P is four times as efficient as Q. P can complete a work in 45 days less than Q. If both of them work together, then in how many days the work will be completed?
1). 10
2). 12
3). 15
4). 30
Let efficiency of Q be q.
⇒ Efficiency of P = 4q.
Time taken by Q = 1/q
Time taken by P = 1/4q
P can complete a work in 45 days less than Q
⇒ 1/4q = 1/q - 45
-3/4q = -45
q = 3/45 = 1/60
Combined efficiency = q + 4q = 5q.
Time taken by them together = 1/5q = 1/(5 × 1/60) = 12 days.