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Area Calculation MCQ 1 (Increase and decrease in length and breadth , to find percent change in area)

Area Calculation MCQ 1: The length of a rectangular increased by 10% and it’s breadth is decreased by 10 %. Then the area of the new rectangle is_________?

a) Neither increased nor decreased               b) Increased by 1%           c) Decreased by 1%       d) Decreased by 10%

Solution:

Let the length of the rectangle is = x

Breadth of the rectangle is = y

drawit diagram

We know the are is ​\( = Length \times Breadth \)

i-e

\[ Area = x \times y=xy \]

Now 10% of length ;

\[ = \frac {10}{100}\times x=\frac{x}{10} \]

Since this is the increament in length so,

New length will be ​\( =x+\frac{x}{10}=\frac{11x}{10} \)

Similarly, 10 % of breadth;

\[ = \frac {10}{100}\times y=\frac{y}{10} \]

Since this is the decrease in breadth so,

New breadth will be ​\( = y-\frac{y}{10}=\frac{9y}{10} \)

New area will be = ​\( = New Length \times NewBreadth=\frac{x}{10}\times \frac{9y}{10}=\frac{9xy}{100}=0.09xy \)

Decrease in ​\( Area = Original Area – New Area \)

i-e ​\( Decrease in Area = xy -0.09xy=0.1xy \)

We suppose this decrease is ‘z%’ of original area ;

i-e    0.1xy = z% of xy (original area)

or ​\( 0.1xy= \frac{z}{100}xy \)

or

\[ z= 10% \]

So area decreased by 10 % — option d is correct!

Note: Some sources have reported option c as answer , which is miscalculated and hence, is wrong !

 

 

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