Pipe A can fill the tank 3 times faster… - CUET UG 2025 Mathematics PYQ

CUET UG 2025 — Mathematics Arithmetic

2025mcqmedium

Pipe A can fill the tank 3 times faster than pipe B. If both pipes A and B running together can fill the tank in 15 minutes, then the time taken by B alone to fill the tank is:

Official previous-year question

Held on 19 May 2025 · Verified 13 Jul 2026.

Options

A
42 minutes
B
72 minutes
C
60 minutes
D
48 minutes

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Solution

The cofactor $C_{ij}$ is given by $(-1)^{i+j} M_{ij}$ , where $M_{ij}$ is the determinant of the submatrix after removing the $i$ -th row and $j$ -th column.

The matrix is:
$A = \begin{bmatrix} 2 & -1 & 3 \\ 1 & 2 & 0 \\ 4 & 1 & 5 \end{bmatrix}$

$C_{23} = (-1)^{2+3} \begin{vmatrix} 2 & -1 \\ 4 & 1 \end{vmatrix}$

$C_{23} = -1(2(1) - (-1)(4))$

$C_{23} = -1(2 + 4)$

$C_{23} = -6$

$C_{31} = (-1)^{3+1} \begin{vmatrix} -1 & 3 \\ 2 & 0 \end{vmatrix}$

$C_{31} = 1((-1)(0) - (3)(2))$

$C_{31} = 1(0 - 6)$

$C_{31} = -6$

$C_{22} = (-1)^{2+2} \begin{vmatrix} 2 & 3 \\ 4 & 5 \end{vmatrix}$

$C_{22} = 1(2(5) - (3)(4))$

$C_{22} = 1(10 - 12)$

$C_{22} = -2$

$C_{23} + C_{31} - C_{22} = -6 + (-6) - (-2)$

$= -6 - 6 + 2$

$= -10$

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