There are two inlets P and Q connected to a tank. P and Q can fill the

1.	There are two inlets P and Q connected to a tank. P and Q can fill the tank in 16 h and 10 h, respectively. If both the inlets are opened alternately for 1 h, starting with P, then how much time will the tank take to fill?1. 62 / 52. 66 / 53. 12 / 54. 14 / 5
Answer» Correct Answer - Option 1 : 62 / 5 Given: P can fill the tank in = 16 h Q can fill the tank in = 10 h Concept Used: Total work is LCM of work done by each pipe. Calculation: Part filled by P in 1 h = 1 / 16 Part filled by Q in 1 h = 1 / 10 Both are opened alternately, Part filled by (P + Q) in 2 h = 1 / 16 + 1 / 10 ⇒ 13/80 Part filled by (P + Q) in 12 h = 6 × 13 / 80 ⇒ 39/40 Remaining part = 1 – 39 / 40 ⇒ 1 / 40 Now, it is P’s turn Time taken by P to fill 1 / 40 part of the tank = 1 / 40 × 16 ⇒ 2 / 5 h Total time taken = 12 + 2 / 5 ⇒ 62 / 5 h ∴ The tank will get filled in 62 / 5 hours.

There are two inlets P and Q connected to a tank. P and Q can fill the tank in 16 h and 10 h, respectively. If both the inlets are opened alternately for 1 h, starting with P, then how much time will the tank take to fill?1. 62 / 52. 66 / 53. 12 / 54. 14 / 5

Answer» Correct Answer - Option 1 : 62 / 5

Given:

P can fill the tank in = 16 h

Q can fill the tank in = 10 h

Concept Used:

Total work is LCM of work done by each pipe.

Calculation:

Part filled by P in 1 h = 1 / 16

Part filled by Q in 1 h = 1 / 10

Both are opened alternately,

Part filled by (P + Q) in 2 h = 1 / 16 + 1 / 10

⇒ 13/80

Part filled by (P + Q) in 12 h = 6 × 13 / 80

⇒ 39/40

Remaining part = 1 – 39 / 40

⇒ 1 / 40

Now, it is P’s turn

Time taken by P to fill 1 / 40 part of the tank = 1 / 40 × 16

⇒ 2 / 5 h

Total time taken = 12 + 2 / 5

⇒ 62 / 5 h

∴ The tank will get filled in 62 / 5 hours.

Discussion

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