Three pipes A, B and C are installed to… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Arithmetic

2025mcqmedium

Three pipes A, B and C are installed to fill a tank. Pipes A and B opened together can fill the tank in the same time in which C can alone fill the tank. If pipe B can fill the tank 15 minutes faster than pipe A and 5 minutes slower than pipe C then the time required by pipe A to fill the tank alone is

Official previous-year question

Held on 13 May 2025 · Verified 13 Jul 2026.

Options

A
20 minutes
B
30 minutes
C
24 minutes
D
36 minutes

Did you get this right?

Solution

Given points: $(2, -3)$ , $(\lambda, -1)$ , and $(0, 4)$

For three points to be collinear, the slope between any two pairs of points must be equal.

Using points $(2, -3)$ and $(0, 4)$ :

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{4 - (-3)}{0 - 2}$

$m = \frac{7}{-2}$

$m = -\frac{7}{2}$

Using points $(2, -3)$ and $(\lambda, -1)$ :

$m = \frac{-1 - (-3)}{\lambda - 2}$

$m = \frac{2}{\lambda - 2}$

Since the points are collinear, the slopes must be equal:

$\frac{2}{\lambda - 2} = -\frac{7}{2}$

$2 \times 2 = -7 \times (\lambda - 2)$

$4 = -7\lambda + 14$

$7\lambda = 14 - 4$

$7\lambda = 10$

$\lambda = \frac{10}{7}$

Therefore, $\lambda = \frac{10}{7}$

Your note

CUET UG Arithmetic in other years

Arithmetic 2024 Arithmetic 2023

Keep practicing Arithmetic

Work through every CUET UG Arithmetic PYQ, year by year.

Browse all Mathematics topics

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