Question

The area of a rectangular plot is increased by
30% and its width remain as it was before. What
will be the ratio between the area of new
rectangle and the original rectangle?
1. 13:10
2: 10:13
3. 7:3
4. 3:7​

Answer 1

Answer:

1. 13 : 10 is the required answer.

Step-by-step explanation:

Given that:

• The area of a rectangular plot is increased by 30% and its width remain as it was before.

To Find:

• What will be the ratio between the area of new rectangle and the original rectangle?

Let us assume:

• Area of original rectangle be x cm².

Finding the ratio between the area of new rectangle and the original rectangle:

Area of new rectangle : Area of original rectangle

⟶ (100 + 30)% of x : x

⟶ 130% of x : x

⟶ 1.3 of x : x

⟶ 1.3x : x

Cancelling x.

⟶ 1.3 : 1

Multiplying by 10.

⟶ (1.3 × 10) : (1 × 10)

⟶ 13 : 10

∴ The ratio between the area of new rectangle and the original rectangle = 13 : 10

Answer 2

Given :-

Area of rectangular plot increased by 30%

To find :-

Ratio between new and original rectangle

Solution :-

Let the

Original rectangle's area = y

New rectangle area

(100 + increased percentage) of original rectangle

$\sf \bigg(100 + 30\bigg) \times y$

$\sf \dfrac{100 + 30}{100} \times y$

$\sf \dfrac{130}{100}\times y$

$\sf \dfrac{13}{10}y$

Finding ratio

$\sf \dfrac{13}{10}y = y$

$\sf 13y = 10\times y$

$\sf 13y = 10y$

$\sf 13 =10$

Ratio = 13:10 [Option A]