Question

A company's sales increased by 20% in 2022 compared to 2021 and by 25% in 2023 compared to 2022. If the sales in 2021 were ₹10 lakhs, what were the sales in 2023?

• A. ₹15 lakhs
• B. ₹18 lakhs
• C. ₹20 lakhs
• D. ₹25 lakhs

Hint:

For successive percentage changes, multiply the factors sequentially.

Answer 1

The Correct Option is A

Step 1: Understand the Growth 
The sales increase by 20% from 2021 to 2022, and by 25% from 2022 to 2023. The initial sales in 2021 are ₹10 lakhs. We need to apply these percentage increases sequentially. 

Step 2: Calculate Sales in 2022
 A 20% increase means the 2022 sales are 120% of the 2021 sales: \[ \text{Sales}_{2022} = \text{Sales}_{2021} \times (1 + 0.20) \] Given \(\text{Sales}_{2021} = 10 \, \text{lakhs}\): \[ \text{Sales}_{2022} = 10 \times 1.20 = 12 \, \text{lakhs} \] 

Step 3: Calculate Sales in 2023
A 25% increase from 2022 to 2023 means the 2023 sales are 125% of the 2022 sales: \[ \text{Sales}_{2023} = \text{Sales}_{2022} \times (1 + 0.25) \] \[ \text{Sales}_{2023} = 12 \times 1.25 \] \[ 1.25 = \frac{5}{4}, \quad \text{so} \quad 12 \times \frac{5}{4} = \frac{12 \times 5}{4} = \frac{60}{4} = 15 \] \[ \text{Sales}_{2023} = 15 \, \text{lakhs} \] 

Step 4: Alternative Method (Compound Growth) The total growth factor over the two years is: \[ (1 + 0.20) \times (1 + 0.25) = 1.20 \times 1.25 \] \[ 1.20 \times 1.25 = 1.20 \times \frac{5}{4} = \frac{6}{4} = 1.5 \] \[ \text{Sales}_{2023} = \text{Sales}_{2021} \times 1.5 = 10 \times 1.5 = 15 \, \text{lakhs} \] This confirms the result. 

Step 5: Final Answer The sales in 2023 are: \[ \boxed{15 \, \text{lakhs}} \]