Question

If the length of a rectangle is decreased by 3 units, and its breadth increased by 5 units, then the area of the rectangle is increased by 10 square units. If the length is increased by 3 units, and breadth decreased by 3 units, then the area is decreased by 18 square units. What is the breadth of the rectangle?

• A. 8 units
• B. 5 units
• C. 3 units
• D. 6 units

Answer 1

The correct option is B 5 units

Let the length and the breadth of the rectangle be $l$ and $b$ respectively. Area of the rectangle = $lb$ square units
By question, $(l-3)(b+5)=lb+10$ and $(l+3)(b-3)=lb-18$
On simplification, $lb+5l-3b-15=lb+10$ and $lb-3l+3b-9=lb-18$
$⟹5l-3b=25...\left(1\right)$
$3l-3b=9...\left(2\right)$
(1)-(2)$⟹2l=16⟹l=8units$
Substituting this value of $l$ in (2), we have $3\left(8\right)-3b=9⟹b=5units$