Question

Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

• A. 30
• B. 36
• C. 70
• D. None of Above

Answer 1

The Correct Option is B

Let's assume W be the total amount of work.
And g and s be the efficiencies of Gautam and Suhani respectively. 
According to the question:
$ \Rightarrow\ g + s = \frac{W}{20} $ (1 day work) ……. (i)

And given that Gautam is doing only 60%: $ \frac{3g}{5} $
Suhani is doing 150%: $ \frac{3s}{2} $
Now, using this, we get:

$ \Rightarrow\ \frac{3g}{5} + \frac{3s}{2} = \frac{W}{20} $ (1 day work)

$ \Rightarrow\ g + s = \frac{3g}{5} + \frac{3s}{2} $

$ \Rightarrow\ \frac{s}{g} = \frac{4}{5} $

This implies that Gautam is more efficient.
By using equation (i), we get:
$ \Rightarrow\ g + \frac{4g}{5} = \frac{W}{20} $

$ \Rightarrow\ \frac{9}{5}g = \frac{W}{20} $

$ \Rightarrow\ g = \frac{W}{36} $

Therefore, Gautam takes 36 days to finish the given work.
So, the correct option is (B) : 36.