Ratio and Proportion — Practice

Question 1

If a : b = 3 : 4 and b : c = 5 : 6, then a : c is:
(a) 1 : 2 (b) 5 : 8 (c) 3 : 6 (d) 15 : 20

Accepted Answer

(b) 5 : 8.

Equalise b: a:b:c = 15:20:24. So a:c = 15:24 = 5:8.

Question 2

The mean proportional between 4 and 25 is:
(a) 10 (b) 14.5 (c) 20 (d) 100

Accepted Answer

(a) 10.

Mean proportional = √(4 × 25) = √100 = 10. Option (b) is the arithmetic mean — the standard distractor.

Question 3

The fourth proportional to 4, 6 and 8 is:
(a) 10 (b) 12 (c) 14 (d) 16

Accepted Answer

(b) 12.

4 : 6 :: 8 : x → 4x = 48 → x = 12.

Question 4

₹782 is divided among three people in the ratio 1/2 : 2/3 : 3/4. The largest share is:
(a) ₹204 (b) ₹272 (c) ₹306 (d) ₹350

Accepted Answer

(c) ₹306.

Multiply by LCM(2,3,4) = 12: ratio = 6 : 8 : 9, sum 23. Each unit = 782 ÷ 23 = 34. Largest share = 9 × 34 = ₹306.

Question 5

Two numbers are in the ratio 3 : 5. If 9 is added to each, the ratio becomes 3 : 4. The sum of the numbers is:
(a) 18 (b) 24 (c) 30 (d) 32

Accepted Answer

(b) 24.

(3x+9)/(5x+9) = 3/4 → 12x + 36 = 15x + 27 → x = 3. Numbers are 9 and 15; sum = 24. Check: 18/24 = 3/4 ✓.

Question 6

A bag contains ₹1, 50-paise and 25-paise coins in the ratio 5 : 6 : 8. If the total amount is ₹210, the number of 50-paise coins is:
(a) 105 (b) 126 (c) 168 (d) 63

Accepted Answer

(b) 126.

Value ratio: 5x + (6x × ½) + (8x × ¼) = 5x + 3x + 2x = 10x rupees = 210 → x = 21. Fifty-paise coins number 6x = 126.

Question 7

The present ages of A and B are in the ratio 4 : 5. Six years from now the ratio will be 5 : 6. A's present age is:
(a) 20 years (b) 24 years (c) 28 years (d) 30 years

Accepted Answer

(b) 24 years.

(4x+6)/(5x+6) = 5/6 → 24x + 36 = 25x + 30 → x = 6. A = 4x = 24 (B = 30). Check: 30/36 = 5/6 ✓.

Question 8

If a/b = 5/3, then (a + b)/(a − b) equals:
(a) 2 (b) 3 (c) 4 (d) 8/3

Accepted Answer

(c) 4.

Componendo–dividendo: (a+b)/(a−b) = (5+3)/(5−3) = 8/2 = 4. No substitution needed.

Question 9

The incomes of two persons are in the ratio 9 : 7 and their expenditures in the ratio 4 : 3. If each saves ₹2000, the income of the first person is:
(a) ₹14,000 (b) ₹16,000 (c) ₹18,000 (d) ₹21,000

Accepted Answer

(c) ₹18,000.

Let incomes be 9x, 7x and expenditures 4y, 3y. Savings: 9x − 4y = 2000 and 7x − 3y = 2000. Multiply the first by 3, the second by 4: 27x − 12y = 6000, 28x − 12y = 8000. Subtract: x = 2000. First income = 9x = ₹18,000 (expenditure ₹16,000, saving ₹2000 ✓).

Question 10

If 20% of x equals 30% of y, then x : y is:
(a) 2 : 3 (b) 3 : 2 (c) 4 : 5 (d) 5 : 4

Accepted Answer

(b) 3 : 2.

0.2x = 0.3y → x/y = 3/2. The ratio flips relative to the percentages — the number carrying the smaller percentage must be larger to keep the products equal.

Question 11

If A : B = 2 : 3 and B : C = 4 : 5, then A's share when ₹3500 is divided in the ratio A : B : C is:
(a) ₹800 (b) ₹1000 (c) ₹1200 (d) ₹1500

Accepted Answer

(a) ₹800.

Chain through B: A:B:C = (2×4) : (3×4) : (3×5) = 8 : 12 : 15, sum 35. A = 3500 × 8/35 = ₹800.

Practice — Ratio and Proportion

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