Question

If the length of a rectangular plot are increased by $50\% $ and $20\% $ respectively, then the new area is how many times the original area
A. $\dfrac{5}{9}$
B. $10$
C. $\dfrac{9}{5}$
D. None of these

Answer 1

Hint- Here we will proceed by using the formula for rectangle that is $length \times breadth$. Then by applying the conditions given in the question, we will get our desired answer.

Complete step by step answer:

Let the original length be $l$
And
Original breadth be $b$
Original area = $l \times b$
Length increased by $50\% $ =$\dfrac{{150l}}{{100}}$
Breadth increased by $20\% = \dfrac{{120b}}{{100}}$
Increase area = $\dfrac{{150l \times 120b}}{{100 \times 100}}$
=$\dfrac{{18000lb}}{{10000}}$
$ = 1.8lb$
Now,
$\dfrac{{1.8lb}}{{lb}} = 1.8$
Changing 1.8 into fraction
$1.8 = \dfrac{{18}}{{10}} = \dfrac{9}{5}$
So,
The increased area will be $\dfrac{9}{5}$ times of the original area.

Hence, the correct option $\left( C \right)$.

Note- Whenever we come up with this type of problem, one must know the formula for the area of the rectangle. By using these basic approaches one can easily solve these types of questions.