d The length of a rectangular increased by 10% - mcqs test

# 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%

mcqs test

Solution:

Let the length of the rectangle is = x

Breadth of the rectangle is = y

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 !