Question

Three faucets P, Q and R can fill a tank in 24, 30 and 40 hours respectively. If P is open all the time and Q and R are open for 2 hours each alternately(start with Q), the tank will be full in?

• A. 14 hrs
• B. 20/3 hrs
• C. 16 hrs
• D. 13 hrs
• E. 127/9 hrs

Answer 1

The correct option is A

14 hrs

(P+ Q)'s 2 hour work =$2(\frac{1}{24}+\frac{1}{30})$ = $\frac{3}{20}$

(P + R)'s 2 hour work = $2(\frac{1}{24}+\frac{1}{40})$ = $\frac{2}{15}$

Part filled in 4 hrs = $(\frac{3}{20}+\frac{2}{15})$ = $\frac{17}{60}$

Part filled in 12 hrs = $3\times \frac{17}{60}$ = $\frac{17}{20}$

Remaining part =$1-\frac{17}{20}$ = $\frac{3}{20}$

Now, it is the turn of P and Q and $\frac{3}{20}$ part is filled by P and Q in 2 hours.

Total time taken to fill the tank = (12 + 2 ) = 14 hrs.