Question

The sales of an article increases by 20% every week. The difference between the sales of the second week and the fourth week is Rs. 660. What were the sales of the article in the third week?

• A. Rs. 1,360
• B. Rs. 1,480
• C. Rs. 1,500
• D. Rs. 1,720
• E. Rs. 1,800

Hint:

Express each week's sales as a multiple of the first week using the 20% growth factor, then use the given difference to find the base value.

Answer 1

Answer: (E)

Let the sales in the first week be \(a\). Since the sales grow by 20% every week, the sales in week \(n\) are \(a(1.2)^{n-1}\).
Sales in week 2 = \(1.2a\), sales in week 4 = \(a(1.2)^3 = 1.728a\).
Given, week 4 sales minus week 2 sales = 660.
\[1.728a - 1.2a = 660 \Rightarrow 0.528a = 660 \Rightarrow a = 1250\]
Sales in week 3 = \(a(1.2)^2 = 1250 \times 1.44 = 1800\).
So the sales in the third week were Rs. 1,800.