Question

Pipes A and B can fill a tank in 12 h and 18 h, respectively, whereas pipe C can empty the full tank in 8 h. A and B opened for $4\frac{1}{2}$ h and then closed. C alone will empty the tank in (in h):

• A. $$5\frac{1}{4}$$
• B. $$9\frac{1}{2}$$
• C. 9
• D. 5

Answer 1

Answer:

D. 5

Solution:

Given:

Pipes A and B can fill a tank in 12 h and 18 h, respectively,

whereas pipe C can empty the full tank in 8 h.

A and B opened for $4\frac{1}{2}$ h and then closed.

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day 

Calculation:

Let total work is 72 units ( LCM of 12, 18 and 8)

The efficiency of A = 72 /12 = 6 units

The efficiency of B = 72 / 18 = 4 units

So A + B together do in one day 6 + 4 = 10 units

So they do in 4.5 hours, 4.5 × 10 = 45 units

c empty 45 units alone

So, the efficiency of C = 72 / 8 =  9 unit

So, C takes 45 / 9= 5 hours to empty the tank

∴ C alone will empty the tank in 5 hr.