The ratio of the length to the width of a rectangle is 3 2 If the length of this rectangle is increa...........

Quantitative Aptitude (MTS) Percentage

The ratio of the length to the width of a rectangle is 3 : 2. If the length of this rectangle is increased by 25% and its width is kept

constant, then the area of the rectangle increases by 24m² . What is the width of this rectangle?

This questions was previously asked in

SSC MTS 22nd July 2022 Shift-1

12 m

10 m

8 m

15 m

- We start with a rectangle whose length to width ratio is 3:2. Represent length as 3x and width as 2x.

- The original area is calculated as \(3x \times 2x = 6x^2\).

- The length is increased by 25%, making it \(3x \times 1.25 = 3.75x\), while the width remains 2x.

- The new area is \(3.75x \times 2x = 7.5x^2\).

- The increase in area is \((7.5x^2 - 6x^2) = 1.5x^2\).

- According to the problem, the increase is 24 m², so \(1.5x^2 = 24\).

- Solving for \(x^2\), we find \(x^2 = 16\) and thus \(x = 4\).

- The width is \(2x = 8\) meters.

- Option 3: 8 m is correct.

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