One-third of a work is finished in four days by P and one-fourth of the same work is finished in six days by Q. P and Q together work for six days and the rest of the work is finished by R in two days. R alone can finish the whole work in _____ days.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 8 .
P's rate = (1/3) ÷ 4 = 1/12 per day
Q's rate = (1/4) ÷ 6 = 1/24 per day
P + Q rate = 1/12 + 1/24 = 1/8 per day
Work done by P and Q in 6 days = 6 × 1/8 = 3/4
Remaining work = 1 − 3/4 = 1/4
R finishes 1/4 work in 2 days ⇒ R's rate = (1/4) ÷ 2 = 1/8 per day
Time for R alone to finish whole work = 1 ÷ (1/8) = 8 days