Problem Solving

What is the % change in the area of a rectangle when its length increases by 10% and its width decrease by 10%?

A. 0%
B. 20% increase
C. 20% decrease
D. 1% decrease
E. Insufficient data

The OA is D.

If you don't know the formula to calculate the change directly, you can try as follows,

First "rectangle" can be 10x10, so its area is 100 m^2.

Now, increase its length by 10% and decrease its width by 10%, so 11x9 its area is 99 m^2

100 - 99 = 1m^2.

1m^2 is a 1% change from a 100m^2 rectangle. Hence the correct answer is D.

Has anyone another strategic approach to solve this PS question? Regards!

Let length be l and breadth be b... then area = l*b
New length and breadth will be 1.1l and 0.9b
=> area = 0.99lb
% change= lb-0.99lb/lb*100=1%