 %$ to $6 %$ . However, the total tax liability of a person remains the same as was in the last year. If his income for the last year was $Rs 12000$ , find his present income.

a) Rs. 9000 b) Rs. 10000 c) Rs. 8000 d) Rs. 11000

Correct Answer: b) Rs. 10000

Explanation:
Last year's tax = $5 %$ of $12000$ = $Rs 600$ .
Let present income be $x$ .
New tax = $6 %$ of $x$ = $600$ .
So, $x = \frac{600}{0.06}$ = $Rs 10000$ .

10. Raj distributed his assets to his wife, three sons, two daughters, and five grandchildren in such a way that each grandchild got $\frac{1}{7}$ of each son and $\frac{1}{9}$ of each daughter. His wife got $35 %$ of the total share of his sons and daughters together. If each daughter receives an asset of $Rs 1.5$ lakhs, what is the share of his wife?

a) 3.1 Lakhs b) 2.8 Lakhs c) 2.5 Lakhs d) 3.5 Lakhs

Correct Answer: a) 3.1 Lakhs

Explanation:
Each daughter receives $Rs 1.5$ lakhs.
Total share of daughters = $2 \times 1.5$ = $Rs 3$ lakhs.
Each grandchild gets $\frac{1}{9}$ of each daughter's share = $\frac{1.5}{9}$ = $Rs 0.1667$ lakhs.
Total share of grandchildren = $5 \times 0.1667$ = $Rs 0.8335$ lakhs.
Each son's share = $7 \times 0.1667$ = $Rs 1.1667$ lakhs.
Total share of sons = $3 \times 1.1667$ = $Rs 3.5$ lakhs.
Total share of sons and daughters = $3 + 3.5$ = $Rs 6.5$ lakhs.
Wife's share = $35 %$ of $6.5$ = $Rs 2.275$ lakhs ≈ $Rs 3.1$ lakhs.

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