Question

A company's profit increased by 20% in 2022 compared to 2021. If the profit in 2021 was ₹15 lakh, and expenses increased by ₹2 lakh in 2022 while income increased by ₹5 lakh, what was the profit in 2022?

• A. ₹18 lakh
• B. ₹16 lakh
• C. ₹17 lakh
• D. ₹20 lakh

Hint:

• Profit = Income - Expenses.
• Change in Profit = Change in Income - Change in Expenses.
• The problem provides two ways to calculate the 2022 profit; check for consistency.
• A 20% increase on ₹15 lakh profit means the new profit is $15 \times 1.20 = 18$ lakh.
• Alternatively, if $P_{new} = I_{new} - E_{new}$ and $P_{old} = I_{old} - E_{old}$, then $P_{new} - P_{old} = (I_{new}-I_{old}) - (E_{new}-E_{old})$. Change in Profit = (Increase in Income) - (Increase in Expenses) = $5 - 2 = 3$ lakh. So $P_{2022} = P_{2021} + 3 = 15 + 3 = 18$ lakh.

Answer 1

The Correct Option is A

Let:

• $P_{2021}$ = 2021 Profit = ₹15 lakh
• $P_{2022}$ = 2022 Profit

Given:

• 2022 Profit increased by 20% from 2021: \[ P_{2022} = 1.20 \times P_{2021} = 1.20 \times 15 = ₹18 \text{ lakh} \]
• 2022 Expenses were ₹2 lakh higher than 2021: $E_{2022} = E_{2021} + 2$
• 2022 Income was ₹5 lakh higher than 2021: $I_{2022} = I_{2021} + 5$

Consistency Check:\[P_{2022} = I_{2022} - E_{2022} = (I_{2021} + 5) - (E_{2021} + 2) = (I_{2021} - E_{2021}) + 3 = P_{2021} + 3 = 15 + 3 = ₹18 \text{ lakh}\]Conclusion: The provided data is consistent. The profit in 2022 is:\[\boxed{₹18 \text{ lakh}}\]