# Gain mastery over ratio and proportion problems

Published: Updated On - 03:45 PM, Thu - 4 August 22

**Hyderabad:** This article is in continuation to the last article focusing on the ratio and proportion topic. Here are some practice questions along with solutions on the ratio and proportion topic that will help you in your preparation for the State government recruitment jobs.

**1. A person distributes his pens among four friends A, B, C, D in the ratio 1/3:1/4:1/5:1/6. What is the minimum number of pens that the person should have?**

a) 55 b) 57 c) 65 d) 67

Ans: b

Solution: 1/3:1/4:1/5:1/6

LCM of 3,4,5,6 is 60

(1/3)×60 : (1/4)×60: (1/5)×60 : (1/6)×60

20 : 15 : 12 : 10

Therefore, minimum number of pens

= 20 15 12 10 = 57

**2. If a³ b³ : a³ – b³ = 185 : 158 then a : b?**

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

Ans: b

Solution: a³ b³ / a³ – b³ = 185/158

By componendo and dividendo

{(a³ b³) (a³ – b³)} / {(a³ b³) – (a³ – b³)} = 185 158 / 185 – 158

2a³ / 2b³ = 343/27

a³ / b³ = 7³ / 3³

7 : 3

**3. The ratio of two weights, 27kg and 108gm is**

a) 1 : 250 b) 1 : 270 c) 250 : 1 d) 270 : 1

Ans: c

Solution: 27 × 1000gm / 108gm

= 1000/4

= 250: 1

**4. If 3/5 of a bottle is filled, what is the ratio of the filled part to the empty part of the bottle?**

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

Ans: b

Solution: 1 (= Full bottle)

Filled part empty part

3/5 2/5

3/5 : 2/5

3 : 2

**5. If A : B = 3 : 4 and B : C = 6 : 5, then A : (A C) = ?**

a) 9 : 19 b) 9 : 10 c) 9 : 11 d) 11 : 9

Ans: a

Solution: A : B = 3 : 4

B : C = 6 : 5

A : B : C = 9 : 12 : 10

A : (A C) = 9 : 19

**6. What is the compound ratio of 45 : 75, 3 : 5, 51 : 68 and 256 : 81?**

a) 64 : 75 b) 128 : 75 c) 32 : 45 d) 75 : 32

Ans: a

Solution: Compound ratio = (45×3×51×256) / (75×5×68×81)

= 64/75

**7. A is twice of B, B is half of D, D is three times of C. A is how many times of D?**

a) 1 b) 0.5 c) 2 d) 3

Ans: a

Solution: A = 2B –>; A : B = 2 : 1

B = D –>; B : D = 1 : 2

D = 3C –>; D : C = 3 : 1

A : B : D = 2 : 1 : 2

D : C = 3 : 1

A : B : D : C = 6 : 3 : 6 : 2

A : D = 6 : 6

= 1 : 1

A = D

**To be continued…**

**M. Venkat**

**Director**

**MVK Publications**

**Dilsukhnagar**

**7671002120**