Concept: The question tests on Rates(Time and Work)
Solution:
A is 40% more efficient than B, there AE=1.4BE
Since efficiency is inversely proportional to Time, BT=1.4∗AT
Let B take x days to Finish.
Then A takes x - 10 days. Substituting in the above equation and solving
x = 1.4(10 - x)
0.4x = 14
x = 35
So A takes 25 days, B takes 35 days
Given that B is 20% more efficient than C. So, BE=1.2CE
In terms of time, CT=1.2∗BT
Time Taken by C = 1.2 * 35 = 42 days
Let C take x days to evaluate the remaining work.
Fraction of work done by A in 10 days = 10 * 1/25=2/5
Fraction of work done by B in 15 days = 15 * 1/35=3/7
Fraction of work done by C in x days = x * 1/42
Sum of fractions of work = 1 (completion of work is always = 1)
2/5+3/7+x/42=1
84+90+5x/210=1
5x = 210 - 174 = 36
x = 7.2 days
Option A