Question

16. The ratio of ages of two persons is 7:11. Seven years hence, the ratio of their ages will be 2:3. Find their present ages.

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Answer 1

S O L U T I O N :

Given :

The ratio of ages of two persons is 7:11. Seven years hence, the ratio of their ages will be 2:3.

Explanation :

Let the present age of one person be 7x years & let the other person be 11x years

A/q

5 years later :

The age of one person will = (7x + 5) years

The age of one person will = (11x + 5) years

Now,

➛ (7x + 5) : (11x + 5) = 2:3

➛ 7x + 5/11x + 5 = 2/3

➛ 3(7x + 5) = 2(11x + 5)

➛ 21x + 15 = 22x + 10

➛ 21x - 22x = 10 - 15

➛ - x = - 5

➛ x = 5 years

Thus,

The present age of one person will be = 7x years = (7×5) = 35 years .

The present age of other person will be = 11x years = (11×5) = 55 years .

Answer 2

Answer:

Given :-

• Ratio of present age of two person = 7:11
• After seven their ratio = 2:3

To Find :-

Present age

Solution :-

Let the ages be x

Their present age

$\sf \dfrac{7x}{11x}$

After 5 years

$\sf \: \dfrac{7x + 5}{11x + 5} = \dfrac{2}{3}$

By cross multiplication

$\sf \: 3(7x + 5) = 2(11x + 5)$

$\sf \: 21x + 15 = 22x + 10$

$\sf \: 21x - 22x = 10 - 15$

$\sf \: - x = -5$

Hence

Present age

Of first person = 7(5) = 35

and Second person 11(5) = 55 years