CAT 2023 Slot 3 · Quant · Question 16

Let Gautam's and Suhani's usual daily outputs be g and s.

On a normal day they together produce g+s.

On the altered day Gautam produces 0.6g and Suhani produces 1.5s, and the total is the same.

So 0.6g+1.5s=g+s.

Collecting terms, 0.5s=0.4g.

Therefore s=0.8g, so Gautam is the faster worker.

Together they finish in 20 days, so g+s=\frac{1}{20}.

Substituting, g+0.8g=1.8g=\frac{1}{20}.

So g=\frac{1}{36}, meaning Gautam alone would take 36 days.

For completeness, s=\frac{0.8}{36}=\frac{1}{45}, so Suhani alone would take 45 days — confirming Gautam is the faster.

Shortcut. The shortfall and the make-up must balance: Gautam loses 0.4g and Suhani adds 0.5s, so 0.4g=0.5s and the ratio g:s=5:4 falls out directly. Then the faster worker's share of the combined rate is \frac{5}{9}, so he takes 20\times \frac{9}{5}=36 days.