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:
\(⇒\) 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:

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

\(⇒ \)g + s = \(\frac{3g}{5}+\frac{3s}{2}\)

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

\(⇒\) \(\frac{9}{5}g=\frac{W}{20}\)

\(⇒\) \(g=\frac{W}{36}\)
Therefore, Gautam takes 36 days to finish the given work.
So, the correct option is (B) : 36.