Problem Solving

[GMAT math practice question]

The length and width of a certain rectangle are in the ratio 4 to 5. The area of the rectangle is 2,000 square units. If the length and width of the rectangle are both increased by 10 units, what is the increase in the area of the rectangle?

A. 800
B. 900
C. 1,000
D. 1,100
E. 1,250

[GMAT math practice question]

The length and width of a certain rectangle are in the ratio 4 to 5. The area of the rectangle is 2,000 square units. If the length and width of the rectangle are both increased by 10 units, what is the increase in the area of the rectangle?

A. 800
B. 900
C. 1,000
D. 1,100
E. 1,250

Hi Max@Math Revolution,
Let's take a look at your question.

Since, the length and width of a certain rectangle are in the ratio 4 to 5, therefore,
Length = 5x
Width = 4x
Area = 2000 sq units

$$Area\ =\ Length\ \times\ Width$$
$$2000\ =\ \left(5x\right)\left(4x\right)$$
$$2000\ =\ 20x^2$$
$$x^2=\frac{2000}{20}=100$$
$$x=10$$

Now we can find the length and width of the rectangle:
$$Length=5x=5\left(10\right)=50$$
$$Width=4x=4\left(10\right)=40$$

If the length and width of the rectangle are both increased by 10 units, then area will be:
$$Area=\left(50+10\right)\left(40+10\right)=\left(60\right)\left(50\right)=3000$$
$$Increase\ in\ area\ =\ 3,000-2,000=1,000$$

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.

=>
Suppose the length is L = 4k and the width is W = 5k for some k. Then
L*W = 4k*5k = 20k^2 = 2,000.
k^2 = 100 and k = 10.
Thus, L = 4k = 40 and W = 5k = 50.
The area of the rectangle after increasing both the length and the width is (L+10)(W+10) = (40 + 10)(50 + 10) = 50*60 = 3,000 square units.
Thus, the increase in the area is 3,000 - 2,000 = 1,000 square units.

Therefore, the answer is C.

Answer : C