A man and a boy, together, can complete a task in 60 days. Their efficiency is in the ratio of 7 : 5. How many days will the boy alone take to complete the task?

Correct option is D

Given:

Man and boy together complete the work in 60 days

Efficiency ratio (Man : Boy) = 7 : 5

Formula Used:

Work = Efficiency × Time

Solution:

Total efficiency = 7 + 5 = 12 units/day

Total work = 12 × 60 = 720 units
Boy's efficiency = 5 units/day
Time taken by boy alone =$$\dfrac{720}{5}$$​= 144 days

Alternate Method:

Concept Used:
Time is inversely proportional to efficiency. So, if efficiencies are in ratio 7:5, their times will be in ratio 5:7.

Solution:

Let the number of days taken by the man alone = x
Then, the boy alone will take $$\frac{7}{5}x$$​ days.

​$$\frac{1}{x} + \frac{1}{\frac{7}{5}x} = \frac{1}{60}$$​​

​$$\frac{1}{x} + \frac{5}{7x} = \frac{1}{60}$$​​

​$$\frac{7 + 5}{7x} = \frac{1}{60}$$​​

​$$\frac{12}{7x} = \frac{1}{60}$$​​

7x = 720

x = 102.857

Boy’s time =$$\frac{7}{5}x = \frac{7}{5} \times 102.857$$​ = 144 days