Question

the ages of A and B are in the ratio 3:5 . Eight years hence , their ahes will be in the ratio 5:7. Find their present ages ​

Answer 1

Given :

• Ratio of age of A and B = 3:5
• Eight years hence, Ratio of age of A and B =5:7

To find :

Present age of A & B

Solution :

Part 1) Present

Let ,

Present age of A = x years

Present age of B = y years

$\sf \implies \: A \: : \: B \: = \: 3 \: : \: 5 \\\\\sf \implies \: \dfrac{x }{y} \: = \: \dfrac{3}{5}\\\\\sf \implies \: x = \dfrac{3}{5} y \: \: \: \: ..........equation \: 1$

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Part 2) 8 year later

Age of A = x+8

Age of B = y+8

$\sf \implies \: (x+8) \: : \: (y+8) \:=\: 5\::\:7\\\\ \sf \implies \: \dfrac{x+8}{y+8}\:=\: \dfrac{5}{7} \\\\ \: \sf \implies \: 7(x + 8) \: = \: 5(y + 8) \\ \\ \sf \implies \: 7x \: + \: 56 \: = \: 5y \: + \: 40 \\ \\ \sf \implies \:7x - 5y = 40 - 56 \\ \\ \sf \implies \:7x - 5y = - 16 \\ \sf \: put \: value \: of \: x \: from \: equation \: 1 \\ \sf \implies \: 7( \dfrac{3y}{5} ) - 5y = - 16 \\ \\ \sf \implies \: \dfrac{21y}{5} - 5y = - 16 \\ \\ \sf \implies \: \: \dfrac{(21y \times 1) - (5y \times 5)}{5} = - 16 \\ \\ \sf \implies \: \dfrac{ 21y - 25y}{5} = - 16 \\ \\ \sf \implies \: \dfrac{ - 4y}{5} = - 16 \\ \\ \sf \implies \: - 4y = - 16 \times 5 \\ \\ \sf \implies \:y = \dfrac{ - 80}{ - 4} \\ \\ \sf \implies \:y \: = \: 20$

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On putting value of y in equation 1, we get;

$\sf \implies \: x \: = \dfrac{3}{5} \times 20 \\ \\ \sf \implies \: x \: = 3 \times 4 \\ \\ \sf \implies \: x \: = 12$

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ANSWER :

• Present age of A = x = 12 years
• Present age of B = y = 20 years