Practice Questions for Ratio, Proportion & Variation

1. CRE 2 - Proportion | Ratio, Proportion & Variation

If a : b = 3 : 1, find a + b : a – b.

(a)
2 : 1
(b)
4 : 3
(c)
3 : 4
(d)
1 : 2

Answer: Option A

Explanation :

Let a = 3x and b = x

a + b = 4x and a – b = 2x

a + b : a – b = 4x : 2x = 2 : 1

Alternately,

Apply Componendo & Dividendo, i.e.

If x/y = p/q, then $\frac{x + y}{x - y} = \frac{p + q}{p - q}$

∴ $\frac{a + b}{a - b} = \frac{3 + 1}{3 - 1} = \frac{4}{2} = \frac{2}{1}$

Hence, option (a).

2. CRE 2 - Proportion | Ratio, Proportion & Variation

If a + b : a – b = 5 : 4, find a : b.

(a)
9 : 1
(b)
1 : 5
(c)
3 : 5
(d)
5 : 3

Answer: Option A

Explanation :

$\frac{a + b}{a - b} = \frac{5}{4}$

⇒ 4a+4b = 5a-5b

⇒ a = 9b

⇒ a/b = 9/1

⇒ a : b = 9 ∶ 1

Alternately,

Apply Componendo & Dividendo, i.e.

If x/y = p/q, then (x+y)/(x-y) = (p+q)/(p-q)

Hence, (a+b)/(a-b) = 5/4

⇒ $\frac{(a + b) + (a - b)}{(a + b) - (a - b)} = \frac{5 + 4}{5 - 4}$

⇒ 2a/2b = 9/1

⇒ a/b = 9/1

Hence, option (a).

3. CRE 2 - Proportion | Ratio, Proportion & Variation

The third proportion to 1 and 2 is?

(a)
2
(b)
3
(c)
4
(d)
1

4. CRE 2 - Proportion | Ratio, Proportion & Variation

The fourth proportional to 12, 14 and 18 is?

(a)
21
(b)
20
(c)
22
(d)
28/3

Answer: Option A

Explanation :

Let the fourth proportional number be x. Then, 12 : 14 :: 18 : x

⇒ $\frac{12}{14} = \frac{18}{x}$

⇒ x = $\frac{14 \times 18}{12}$ = 21

Hence, option (a).

5. CRE 2 - Proportion | Ratio, Proportion & Variation

The mean proportional between 4 and 9 is?

(a)
√3
(b)
√6
(c)
6
(d)
None of these

Answer: Option C

Explanation :

Let mean proportion of 4 and 9 be x.

⇒ $\frac{4}{x} = \frac{x}{9}$

∴ Mean proportional = $\sqrt{4 \times 9}$ = 2 × 3 = 6.

[Remember: Mean proportion of 2 numbers a and b is always $\sqrt{a \times b}$ ]

Hence, option (c).

6. CRE 2 - Proportion | Ratio, Proportion & Variation

Find the Mean proportion of 64 and 4.

(a)
64
(b)
16
(c)
8
(d)
14

Answer: Option B

Explanation :

Mean proportional of p, q is √pq

⇒ Mean proportional of 64, 4 is $\sqrt{64 \times 4}$ = 16

Hence, option (b).

7. CRE 2 - Proportion | Ratio, Proportion & Variation

The compound ratio of 2 : 3, 6 : 7, 1 : 3 and 1 : 8 is?

(a)
1/32
(b)
1/42
(c)
1/16
(d)
12/71

Answer: Option B

Explanation :

Compounded ratio is : $\frac{2 \times 6 \times 1 \times 1}{3 \times 7 \times 3 \times 8} = \frac{1}{42}$

Hence, option (b).

8. CRE 2 - Proportion | Ratio, Proportion & Variation

The inverse ratio of 3 : 2 : 1 is?

(a)
1 : 2 : 3
(b)
2 : 3 : 1
(c)
3 : 1 : 2
(d)
2 : 3 : 6

Answer: Option D

Explanation :

Inverse ratio would be, $\frac{1}{3} : \frac{1}{2} : \frac{1}{1}$ or $\frac{6}{3} : \frac{6}{2} : \frac{6}{1}$ or 2 : 3 : 6

Hence, option (d).

9. CRE 2 - Proportion | Ratio, Proportion & Variation

Find the Duplicate ratio of 4 : 9.

(a)
2 : 3
(b)
9 : 4
(c)
4 : 6
(d)
16 : 81

10. CRE 2 - Proportion | Ratio, Proportion & Variation

Find the Triplicate ratio of 3 : 4.

(a)
9 : 12
(b)
12 : 2
(c)
27 : 64
(d)
5 : 8

11. CRE 2 - Proportion | Ratio, Proportion & Variation

Find the Sub-duplicate ratio of 25 : 16.

(a)
5 : 4
(b)
4 : 3
(c)
4 : 9
(d)
8 : 3

12. CRE 2 - Proportion | Ratio, Proportion & Variation

Find the Sub-triplicate ratio of 8 : 125.

(a)
2 : 3
(b)
2 : 5
(c)
2√2 : 5√5
(d)
None of these

CRE 2 - Proportion | Ratio, Proportion & Variation

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