The sales of an item increases by 20% every week. If the difference between the sales of the fourth week and the second is 157, what are the sales in the third week?
Answers
Let the sales of the first week be x.
Since the sales of an item increases by 20% each week, therefore, the sales of the second week will be: x + 0.2x
The sales of the third week will be: x + 0.4x
Finally, the sales of the fourth week will be: x + 0.6x
It is given that the difference between the sales of the fourth week and the second is 157.
Therefore, x + 0.6x - (x + 0.2x) = 157
0.4x = 157
Therefore, x = 392.5
Which means that the third week sales = x + 0.4x = 392.5 + 0.4(392.5) = 549.5
Define x:
First week sales = x
Find the second week sales:
Increase = 20% of x = 0.2x
Sales = x + 0.2x = 1.2x
Find the third week sales:
Increase = 20% of 1.2x = 0.24x
Sales = 1.2x + 0.24x = 1.44x
Find the fourth week sales:
Increase = 20% of 1.44x = 0.22x
Sales = 1.44 + 0.288 = 1.728x
Find the difference in sales of the second week and fourth week.
Difference = 1.728x - 1.2 = 0.528x
Solve x:
Difference in the sales of second and fourth week is 157
1.728x - 1.2x = 157
0.528x = 157
x = 157 ÷ 0.528 = 296.35
Find the sales for third week:
Sales = 1.44x = 1.44 (296.35) = Rs 428.18
Answer: Rs 428.18