CAT 2025 Slot 3 · Quant · Question 10

Team A does \frac{1}{40} of the job per hour across 5 members, so one member of A does \frac{1}{200} per hour.

Team B does \frac{1}{50} per hour across 8 members, so one member of B does \frac{1}{400} per hour.

Team C does \frac{1}{4} per hour across 10 members, so one member of C does \frac{1}{40} per hour.

Measuring everything in four-hundredths, one member of A is 2 units, one of B is 1 unit and one of C is 10 units, where a unit is \frac{1}{400} of the job per hour.

The starting group of 2 from A, 3 from B and 1 from C works at 2\times 2+3\times 1+10=17 units per hour.

In 23 hours they complete 23\times 17=391 units, out of the 400 units that make up the job.

That leaves 9 units, to be done in one hour by the remaining 2 from A and 3 from B plus n extra members of B.

Their combined rate is 4+3+n=7+n units per hour, so 7+n=9 and n=2.

Shortcut. Scale so that one member of B is exactly 1 unit. Then A's member is 2 and C's is 10, the job is 400 units, and every step is whole-number arithmetic with no fractions at all.