Question

The present Age of Prince and Saleem are in the ratio 5:7 . four years later the sum of their ages will be 3:4 . Find their present age

Answer 1

Answer:

Step-by-step explanation:

Given :-

The present Age of Prince and Saleem are in the ratio 5 : 7.

Four years later the sum of their ages will be 3 : 4 .

To Find :-

Their present age.

Solution :-

Let the Prince's present age be 5x years

And the Saleem's present age be 7x years

After 4 years

Prince's age 4 yrs later = (5x + 4) years

Saleem's age 4 yrs later = (7x + 4) years

Sum of their ages = (5x + 4 + 7x + 4) = (12x + 8) years

According to the Question,

⇒ (12x)/(12x + 8) = 3/4

By Cross Multiplication, we get

⇒ 12x × 4 = 3 × (12x + 8)

⇒ 48x = 36x + 24

⇒ 48x - 36x = 24

⇒ 12x = 24

⇒ x = 24/12

⇒ x = 2

Prince's present age = 5x = 5 × 2 = 10 years

Saleem's present age = 7x years = 7 × 2 = 14 years.

Hence, the present ages of Prince and Saleem are 10 years and 14 years.

Answer 2

$\large \underline{ \underline{ \sf \: Solution : \: \: \: }}$

Let ,

The Prince's present age = 5x years

The Saleem's present age = 7x years

Then ,

The sum of present ages of Prince and Saleem = (5x + 7x) years

= 12x

4 years later ,

Prince's age = ( 5x + 4 ) years

Saleem's age = ( 7x + 4 ) years

Then,

The sum of Prince's and Saleem's ages after 4 years

= ( 5x + 4 + 7x + 4 )

= ( 12x + 8 )

Now ,

According to the question ,

The ratio of the sum of their presents ages and the sum of their ages 4 years later is 3 : 4

$\to \sf (12x): (12x+8) = 3:4 \\ \\ \to \sf</p><p> \frac{(12x)}{(12x+8)} = \frac{3}{4} \\ \\ \to \sf</p><p></p><p> 12x \times 4 = 3 \times (12x+8) \\ \\ \to \sf</p><p></p><p>48x = 36x + 24 \\ \\ </p><p>\to \sf</p><p>48x - 36x = 24 \\ \\ \to \sf</p><p> 12x = 24</p><p> \\ \\ \to \sf</p><p> x = \frac{24}{12} </p><p> \\ \\ \to \sf</p><p>x = 2</p><p>$

Thus,

Prince's present age = 5x years

= 5 × 2

= 10 years

And,

Saleem's present age = 7x years

= 7 × 2 years

= 14 years

$\therefore$The present ages of Prince and Saleem are 10 years and 14 years