Question

Vayu and Antara have their present ages in ratio 3:4. Ratio of their ages after 10 years is 4:7. Find their present ages.​

Answer 1

Answer:

Vayu is 18 years old and Antara is 24 years old.

Step-by-step explanation:

Given :

Present age Ratio of Vayu and Antara = 3 : 4

Ratio of ages after 10 years = 4 : 7

To find :

Their present ages

Solution :

Let the present ages be -

• Vayu = 3y
• Antara = 4y

Ages after 10 years -

• Vayu = (3y + 10)
• Antara = (4y + 10)

$\sf{\longrightarrow} \: \dfrac{3y + 10}{4y + 10 } = \dfrac{4}{7} \\ \\ \sf{\longrightarrow} \: 7(3y + 10) = 4(4y + 10) \\ \\ \sf{\longrightarrow} \: 21y + 70 = 16y + 40 \\ \\ \sf{\longrightarrow} \: 21y - 16y = 70 - 40 \\ \\ \sf{\longrightarrow} \: 5y = 30 \\ \\ \sf{\longrightarrow} \: y = \dfrac{30}{5} \\ \\ \sf{\longrightarrow} \: y = 6$

$\rule{300}{1.5}$

★ Vayu's present age -

$\sf{\longrightarrow} \: 3(6) \\ \\ \sf{\longrightarrow} \: 18$

Vayu is presently 18 years old.

$\rule{300}{1.5}$

★ Antara's present age -

$\sf{\longrightarrow} \: 4(6) \\ \\ \sf{\longrightarrow} \: 24$

Antara is presently 24 years old.

$\therefore$ Vayu is 18 years old and Antara is 24 years old.

Answer 2

Correct question: Vayu and Antara have their present ages in ratio 3 : 4. Ratio of their ages before 10 years was 4 : 7. Find their present ages.

Given:

• ratio of their present ages = 3 : 4
• ratio of their ages before 10 years = 4 : 7

To find: Their present ages = ?

Solution:

• Let their present ages be 3x years and 4x years respectively.
• Before 10 years, their ages were (3x - 10) years and (4x - 10) years respectively.

ATQ, (3x - 10) : (4x - 10) = 4 : 7

or, (3x - 10)/(4x - 10) = 4/7

or, 7 (3x - 10) = 4 (4x - 10)

or, 21x - 70 = 16x - 40

or, 21x - 16x = 70 - 40

or, 5x = 30

or, x = 6

Therefore, x = 6.

Answer:

• Age of Vayu = 3 × 6 years = 18 years
• Age of Antara = 4 × 6 years = 24 years