18 men or 36 boys working 6 hours a day can plough a field in 24 days. In how many days will 24 men and 24 boys working 9 hours a day plough the same field ?

18 men 6 hrs a day take 24 days

Time taken by 1 man in 1 hour = $$\frac{1}{18} \times \frac{1}{6} \times \frac{1}{24} = \frac{1}{2592}$$

36 boys 6 hours take 24 days

Time taken by 1 boy in 1 hour = $$\frac{1}{18} \times \frac{1}{6} \times \frac{1}{24} = \frac{1}{2592}$$

=> 24 men 9 hours/day will cover = 24 × 9 × 1/2592 = 216/2592 of the field

and 24 boys 9 hours/day will cover = 24 × 9 × 1/5184 = 216/5184 of the field

Thus, the size of field covered in 1 day by the 24 men and the 24 boys

= $$\frac{216}{2592}+\frac{216}{5184}=\frac{(432+216)}{5184}$$

= $$\frac{648}{5184}=\frac{1}{8}$$

=> Ans - (D)