Question 4

# Two valves A and B can fill a sump in $$37\frac{1}{2}$$ minutes and 45 minutes respectively. Both valves are opened. The sump will be filled in just 30 minutes, if valve B is turned off after:

Solution

Let's Solve with LCM method.

LCM of ( $$\frac{75}{2}$$ and 45) = 225, assume this is total unit of work.

Thus, efficiency of A = $$\frac{225}{75/2}$$= 6 units/min and B = $$\frac{225}{45}$$ = 5 units/min.

Since A works for 30 mins, he will finish = 6 x 30 = 180 units.

Remaining Work = 225 - 180

= 45 units to be completed by B in = $$\frac{45}{5}$$ = 9 mins.