P and Q together complete a job in 4 2/5 days, and R and S complete the same job in 4 8/9 days. If P, Q, R, and S work together, how many days do they need to complete the same job?

P and Q together complete a job in 4 2/5 days, and R and S…

P and Q together complete a job in 4 $\frac{2}{5}$ days, and R and S complete the same job in 4 $\frac{8}{9}$ days. If P, Q, R, and S work together, how many days do they need to complete the same job?

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 2 $\frac{6}{19}$ .

Time required for P and Q = $4\frac{2}{5}$ days = 22/5 days

Time required for R and S = $4\frac{8}{9}$ days = 44/9 days

Total work = 44 (LCM of 22/5 and 44/9)

Efficiency of P and Q = 44/(22/5) = 10 work/day

Efficiency of R and S = 44/(44/9) = 9 work/day

Total efficiency of P, Q, R, and S = 10 + 9 = 19 work/day

Time required = 44/19 = $2\frac{6}{19}$ days

Therefore, P, Q, R, and S work together to complete the job in $2\frac{6}{19}$ days.

SSC CGL 2023 PYQ — Question 55