Question

Working together, P, Q and R reap a field in 6 days. If P can do it alone in 10 days and Q in 24 days, in how many days will R alone be able to reap the field?

• A. 32 days
• B. 40 days
• C. 45 days
• D. 60 days

Answer 1

Answer:

B. 40 days

P alone can do it in 10 days , $Efficiency of P =\frac{1}{10}$

Q alone can do it in 24 days,

$Efficiency of Q =\frac{1}{24}$

Together they can do it in 6days

$Efficiency of Q=\frac{1}{6}$

$\frac1{10}+\frac{1}{24}+\frac{1}{R}=\frac{1}{6}$

$\frac1{R}=\frac{1}{40}$

$R=40 Days$

Alternate method

$Effrciciency of P+Q+R=20$

$R=20-(12+5)$

$Efficiency of R=3$

$$Time taken by R alone to complete a work is$=\frac{120}{3} = 40 days$