IPMAT Indore 2022 · Quantitative Ability · Question 5

IPMAT Indore 2022 previous year question on Profit Loss and Discount, with the answer and a step-by-step solution.

Profit Loss and DiscountArithmeticType in the answer (TITA)Medium

Aruna purchases a certain number of apples for INR 20 each and a certain number of mangoes for INR 25 each. If she sells all the apples at 10% profit and all the mangoes at 20% loss, overall she makes neither profit nor loss. Instead, if she sells all the apples at 20% loss and all the mangoes at 10% profit, overall she makes a loss of INR 150. Then the number of apples purchased by Aruna is _________

Answer & solution

Answer: 50

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.

IPMAT Indore 2022 · Quantitative Ability · Question 5

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