Three Pipes P, Q, and R together can fill an empty cistern in 10 min.

1.	Three Pipes P, Q, and R together can fill an empty cistern in 10 min. The pipe P alone can fill the cistern in 30 min and pipe Q alone can fill it in 40 min. How long will pipe R alone will take to fill it?1. 24 min2. 26 min3. 25 min4. 22 min
Answer» Correct Answer - Option 1 : 24 min Given: Pipe P alone can fill the cistern in 30 min Pipe Q alone can fill the cistern in 40 min Pipes P, Q, and R can fill it in 10 min Concept Used: Total work is LCM of work done by each pipe. Calculation: Part filled by (P + Q + R) in 1 min = 1 / 10 Part filled by P in 1 min = 1 / 30 Part filled by Q in 1 min = 1/40 Part filled by (P + Q) = 1 / 30 + 1 / 40 ⇒ 7 / 120 Part filled by R = 1 / 10 – 7 / 120 ⇒ (12 - 7) / 120 ⇒ 5 / 120 ⇒ 1 / 24 ∴ Pipe C will take 24 min to fill the tank alone.

Three Pipes P, Q, and R together can fill an empty cistern in 10 min. The pipe P alone can fill the cistern in 30 min and pipe Q alone can fill it in 40 min. How long will pipe R alone will take to fill it?1. 24 min2. 26 min3. 25 min4. 22 min

Answer» Correct Answer - Option 1 : 24 min

Given:

Pipe P alone can fill the cistern in 30 min

Pipe Q alone can fill the cistern in 40 min

Pipes P, Q, and R can fill it in 10 min

Concept Used:

Total work is LCM of work done by each pipe.

Calculation:

Part filled by (P + Q + R) in 1 min = 1 / 10

Part filled by P in 1 min = 1 / 30

Part filled by Q in 1 min = 1/40

Part filled by (P + Q) = 1 / 30 + 1 / 40

⇒ 7 / 120

Part filled by R = 1 / 10 – 7 / 120

⇒ (12 - 7) / 120

⇒ 5 / 120

⇒ 1 / 24

∴ Pipe C will take 24 min to fill the tank alone.

Discussion

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