IPMAT Indore 2022 · Quantitative Ability · Question 5

Step 1 — set up. Let a be the number of apples and m the number of mangoes. Then

\text{cost of apples}=20a, \text{cost of mangoes}=25m

Step 2 — first scenario (no net profit or loss). Profit on apples equals loss on mangoes:

0.10\left( 20a \right)=0.20\left( 25m \right) \Rightarrow 2a=5m

Step 3 — second scenario (net loss of 150). Loss on apples exceeds profit on mangoes by 150:

0.20\left( 20a \right)-0.10\left( 25m \right)=150 \Rightarrow 4a-2.5m=150

Step 4 — solve. From (1), m=\frac{2a}{5}. Substituting into (2):

4a-2.5\left( \frac{2a}{5}\right)=4a-a=3a=150 \Rightarrow a=50

and m=20.

Check: costs are 20\left( 50 \right)=1000 and 25\left( 20 \right)=500. Scenario 1: +100 on apples, -100 on mangoes — net zero ✔ Scenario 2: -200 on apples, +50 on mangoes — net -150 ✔

Answer: 50 apples

Shortcut. Work with the two cost totals, not the counts. Let A=20a and M=25m be the money spent on each. The conditions become

0.1A=0.2M \Rightarrow A=2M, 0.2A-0.1M=150

Substituting: 0.4M-0.1M=0.3M=150\Rightarrow M=500, so A=1000 and the apple count is 1000/20=50.

This re-framing is the real shortcut — percentages act on amounts of money, so putting the money (not the fruit) at the centre removes the unit prices from the algebra until the very last division.