C and D together can complete work in 40 days. C is 40 percent more efficient than D. C alone can complete the same work in how many days?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 480/7.
Let the efficiency of D be x
Since C is 40% more efficient than D, the efficiency of C is 1.4x
Together, C and D can complete the work in 40 days
Therefore, their combined efficiency is 1/40 (work per day)
The combined efficiency of C and D = x + 1.4x = 2.4x
Given this combined efficiency completes the work in 40 days, we have
⇒ 2.4x = 1/40
⇒ x = 1/96
The efficiency of C is 1.4x
⇒ 1.4x = 1.4 × 1/96 = 480/7
Thus, Time taken = 1/efficiency
⇒ Time = 1/(7/480)
⇒ Time = 480/7 days