The lengths the breadths and the volumes of two cuboids are in the ratios of 4 5 3 4 and 2 3 respect...........

Quantitative Aptitude (MTS) Mensuration 2D

The lengths, the breadths, and the volumes of two cuboids are in the ratios of 4 : 5, 3: 4, and 2 . 3, respectively. What is the ratio

of their heights?

This questions was previously asked in

SSC MTS 25th July 2022 Shift-2

3 : 5

10 : 9

8 : 15

2 : 3

Let's break it down step by step:

- Let the lengths be 4x and 5x.

- Let the breadths be 3y and 4y.

- Let heights be h1 and h2.

- Volumes: 4x × 3y × h1 and 5x × 4y × h2.

- The ratio of volumes = (4x × 3y × h1) : (5x × 4y × h2) = 2 : 3.

So,

(4x × 3y × h1) / (5x × 4y × h2) = 2 / 3

(12xyh1) / (20xyh2) = 2 / 3

(3h1) / (5h2) = 2 / 3

Cross multiply: 3h1 × 3 = 2 × 5h2 ? 9h1 = 10h2

So h1 / h2 = 10 / 9.

Option 2: 10 : 9 is correct.

Statements on options:

- 3 : 5 - Not matching with derived ratio.

- 10 : 9 - Correct, matches calculation.

- 8 : 15, 2 : 3 - Also don't match with result.

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