NIMCET 2020 — Reasoning PYQ

Given:

A can fill the cistern= 37. 5 minutes= 75/ 2 minutes
$B$ can fill the cistern=45 minutes

Concept used:

Total work=Efficiency of a person$\times$Time

Calculation:

Taking the L.C.M. of 75/2 &45=225(which is total work)

Work done by A in 75/ 2 minutes= 225

$\mathsf{Efficiency}\mathsf{of}\mathsf{A}\mathsf{in}1\mathsf{minute}=(225\times 2)/75=6$

Work done by B in 45 minutes =225

Efficiency of B in 1 minute= 225/ 45= 5

Let the turned off time of B be x minutes.

Efficiency of A in 1 minute$\times$Time+Efficiency of B in 1 minute$\times$Time=Total work

$\Rightarrow 6\times 30+5\times \mathbf{x}=225$

$\Rightarrow 180+5\mathbf{x}=225$

$\Rightarrow 5\mathbf{x}=225-180$

$\Rightarrow \mathbf{x}=45/5$

$\Rightarrow \mathbf{x}=9$ minutes

$\therefore$B is turned off after 9 minutes.