Question

chapater linear equations in one variable word
21Q​

Answer 1

Let the ages of Tanay and Vihaan be -

8x and 7x

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After 6 years Tanay's age = 8x + 6

Vihaan's age = 7x + 6

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Given that the ratio of their ages after 6 years will be 10:9 :-

a/b = 8x+6/7x+6 = 10/9

= 9(8x + 6) = 10(7x + 6)

= 72x + 54x = 70x + 60

= 72x - 70x = 60 - 54

= 2x = 6

= x = 3

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Tanay's age = 8 × 3 = 24 years

Vihaan's age = 7 × 3 = 21 years

Answer 2

Question :-

The ages of Tanay and Vihaan are in the ratio of 8 : 7. Six years later their ages will be in the ratio 10 : 9. Find their ages.

Answer :-

The present age of Tanay is 24 years and present age of Vihaan is 21 years

Solution :-

Ratio of present ages of Tanay and Vihaan = 8 : 7

Consider age of Tanay as 8x and age of Vihaan as 7x

Six years later

• Tanay's age = 8x + 6

• Vihaan's age = 7x + 6

Ratio of ages of Tanay and Vihaan six years later = 10 : 9

According to the question :-

$\bf \dfrac{8x + 6}{7x + 6} = \dfrac{10}{9}$

By cross multiplication :-

⇒ (8x + 6)9 = 10(7x + 6)

⇒ 8x(9) + 6(9) = 10(7x) + 10(6)

⇒ 72x + 54 = 70x + 60

⇒ 72x + 54 - 70x = 60

⇒ 2x + 54 = 60

⇒ 2x = 60 - 54

⇒ 2x = 6

⇒ x = 6/2

⇒ x = 3

Pranay's present age = 8x = 8(3) = 24

Vihaan's present age = 7x = 7(3) = 21

Therefore the present age of Tanay is 24 years and present age of Vihaan is 21 years.

Verification :-

$\sf \dfrac{8x + 6}{7x + 6} = \dfrac{10}{9}$

Substitute their present ages in the above equation

$\sf \dfrac{24 + 6}{21 + 6} = \dfrac{10}{9}$

$\sf \dfrac{30}{27} = \dfrac{10}{9}$

$\sf \dfrac{30 \div 3}{27 \div 3} = \dfrac{10}{9}$

$\sf \dfrac{10}{9} = \dfrac{10}{9}$