C and D together can complete a work in 40 days. C is 40 percent more efficient than D. C alone can complete the same work in how many days?

Correct option is C

Given:

C and D together can complete the work in 40 days.

C is 40% more efficient than D.

Solution:

Let the efficiency of D be x units/day.

Then, the efficiency of C = 1.4x units/day.

Combined efficiency of C and D = x + 1.4x = 2.4x units/day.

Time taken by C and D together to complete the work = 40 days.

Work = Efficiency × Time = 2.4x × 40 = 96x units.

​$$\text{Time taken by C alone} = \frac{\text{Total work}}{\text{Efficiency of C}} \\[10pt]\text{Time taken by C alone}= \frac{96x}{1.4x} = \frac{96}{1.4} = \frac{960}{14} = \frac{480}{7} \, \text{days}. \\[5pt]\therefore \, \text{C alone can complete the work in approximately } \frac{480}{7} \, \text{days}.$$​​

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