IPMAT Rohtak 2019 (QA) - Work done by P in one day is double the work done by Q in one day and work done by Q in one day is thrice the work done by R in one day. If P, Q, and R together can complete the work in 30 days, then in how many days P alone can do the work? | PYQs + Solutions

IPMAT Rohtak 2019

Arithmetic

Time & Work

Medium

Work done by P in one day is double the work done by Q in one day and work done by Q in one day is thrice the work done by R in one day. If P, Q, and R together can complete the work in 30 days, then in how many days P alone can do the work?

52 days

42 days

30 days

50 days

Correct Option: 4

Let P's work per day =

x

units

\newline

Then Q's work per day =

\frac{x}{2}

units

\newline

And R's work per day =

\frac{x}{6}

units

Total work per day by all three =

x + \frac{x}{2} + \frac{x}{6}

\newline

= \frac{6x + 3x + x}{6}

\newline

= \frac{10x}{6}

units per day

If total work =

1

unit and time taken =

30

days

\newline

\frac{10x}{6} \times 30 = 1

10x = \frac{6}{30}

x = \frac{6}{300} = \frac{1}{50}

Therefore, P can do

\frac{1}{50}

unit work per day

So P alone will take

50

days to complete the work.