CAT 2023 Set-3 | Quantitative Aptitude | Question: 14

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

Answer 1

Let the amount of work done by Gautam and Suhani be $G$ and $S$ respectively.

it is given that $(G+S)20=1$ meaning when gautam and suhani work together for $20$ Days then they complete $1 unit$ of work. 

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.

This line here is the key, it translates to $0.4G=0.5S$ , Gautam is faster worker here because $G=\frac{5}{4}S$ , it is multiple of Suhani's work whereas $S=\frac{4}{5}G$ means Suhani's work is fraction of Gautam's work. 

$(G+\frac{4}{5}G)20=1$ which will gives us $9*4*G=1$ or $36G=1$ meaning it would take Gautam 36 days to complete $1 unit$ of work.

Hence answer is $\boxed{36}$.

Comments

Nice obeservation @rhl 

That 0.4G = 0.5S

Saves time from solving the linear equation

It can be understood as one compensating the work for the other

Since G is operating only at 60% efficiency , its rest 40% should be getting compensated by the extra 50% done by S.

Nice solution