Question

The ages of A and B are in the ratio 9:4. Seven years hence the ratio of their ages will be 5:3. Find their present age's.

Answer 1

Let A's age is 9x

Let B's age is 4x

Seven years later --

A's age = 9x + 7

B's age = 4x + 7

According to the given question

$\frac{9x + 7}{4x + 7} = \frac{5}{3}$

cross multiplication --

3(9x + 7) = 5(4x + 7)

27x + 21 = 20x + 35

27x - 20x = 35 - 21

7x = 14

x = 14/7 = 2

X = 2

A's age = 9(2) = 18 years

B's age = 4(2) = 8 years.

$\bold{Answer \: =}$

$\bold{A's \: Age \: is \: 18years \: and \: B's \: Age \: is \: 8years}$

Answer 2

$\huge\bf{Answer:-}$

Let 9y and 4y be the ages.

So,

$= ( \frac{9y + 7}{45 + 7} = \frac{5}{3} )$

$= 3(9y+7) = 5(4y+7) \\ </p><p> = (27y+21) = (20y+35) \\ </p><p> = (27y-20y) = (35-21) \\ </p><p> = (7y = 14) \\ </p><p> = (y= \frac{14}{7} \\ = (y = 2)$

• 9x = 9 =2 = 18 is A age.
• 4x = 4 =2 = 8 is B age.

Therefore, 18 years = A and 8 years = B.