**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**