If the length and width of a rectangular garden plot were each

Question

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

Bunuel · Accepted Answer

SOLUTION

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

Original area = LW;
New area = (1.2L)(1.2W) = 1.44LW.

The percent increase = 44%.

Answer: E.

nutshell · Answer

The quickest way to do this is to pick numbers: l = 10 & w = 10;
 Note:  Both l & w can be same as a square is also a rectangle.

Original area = lw =10 * 10 = 100;

Since l & w are increased by 20% each, l & w = 12;
New area = lw = 12 * 12 = 144;

% increase in area = 144 - 100 = 44%.

Ans is (E).

b2bt · Answer

Diffculty - Sub600

My method might seem long but once you get a hang of it, it seems easier.

Whenever we are asked to "increase" any quantity by some precentage value. Add that value with 100 and then perform the operations.

As in this case the sides are increased by 20%
By adding 20 to 100 we will get 120%
Both the sides are increased by 20% , therefore we have l=120% and b=120%

We have to find the area, formula for the area is l*b = 120%*120% = 14400 = 14400/100 = 144%

Remove the original 100 back to get 44%

Remember when we say 120 percent length, it means 100% of original length + 20% is the increament

You can use it with decimal too.
suppose l = x and b = y
Area = xy
New l2 = 1.2x (Why 1.2? becasuse original was 1x and it increased by 20% which is 0.2)
b2 = 1.2y
Area = 1.2x *1.2y = 1.44 xy

ScottTargetTestPrep · Answer

We can let the original area = lw, and thus the increased area is 1.2(l) x 1.2w = 1.44lw.
 
Thus, the percentage increase is:
 
(1.44lw - lw)/lw x 100
 
0.44lw/lw x 100 = 44%.
 
Answer: E

susheelh · Answer

This is also be solved by using the successive percentage increase approach. Here's why - Lets say the original area is  a . When length and breath are increased by 20% it means we are successively increasing  a  by 20%.

If any number is successively increased by a% and then b%, the effective percentage increase is given by  a + b + \frac{ab}{100}

In our case this becomes  20 + 20 + \frac{20*20}{100} = 40 +4 = 44 %

Answer choice E

pushpitkc · Answer

Let the length of the rectangular plot be x and the width be y.
The area of this plot is xy.

If the length and breadth of the rectangular plot were to increase by 20% each, 
the length and width will be 1.2x and 1.2y. Therefore, the area will be 1.44xy

Hence, the area increase by 44%(Option E)

Adityagmatclub · Answer

easy way to solve above is to consider length equals 100, Breadth equals 100.
Increased by 20%.. length equals 120 breadth equals 120
 Area difference = 4400
percentage is 44 
answer 44 percent

Abhishek009 · Answer

0
 20+20+\frac{20*20}{100}

=  44 %

Answer must be (E)

JeffTargetTestPrep · Answer

If we let L = the original length and W = the original width, then the original area of the rectangle is LW.

The new area is 1.2L x 1.2W = 1.44LW.

Thus, we see that there is a 44% increase in the area.

Alternate Solution:

We can let the original length = 10 and the original width = 10. We see that the increased length will be 12 and the increased width will be 12.

The original area is length x width = 10 x 10 = 100. The new area is 12 x 12 = 144.

We find the percentage increase in the area by using the formula (new – old)/old x 100, and we obtain:
(144 – 100)/100 x 100 = 44/100 x 100 = 44%.

Answer: E

ArnauG · Answer

To find the percent increase in the area of a rectangular garden plot when both the length and width are increased by 20 percent, we can use the following steps:

Let's assume the original length of the garden plot is L and the original width is W. The original area of the plot is given by A = L * W.

When the length and width are increased by 20 percent, the new length becomes 1.2L (20 percent more than L) and the new width becomes 1.2W (20 percent more than W).

The new area of the plot is given by A' = (1.2L) * (1.2W) = 1.44LW.

The percent increase in the area is calculated as ((A' - A) / A) * 100.

Substituting the values, we have ((1.44LW - LW) / LW) * 100 = (0.44LW / LW) * 100 = 44 percent.

Therefore, the percent increase in the area of the plot is 44 percent, corresponding to option (E).

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