CUET · MATHS · PYQ PAPER 2025

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

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

Verified Solution

Answer & Solution

Correct Answer

(C) \(15 \frac{5}{13}\) hours

Step-by-step Solution

Detailed explanation

Combined rate \( = \frac{1}{20} + \frac{1}{25} - \frac{1}{40} \) \( = \frac{10+8-5}{200} = \frac{13}{200} \) tank/hour Time needed \( = \frac{1}{\frac{13}{200}} = \frac{200}{13} = 15 \frac{5}{13} \) hours

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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List-I	List-II
(A) \(\|A\|=0\)	(I) A is a symmetric matrix
(B) \(\|A\| \neq 0\)	(II) A is a skew-symmetric matrix
(C) \(A^T=A\)	(III) A is a singular matrix
(D) \(A^T=-A\)	(IV) A is a non-singular matrix