# Question

A rectangle tank has 3 taps X,Y and Z attached to it. Tap X takes 2 minutes to fill the tank with water completely and Tank Y and Tank Z take 6 minutes and 4 minutes respectively to drain water out completely. If all 3 taps are turned on at the same time and the tank is empty,

a) how long does it take to fill the whole tank with water?

b)what is the capacity of the tank if it has 12 litres of water after 3 minutes?

Tap X

2 minutes to fill the tank.

In 1 minute, it can fill ½ tank

Tap Y

6 minutes to empty the tank

In 1 minute, it can drain 1/6 tank

Tap Z

4 minutes to empty the tank

In 1 minute, it can drain ¼ tank

Net flow in 1 minute -> ½ – 1/6 – ¼ = 1/12

1/12 -> 1 minute

(a) 12/12 -> 12 minutes

1 minute -> 1/12

3 minutes -> 3/12

3/12 of the tank = 12 litres

(b) Capacity of tank -> 12 × 12/3 = 48 litres

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(a)
Fraction of tank filled with water in 1 min from :
Tap X  : 1/2

Fraction of water drained from tank in 1 min by :
Tap Y : 1/6
Tap Z : 1/4

1/2 – 1/6 – 1/4 = 1/12 ——- 1 min
12/12 ——- 12 min

(b)
3 min ——- 12 l
12 min ——- 48 l

Ans : (a) 12 min; (b) 48 l.

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