CAT 2024 Slot 2 · Quant · Question 10

Split the 40 employees into three blocks: the first 10, the middle 20 and the last 10, with total bonuses A, B and C.

The first 30 employees are the first two blocks, so A+B=30\times 40000=1200000.

The last 30 employees are the last two blocks, so B+C=30\times 60000=1800000.

The first 10 and last 10 together give A+C=20\times 50000=1000000.

Adding all three equations, 2\left( A+B+C \right)=4000000, so A+B+C=2000000.

Subtracting each equation in turn, C=2000000-1200000=800000, A=2000000-1800000=200000 and B=2000000-1000000=1000000.

In 2023 the first block doubles to 2A=400000, the last block triples to 3C=2400000, and the middle block stays at B=1000000.

The new total is 400000+1000000+2400000=3800000.

The average is \frac{3800000}{40}=95000, that is ₹95000, the second option.

Shortcut. Only the totals of the three blocks matter, and the three given conditions pin them down exactly. Adding them gives the grand total in one step, after which each block is a single subtraction. An increase of 100% means multiply by 2, and 200% means multiply by 3 — not by 1 and 2.