Question

The ratio of Prathibha's age to Aradhana's age is 5:6. After twelve years, the ratio of their ages will be 9:10. Find their present ages.

Answer 1

Given :

• The ratio of Prathibha's age to Aradhana's age is 5:6.

• After twelve years, the ratio of their ages will be 9:10.

To find :

• Their present ages =?

Step-by-step explanation :

Let, the Prathibha's present age be 5x.

Then, the Aradhana's present age be 6x.

After 12 years Prathibha's present age will be, 5x + 12

After 12 years Aradhana's present age will be, 6x + 12

According to the question :

➮ 5x + 12/6x + 12 = 9/10

➮ 10(5x + 12) = 9(6x + 12)

➮ 50x + 120 = 54x + 108

➮ 50x - 54x = 108 - 120

➮ -4x = - 12

➮ x = - 12/-4

➮ x = 3.

Therefore, We got the value of, x = 3.

Hence,

Prathibha's present age, 5x = 5 × 3 = 15 years

Aradhana's present age, 6x = 6 × 3 = 18 years

Answer 2

$\huge\sf\pink{Answer}$

☞ Prathibha's age = 15 years

☞ Aradhana's age = 18 years

$\rule{110}1$

$\huge\sf\blue{Given}$

➢ The Ratio of Pratibha's age to Aradhana's age is 5:6

➢ After 12 years the ratio of their ages will be 9:8

$\rule{110}1$

$\huge\sf\gray{To \:Find}$

✭ Their Present ages?

$\rule{110}1$

$\huge\sf\purple{Steps}$

➳ Let the age of Pratibhan be 5x

➳ Let the age of Aradhana be 6x

So now after 12 years,

➝ Their ages become,

$\qquad$◕ 5x + 12

$\qquad$◕ 6x + 12

Calculating,

$\twoheadrightarrow\sf 5x+\dfrac{12}{6x} + 12 = \dfrac{9}{10}$

$\twoheadrightarrow\sf 10(5x+12) = 9(6x+12)$

$\twoheadrightarrow\sf 50x + 120 = 54x + 108$

$\twoheadrightarrow\sf 50x - 54x = 108 - 120$

$\twoheadrightarrow\sf (-4x) = (-12)$

$\twoheadrightarrow\sf x = \dfrac{-12}{-4}$

$\red{\twoheadrightarrow\sf x = 3}$

So now finding their ages,

$\sf\bullet\orange{Pratibhan's \ age = 15\: years}$

$\sf\bullet\orange{Aradhana's \ age = 18\: years}$

$\rule{170}3$