## Ratio and Proportion of Aptitude Questions and Answers

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**Ratio and Proportion of **Aptitude Questions and Answers

**Ratio & Proportion** is an important topic from Banking exams point of view as 1-2 questions are asked from this topic directly. Further indirect questions which make use of the concept of Ratio & Proportion are also frequently asked. Ratio & Proportion also plays an important role in D.I. based problems which make this chapter very important for banking aspirants.

**Q:1** If A: B = 5: 7

B: C = 3: 4, then what is A: B: C?

(a) 4: 7: 9 (b) 15: 21: 28 (c) 3: 8: 15 (d) 4: 9: 15 (e) None of these

Sol: A: **B** = 5: 7……..× 3

**B**: C = 3: 4……..×7 (We will make B equal in both the ratios)

So, A: B = 15: 21

B: C = 21: 28

Therefore, A: B: C = **15: 21: 28**

**Ans (b)**

**Q:2** The ratio of two numbers is 5: 4. If their sum is 135, Find the smaller of the two numbers.

(a) 30 (b) 40 (c) 55 (d) 65 (e) None of these

Sol: Let the two numbers be 5x and 4x.

So, 5x + 4x = 135

9x = 135

So, x = 15

Therefore, smaller number = 4 × 15 = **60**

**Ans (e)**

**Q:3** An employer reduces the number of his employees in the ratio 9:8 & increases their wages in the ratio 14:15. If the original wage bill was Rs 18,900, Find the ratio in which the wage bill is decreased.

(a) 21:20 (b) 36:41 (c) 5:8 (d) 32:37 (e) None of these

Sol: Let the initial no of employees be 9x& the employer gives Rs 14y as a wage to each.

So, 9x × 14y = 18900

So, xy = 150

The new bill is 8x × 15y = 120 xy

= 120 × 150 = 18000

So, the required ratio 18900:18000

= **21:20**

**Ans (a)**

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**Q:4** The cost of a piece of stone worth Rs 10,872 fell & broke into 3 pieces, the weights of which are proportional to 1:2:3. The value of each stone is directly proportional to the square of its weight. Find the loss in the value caused by the breakage.

(a) 3624 (b) 4228 (c) 6644 (d) 7510(e) None of these

Sol: Let the initial weight of the stone (before breaking) be 6w

So, Weights of the broken stones are w, 2w & 3w resp.

The initial value of the stone is Rs. 10,872

10,872 α (6w)^{2}

So, 10,872= 36w^{2}k

W^{2}k = 10,872 / 36 ……..1

Total value of the pieces of the stone = (1^{2} + 2^{2} + 3^{2})w^{2}k

= 14w^{2}k

Loss in the value = 36w^{2}k – 14 w^{2}k

= 22w^{2}k

= 22 × 10,872 / 36 ……From 1

= 22 × 302

= **6644**

**Ans (c)**

**Q:5** If the income of Amit & Mohit is in the ratio 4:5 & their expenses are in the ratio of 6:7. Find the ratio of their savings, if Amit manages to save one-fourth of his salary.

(a) 4:5 (b) 7:3 (c) 5:8 (d) 3:2 (e) None of these

Sol: Let the salary of Amit&Mohit be 4x & 5x resp.

&their expenses are 6y & 7y resp.

Savings of Amit = 4x- 6y

Savings of Mohit = 5x- 7y

- T. Q

4x- 6y = 4x / 4

3x = 6y

x = 2y

Ratio of their savings: 4(2y) – 6y / 5(2y) – 7y

= 8y – 6y / 10y – 7y

= 2y / 3y

= **2: 3**

**Ans (e)**

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