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CUET Mathematics 2025 PYQs13 May Shift 1. Free, no login required.

Arithmetic

past year questions, CUET Mathematics 2025 13 May Shift 1

Time & Work

past year questions, Arithmetic, CUET Mathematics 2025 13 May Shift 1

Medium

applied

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

Solution

✅ Correct Option: 2

Let Pipe A take aa minutes to fill the tank alone.

Since Pipe B is 15 minutes faster than Pipe A:

Pipe B takes a−15a - 15 minutes

Since Pipe B is 5 minutes slower than Pipe C:

Pipe C takes (a−15)−5=a−20(a - 15) - 5 = a - 20 minutes

The rate of filling for each pipe:

Rate of A =1a= \dfrac{1}{a}

Rate of B =1a−15= \dfrac{1}{a-15}

Rate of C =1a−20= \dfrac{1}{a-20}

Pipes A and B together fill the tank in the same time as Pipe C alone:

1a+1a−15=1a−20\dfrac{1}{a} + \dfrac{1}{a-15} = \dfrac{1}{a-20}

Multiplying throughout by a(a−15)(a−20)a(a-15)(a-20):

(a−15)(a−20)+a(a−20)=a(a−15)(a-15)(a-20) + a(a-20) = a(a-15)

Expanding:

a2−35a+300+a2−20a=a2−15aa^2 - 35a + 300 + a^2 - 20a = a^2 - 15a

2a2−55a+300=a2−15a2a^2 - 55a + 300 = a^2 - 15a

a2−40a+300=0a^2 - 40a + 300 = 0

Using the quadratic formula:

a=40±1600−12002a = \dfrac{40 \pm \sqrt{1600 - 1200}}{2}

a=40±4002a = \dfrac{40 \pm \sqrt{400}}{2}

a=40±202a = \dfrac{40 \pm 20}{2}

This gives a=30a = 30 or a=10a = 10

If a=10a = 10: Pipe B takes 10−15=−510 - 15 = -5 minutes (impossible)

If a=30a = 30: Pipe B takes 30−15=1530 - 15 = 15 minutes and Pipe C takes 15−5=1015 - 5 = 10 minutes (valid)

Therefore, Pipe A takes 30 minutes to fill the tank alone.

Related questions:

2025: 30 May Shift 2

Two pipes A and B can fill a tank respectively in 30 min and 45 min. Both A and B are opened together for some time and then pipe B is turned off. If the tank is filled in 20 min, then find after how many minutes the pipe B is turned off?

2025: 29 May Shift 2

Pipe A and B can fill a tank in 15 hours and 20 hours respectively. Pipe C can empty the tank in 25 hours. Pipes A, B and C works together but pipe C is closed after 10 hours , then time taken by pipe A and B to fill the remaining tank is:

2026: 15 May Shift 1

Three pipes A, B, and C can fill a tank together in 10 hours. After working at it together for 2 hours, B is closed and A and C can fill the remaining part in 12 hours. The time in which B alone can fill the tank is

2025: 2 June Shift 1

Three pipes A, B & C fill a tank in 3 hours working simultaneously. The pipe C is twice as faster as B and B is twice as fast as A. The time taken by pipe A alone to fill the tank is:

2025: 15 May Shift 2

Two pipes A and B can fill a tank in 20 minutes and 30 minutes respectively. Both pipes A and B are opened together for some time and pipe B is turned off. If the tank is filled in 15 minutes, then after how many minutes pipe B is turned off?

2026: 31 May Shift 2

A tap can fill a tank in 45 minutes whereas another tap can empty it in 1 hour 30 minutes. If both taps are opened at 9 A.M., then the time at which the tank will be filled is

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