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

Answer: (B)

36

Answer 2

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.