Management Aptitude Test 2016 Paper

(a) ∵ Part of tank filled by A in 1 h = $\frac{1}{20}$
and part of tank filled by Bin 1 h = $\frac{1}{30}$
∴ Part of tank filled by A and B in 1 h
= $\frac{1}{20}+\frac{1}{30}$ = $\frac{5}{60}=\frac{1}{12}$
Time taken to fill $\frac{1}{3}$ rd tank by A and B = 12 x $\frac{1}{3}$ = 4h
Now. part of tank emptied by leak in 1 h = $\frac{1}{12}\times \frac{1}{4}=\frac{1}{48}$
∴ Part of tank filled by A, B and leak in 1h
= $\frac{1}{12}-\frac{1}{48}$
= $\frac{4-1}{48}$
= $\frac{3}{48}=\frac{1}{16}$
Remaining part to be filled = $\frac{2}{3}$
Time taken to fill remaining tank = 16 × $\frac{2}{3}=\frac{32}{3}$
∴ Total time to fill the tank
= $\frac{32}{3}$ + 4
= $\frac{44}{3}=14\frac{2}{3}$ h