Question

10. The ratio of Reema's age to Sudha's age is 1 : 5. Ten
years later, the ratio of their ages will be 3: 7. Find
their present ages.
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Answer 1

Answer:

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Answer 2

Answer:-

$\red{\bigstar}$ The present ages are

• Reema $\large\leadsto\boxed{\tt\purple{5 \: years}}$

• Sudha $\large\leadsto\boxed{\tt\purple{25 \: years}}$

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• Given:-

• Ratio of Reema's age to Sudha's age = 1:5
• Ten years later the ratio will be = 3:7

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• To Find:-

• Present ages.

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• Solution:-

Let the present age of Reema be 'x' and that of Sudha be 'y'.

• According to the question:-

✯ Ratio of Reema's age to Sudha's age is 1:5.

Hence,

➪ $\sf \dfrac{x}{y} = \dfrac{1}{5}$

➪ $\sf x \times 5 = 1 \times y$

➪ $\sf 5x = y$

➪ $\sf y = 5x \dashrightarrow\bf\red{[eqn.i]}$

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Now,

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✯ Ratio of Reema's age to Sudha's age after 10 years will be 3:7.

Hence,

➪ $\sf \dfrac{x + 10}{y +10} = \dfrac{3}{7}$

➪ $\sf 7(x+10) = 3(y+10)$

➪ $\sf 7x + 70 = 3y + 30$

➪ $\sf 7x + 70 - 30 = 3y$

➪ $\sf 7x + 40 = 3y$

➪ $\sf 7x - 3y = -40\dashrightarrow\bf\red{[eqn.ii]}$

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• Substituting eqn.[i] in eqn.[ii]:-

➪ $\sf 7x - 3y = -40$

➪ $\sf 7x - 3(5x) = -40$

➪ $\sf 7x - 15x = -40$

➪ $\sf - 8x = - 40$

➪ $\sf x = \dfrac{-40}{-8}$

★ $\large{\underline{\underline{\rm\pink{x = 5}}}}$

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• Substituting the value of x in [eqn.i]:-

➪ $\sf y = 5x$

➪ $\sf y = 5 \times 5$

★ $\large{\underline{\underline{\rm\pink{y = 25}}}}$

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Therefore, the ages are

• Reema = 5 years
• Sudha = 25 years