Pipe A and B can fill a tank in 20 hours… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Arithmetic

2025mcqmedium

Pipe A and B can fill a tank in 20 hours and 25 hours respectively, and pipe C can empty the full tank in 40 hours.If all the pipes are opened together, then how much time will be needed to make the tank full?

Official previous-year question

Held on 3 Jun 2025 · Verified 13 Jul 2026.

Options

A
$15\frac{1}{13}$ hours
B
$15\frac{4}{13}$ hours
C
$15\frac{5}{13}$ hours
D
$15\frac{3}{13}$ hours

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Solution

The sides of an equilateral triangle are increasing at the rate of 5 cm/sec, with the current side length at 20 cm.

The area of an equilateral triangle with side $a$ is given by:

$A = \dfrac{\sqrt{3}}{4} \times a^2$

Differentiating both sides with respect to time $t$ :

$\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{4} \times \dfrac{d(a^2)}{dt}$

$\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{4} \times 2a \times \dfrac{da}{dt}$

$\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{2} \times a \times \dfrac{da}{dt}$

Given:
$a = 20$ cm
$\dfrac{da}{dt} = 5$ cm/sec

Substituting the values:

$\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{2} \times 20 \times 5$

$\dfrac{dA}{dt} = \dfrac{\sqrt{3}}{2} \times 100$

$\dfrac{dA}{dt} = 50\sqrt{3}$ cm²/sec

Therefore, the rate at which the area increases is $50\sqrt{3}$ cm²/sec.

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