Question

six years ago the ratio of Ages of Karan and Arjun was 6:5,
4 years from now the ratio of their ages will be 11:10 .

find their present ages
​

Answer 1

Answer:-

Let the present age of Karan be x years and Arjun be y years.

Given:-

Six years ago, the ratio of their ages was 6 : 5.

• Karan's age before 6 years = (x - 6) years.

• Arjun's age before 6 years = (y - 6) years.

So,

⟹ (x - 6) / (y - 6) = 6/5

⟹ 5(x - 6) = 6(y - 6)

⟹ 5x - 30 = 6y - 36

⟹ 5x - 6y = - 36 + 30

⟹ 5x - 6y = - 6 -- equation (1)

Also given that,

After 4 years, the ratio of their ages will be 11 : 10.

So,

According to the above condition;

⟹ (x + 4) / (y + 4) = 11/10

⟹ 10(x + 4) = 11(y + 4)

⟹ 10x + 40 = 11y + 44

⟹ 10x - 11y = 44 - 40

⟹ 10x - 11y = 4 -- equation (2)

Now,

Multiply equation (1) by 2 and subtract equation (1) from equation (2).

⟹ 10x - 11y - 2(5x - 6y) = 4 - 2(- 6)

⟹ 10x - 11y - 10x + 12y = 4 + 12

⟹ y = 16

Substitute y = 16 in equation (1).

⟹ 5x - 6(16) = - 6

⟹ 5x - 96 = - 6

⟹ 5x = - 6 + 96

⟹ 5x = 90

⟹ x = 90/5

⟹ x = 18

∴

• Present age of Karan = x = 18 years.
• Present age of Arjun = y = 16 years.

Answer 2

Answer:

Given :-

• Six years ago, the ratio of ages of Karan and Arjun was 6 : 5.
• Four years from now the ratio of their ages will be 11 : 10.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \sf Present\: age\: of\: Karan =\: 6x\: years$

$\mapsto \sf Present\: age\: of\: Arjun =\: 5x\: years$

Hence,

$\leadsto \bf{Present\: age\: of\: Karan =\: (6x + 6)\: years}$

$\leadsto \bf{Present\: age\: of\: Arjun =\: (5x + 6)\: years}$

$\pink{\bigstar}\: \: \bf{According\: to\: the\: question\: :-}$

$\implies \sf \dfrac{(6x + 6) + 4}{(5x + 6) + 4} =\: \dfrac{11}{10}$

$\implies \sf \dfrac{6x + 10}{5x + 10} =\: \dfrac{11}{10}$

$\small\pink{\bigstar}\: \: \bf{By\: doing\: cross\: multiplication\: we\: get\: :-}$

$\implies \sf 10(6x + 10) =\: 11(5x + 10)$

$\implies \sf 60x + 100 =\: 55x + 110$

$\implies \sf 60x - 55x =\: 110 - 100$

$\implies \sf 5x =\: 10$

$\implies \sf x =\: \dfrac{\cancel{10}}{\cancel{5}}$

$\implies \sf\bold{\purple{ x =\: 2\: years}}$

Hence, the required present age of Karan and Arjun are :

❒ Present age of Karan :

$\longrightarrow \sf Present\: Age_{(Karan)} =\: (6x + 6)\: years$

$\longrightarrow \sf Present\: Age_{(Karan)} =\: \{6(2) + 6\}\: years$

$\longrightarrow \sf Present\: Age_{(Karan)} =\: (12 + 6)\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Karan)} =\: 18\: years}}$

❒ Present age of Arjun :

$\longrightarrow \sf Present\: Age_{(Arjun)} =\: (5x + 6)\: years$

$\longrightarrow \sf Present\: Age_{(Arjun)} =\: \{5(2) + 6\}\: years$

$\longrightarrow \sf Present\: Age_{(Arjun)} =\: (10 + 6)\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Arjun)} =\: 16\: years}}$

$\therefore$ The present age of Karan and Arjun is 18 years and 16 years respectively.