Question

Question ?


The ages of Rahul and Haroon are in the ratio 5:7. Four years later the sum of their ages will be 56 years. What are their present ages?




​

Answer 1

Answer:

The age of Rahul and Haroon are in the ratio 5:7. Four years later the sum of ages will be 56 years. What are their present ages?

add

The given question can be simplified using the linear equations in one variable and the concept of ratios.

Answer: The present ages of Rahul and Haroon are 20 years and 28 years respectively.

Let's try to rewrite the given information mathematically using linear equations.

Explanation:

Let the age of Rahul be 5x and the age of Haroon be 7x, given that their ages are in the 5:7 ratio.

4 years later: the age of Rahul will be (5x + 4) and age of Haroon will be (7x + 4).

Present age After 4 years

Rahul 5x (5x + 4)

Haroon 7x (7x + 4)

The sum of their ages after 4 years will be 56 years.

⇒ (5x+4) + (7x+4) = 56

⇒ 5x + 7x + 4 + 4 = 56

⇒ 12x + 8 = 56

⇒ 12x = 56 - 8

⇒ 12x = 48

⇒ x = 48/12 = 4

⇒ age of Rahul = 5x = 5(4) = 20 years

⇒ age of Haroon = 7x = 7(4) = 28 years

Thus, the present ages of Rahul and Haroon are 20 years and 28 years respectively.

Answer 2

$❒\: \: \sf\bold{\red{Given\: :-}}$

➯ The ages of Rahul and Haroon are in the ratio 5:7

➯ Four years later the sum of their ages will be 56 years.

$❒\: \: \sf\bold{\red{To \: find\: :-}}$

➯ What are their present ages?

$❒\: \: \sf\bold{\red{ Let's \: start:-}}$

✏ Let the age of Rahul be 5x

Let the age of Haroon be 7x

Given in the Question :-

➳ ( Four years later the sum of Rahul ) + ( Four years later the sum of Haroon ) = 56

➳ ( 5x + 4 ) + ( 7x + 4 ) = 56

➳ 5x + 4 + 7x + 4 = 56

➳ 12x + 8= 56

➳ 12x = 56 - 8

➳ 12x = 48

$➳ \: \sf \: x = \frac{48}{12}$

➳ x = 4

So we can say ,

The present age of Rahul = 5x

➳ = 5× 4

➳ = 20

The present age of Haroon = 7x

➳ = 7 × 4

➳ = 28

Answer :-

• The present age of Rahul = 20

• The present age of Haroon = 28

Verify :-

➳ ( Four years later the sum of Rahul ) + ( Four years later the sum of Haroon ) = 56

➳ ( 4 + 20 ) + ( 4 + 28 ) = 56

➳ 4 + 20 + 4 + 28 = 56

➳ 24 + 32 = 56

➳ 56 = 56

Hence verified