**Problem 1:** 12 taps are fitted in a tank, some are inlet water taps and rest are outlet taps each water tap can fill the tank in 6 hours and outlet can empty the tank in 12 hours. If all taps are open together then the tank is full in 4 hours. find the number of inlet water taps?

Solution:

Total number of taps are=12

Let the number of inlets taps=X

The number of outlet taps =12-X

A———->6 +2

L.C.M12

B———->12 -1

X*2*4 + (12-X)*(-1)*4=12

8X-48+4X = 12

12X = 60

X = 5

The inlet water taps are 5 and outlet taps are 7.

**Problem 2:** 8 taps are fitted in a tank, some are inlet water taps and rest are outlet taps each water tap can fill the tank in 12 hours and outlet can empty the tank in 36 hours. lf all taps are open together then the tank is full in 3 hours. Find the number of inlet water taps?

Solution:

Total number of taps are=8

Let the number of inlet taps=X

The number of outlet taps =8-X

A———->12 +3

L.C.M 36

B———->36 -1

X*3*43 + (8-X)*(-1)*3=36

9X-24+3X=36

12X = 60

X=5

The inlet water tapes are 5 and outlet taps are 3