Given:
C is four times as efficient as D.
C takes 63 days less than D to complete a work.
Formula Used:
Work = Efficiency × Time
If C is 4 times as efficient as D, let efficiency of D be 1 unit, then efficiency of C = 4 units.
If D takes x days to complete the work, then C takes (x - 63) days to complete the work.
When both work together, their combined efficiency = Efficiency of C + Efficiency of D.
Time taken = Work / Combined Efficiency.
Calculation:
Let D takes x days to complete the work.
Then, C takes (x - 63) days to complete the same work.
Since Work = Efficiency × Time, we have:
Work done by D in x days = 1 × x = x
Work done by C in (x - 63) days = 4 × (x - 63) = 4(x - 63)
Since both do the same work:
⇒ x = 4(x - 63)
Solving for x:
⇒ x = 4x - 252
⇒ 252 = 3x
⇒ x = 84
D takes 84 days to complete the work.
C takes 84 - 63 = 21 days to complete the work.
Combined efficiency of C and D = 4 + 1 = 5 units
Time taken to complete the work together = Work / Combined Efficiency
Time taken = 1 work / 5 units
Time taken = 84/5 = 16.8 days
The correct answer is option 1: 16.8 days