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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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.

CUET UG 2025 — Mathematics Arithmetic

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Solution

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CUET UG 2025 — Mathematics Arithmetic

Options

Did you get this right?

Solution

Your note

CUET UG Arithmetic in other years

More CUET UG Arithmetic questions

Other Mathematics topics for CUET UG

Algebra

Calculus

Applied-Mathematics

Statistics & Applications

Geometry

Coordinate Geometry

Keep practicing Arithmetic