cat 2023 Question 16

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

Accepted Answer

Let 'g' and 's' be the efficiencies of Gautam and Suhani. Let W is the total amount of work.

=> g + s = W/20 (1 day work) ----(1)

Also Gautam doing only 60% => 3g/5 and Suhani doing 150% => 3s/2

=> 3g/5 + 3s/2 = W/20 (1 day work)

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

=> $\frac{s}{g}$ = $\frac{4}{5}$ => Gautam is the more efficient person.

Now, from the 1st equation

=> g + $\frac{4g}{5}$ = $\frac{W}{20}$

=> $\frac95$g = $\frac{W}{20}$

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

=> Gautam takes 36 days to finish the complete work.

Question 16.

Question Explanation