Question

The present ages of Aand B are in the ratio 7:5. Ten years later, their ages will be in the ratio9:7 .Find their present ages ​

Answer 1

Answer:

A is 35 years old and B is 25 years old.

Step-by-step explanation:

Given :

Present age = 7 : 5

Ten years later = 9 : 7

To find :

Their present ages

Solution :

Let the present ages be -

• A as 7y
• B as 5y

Ages after 10 years -

• A = (7y + 10)
• B = (5y + 10)

★ $\sf{\dfrac{7y + 10}{5y + 10} = \dfrac{9}{7}}$

⇒ 7(7y + 10) = 9(5y + 10)

⇒ 49y + 70 = 45y + 90

⇒ 49y - 45y = 90 - 70

⇒ 4y = 20

⇒ y = 5

$\rule{300}{1.5}$

★ A's present age -

⇒ 7(5)

⇒ 35

A is 35 years old.

$\rule{300}{1.5}$

★ B's present age -

⇒ 5(5)

⇒ 25

B is 25 years old.

Therefore, A is 35 years old and B is 25 years old.

Answer 2

Answer:

the present ages of A and B are 35 and 25 respectively.

Step-by-step explanation:

Let the present ages of A and B be x and y respectively.

Condition- 1

    x/y = 7/5

or, 5x = 7y (cross multiplication)

or, x = 7y/5 ----- eqn i

Condition- 2

    (x+10)/(y+10) = 9/7

or, 7x+70 = 9y+90 ( same reason)

putting the value of x,

or, 7(7y/5) + 70 = 9y +90

or, 49y + 350 = 45y +450 (Calculation)

or, 4y = 100 (same as above)

therefore, y = 25

Again, Substituting the value of y in eqn i,

x = (7 * 25)/5

therefore, x = 35