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 sales of the article in the third week?

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

Hint:

Write each week's sales as a multiple of week 1 using the common ratio 1.2, then use the given difference between week 2 and week 4 to find the actual numbers.

Answer 1

The Correct Option is D

Step 1: Set up the sales as a growing sequence.
Since sales grow by 20% every week, each week's sales is 1.2 times the previous week's. Let the first week's sales be S. Then:
Week 1 = S, Week 2 = 1.2S, Week 3 = \(1.2^2S=1.44S\), Week 4 = \(1.2^3S=1.728S\).

Step 2: Use the given difference to find S.
The difference between week 4 and week 2 sales is Rs. 660: \[ 1.728S - 1.2S = 660 \] \[ 0.528S = 660 \] \[ S = \frac{660}{0.528} = 1250 \]

Step 3: Find week 3 sales.
\[ \text{Week 3 sales} = 1.44 \times 1250 = 1800 \]

Final Answer:
The sales in the third week were Rs. 1,800. \[ \boxed{Rs.\ 1{,}800} \]