CAT 2022 Slot 2 · Quant · Question 2

Times in the ratio 5:8:10 mean rates in the inverse ratio \frac{1}{5}:\frac{1}{8}:\frac{1}{10}.

Multiplying through by 40 clears the fractions, giving rates in the ratio 8:5:4.

So take Anu at 8 units an hour, Tanu at 5 and Manu at 4.

All three together produce 8+5+4=17 units an hour.

They would finish in 4 days of 8 hours, that is 4\times 8=32 hours.

So the whole job is 17\times 32=544 units.

Anu and Tanu together produce 8+5=13 units an hour.

Six hours forty minutes is 6\frac{2}{3}=\frac{20}{3} hours, so over 6 days they work 6\times \frac{20}{3}=40 hours.

In that time they complete 13\times 40=520 units.

The remainder is 544-520=24 units.

Manu works at 4 units an hour, so he needs \frac{24}{4}=6 hours.

Shortcut. Scaling the rates to whole numbers by the LCM of 5, 8 and 10 keeps every figure an integer, and the awkward 6 hours 40 minutes becomes a clean \frac{20}{3} that cancels against the 6 days. No fractions survive past that point.