Correct Answer - Option 4 : 3 days
Given :-
A can do a piece of work in 15 days
B is 25% more efficient than A and
C is 40% more efficient than B
Concept :-
Ratio of efficiency is reciprocal of time.
Number of days required to complete a certain work = (Work to be completed/Work efficiency)
Calculation :-
Let efficiency of A be 100
⇒ Efficiency of B = 100 + (100 × 25%)
⇒ Efficiency of B = 100 + 25 = 125
⇒ Efficiency of C = 125 + (125 × 40%)
⇒ Efficiency of C = 125 + 50 = 175
⇒ Ratio of efficiency of A ∶ B ∶ C = 100 ∶ 125 ∶ 175
⇒ Ratio of efficiency of A ∶ B ∶ C = 4 ∶ 5 ∶ 7
A work for 15 days with efficiency 4
⇒ Total work done by A = 15 × 4 = 60 unit
Now,
(A + C) together work for 3 days.
⇒ Total efficiency of A and C together = 4 + 7 = 11 unit/day
⇒ Total work done by A and C together = 11 × 3 = 33 unit
⇒ Remaining work = Total work - Work done by A and C together
⇒ Remaining work = 60 - 33
⇒ Remaining work = 27 unit
⇒ Total efficiency of A and B together = 4 + 5 = 9 unit/day
⇒ Required number of days = (27/9) = 3 days
⇒ Time required to complete remaining work = 3 days.
∴ Time required to complete remaining work is 3 days.