CAPF AC 2020 Q118: General Mental Ability – Quantitative Aptitude

CAPF AC 2020, Paper I (General Ability and Intelligence) · General Mental Ability

A wire of length 6 m is stretched such that its radius is reduced by 20%. Which one of the following is the value of increase in its length?

Answer: (b) 56.25%

Explanation

Stretching a wire

Given: a wire of length 6 m is stretched so that its radius is reduced by 20%.

We need the percentage increase in its length.

How to think: stretching does not add or remove metal.

So the volume stays the same.

Volume = area of cross-section × length.

In metres: the new length is 6 × 1.5625 = 9.375 m.

The increase is 3.375 m, which is 56.25% of 6 m.

The actual length of 6 m does not matter.

The percentage is the same for any wire.

Answer: (b) 56.25%.

(a) Incorrect. 50% does not follow from a 20% cut in radius.
(b) CORRECT. Area falls to 0.64, so the length rises to 1 ÷ 0.64 = 1.5625, an increase of 56.25%.
(c) Incorrect. 62.25% is a near miss placed to trap careless working.
(d) Incorrect. 75% would need a much larger cut in radius.

Wire stretched: volume constant, so length × radius² is constant. Radius × 0.8 gives area × 0.64 and length × 1.5625: a 56.25% increase.

Stretched wire: volume is constant; length varies as 1 ÷ radius².

Taking the area as falling by 20% instead of 36%.
Saying the length rises by 36%, the fall in area; the right step is 1 ÷ 0.64.
Wasting time on the 6 m, which is not needed.

Shortcut: 0.8 is 4/5. Length becomes (5/4)² = 25/16 = 1.5625.