SSC GD 2024 PYQ — Question 54

The correct answer is option 3 i.e. 32.5 days.

X can complete the work in 20 days, so X's rate of work is:

⇒ 1/ 20  of the work per day

Y can complete the work in 50 days, so Y's rate of work is:

⇒ 1 /50  of the work per day

Together, they complete:

⇒ $\frac{1}{20} + \frac{1}{50} = \frac{5}{100} + \frac{2}{100} = \frac{7}{100}$  of the work per day.

 In 5 days, they will complete:

⇒  5 × (7) / (100) = (35) / ( 100) = (7) / (20)  of the work.

Remaining work after 5 days:

⇒   1 - ( 7) / (20)  = (13) / (20)     of the work.

Time for Y to finish the remaining work:

  ⇒ $\frac{\frac{13}{20}}{\frac{1}{50}} = \frac{13}{20} \times 50 = \frac{650}{20} = 32.5$days