Question

the present ages of A and B are in the ratio of 4:7. after 4 years their ages will be the ratio 2:3. find their present ages​

Answer 1

Answer:-

$\blue{\bigstar}$ Present ages are,

• $\large\leadsto\boxed{\tt\pink{A = \: 8 \: years}}$

• $\large\leadsto\boxed{\tt\pink{B = \: 14 \: years}}$

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• Given:-

• Present ages of A and B are in ratio of 4:7.

• After 4 years their ages will be in ratio of 2:3.

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• To Find:-

Let the present age of A be 'x' and that of B be 'y'.

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Given that,

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✯ Present ages of A and B are in ratio of 4:7.

Therefore,

➪ $\sf \dfrac{x}{y} = \dfrac{4}{7}$

➪ $\sf 7x = 4y$

✯ $\bf x = \dfrac{4y}{7}\dashrightarrow\bf\red{[eqn.i]}$

Also,

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✯ After 4 years their ages will be in ratio 2:3.

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Therefore,

➪ $\sf \dfrac{x+4}{y+4} = \dfrac{2}{3}$

➪ $\sf 3(x+4) = 2(y+4)$

➪ $\sf 3x + 12 = 2y + 8$

➪ $\sf 3x - 2y +12 - 8 = 0$

✯ $\bf 3x - 2y + 4 = 0 \dashrightarrow\bf\red{[eqn.ii]}$

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• Substituting eqn.[i] in eqn.[ii]:-

➪ $\sf 3 \times \bigg(\dfrac{4y}{7}\bigg) - 2y + 4 = 0$

➪ $\sf \dfrac{12y}{7} - 2y + 4 = 0$

➪ $\sf \dfrac{12y - 14y + 28}{7} = 0$

➪ $\sf \dfrac{-2y + 28}{7} = 0$

➪ $\sf -2y + 28 = 0$

➪ $\sf -2y = -28$

➪ $\sf y = \dfrac{28}{2}$

★ $\large{\bf\purple{y = 14}}$

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Now,

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

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➪ $\sf x = \dfrac{4y}{7}$

➪ $\sf x = \dfrac{4 \times 14}{7}$

➪ $\sf x = \dfrac{56}{7}$

★ $\large{\bf\purple{x = 8}}$

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Therefore, the present ages are,

• A = 8 years

• B = 14 years

Answer 2

Answer:

Given :-

• The present ages of A and B are in the ratio of 4:7.
• After 4 years their ages will be the ratio of 2:3.

Find Out :-

• What is the ratio of their present ages.

Solution :-

Present age of A = 4x

Present age of B = 7x

Now, after 4 years,

Age of A = 4x + 4

Age of B = 7x + 4

According to the question,

⇨ $\dfrac{4x + 4}{7x + 4}$ = $\dfrac{2}{3}$

⇨ 3(4x + 4) = 2(7x + 4)

⇨ 12x + 12 = 14x + 8

⇨ 12x - 14x = 8 - 12

⇨ - 2x = - 4

⇨ x = $\dfrac{- 4}{- 2}$

➙ x = 2

Hence,

Present age of A = 4x = 4 × 2 = 8 years

Present age of B = 7x = 7 × 2 = 14 years