Question

15. The ages of A and B are in the ratio 8:3. Six years hence, their ages will be in the ratio 9:4.
Find their present ages.
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Answer 1

Correct Question: The ages of A and B are in the ratio 8:3. Six years hence, their ages will be in the ratio 9:4.

Find their present ages.

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Given: The ages of A and B are in the ratio of 8:3.

Need to find: What's their present ages.

❒ Let the present age of A and present age of B is 8x and 3x.

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$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: According\: to \; the\; Question \: :}}}}}\mid}$⠀

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• Six years hence, their ages will be in the ratio 9:4.

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Therefore,

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$:\implies\sf \dfrac{8x + 6}{ 3x + 6} = \dfrac{9}{4} \\\\\\:\implies\sf 4(8x + 6) = 9(3x + 6) \\\\\\:\implies\sf 32x + 24 = 27x + 54\\\\\\:\implies\sf 32x - 27x = 54 - 24\\\\\\:\implies\sf 5x = 30\\\\\\:\implies\sf x = \cancel\dfrac{30}{5}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 6}}}}}\;\bigstar$

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❒ Hence, their present ages are:

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• A's present age, 8x = 8(6) = 48 years.

• B's present age, 3x = 3(6) = 18 years.

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$\therefore{\underline{\sf{Hence, \; their\; present\; ages \; are\; \bf{48\:years\: and \; 18 \; years }.}}}$

Answer 2

Answer:

Given :-

The ages of A and B are in the ratio 8:3. Six years hence, their ages will be in the ratio 9:4.

To Find :-

Present ages

Solution :-

Let the present age of A and B be 8x and 3x.

$\sf \dfrac{8x + 6}{3x + 6} = \dfrac{9}4$

By Cross Multiplication

$\sf \: 9(3x + 6) = 4(8x + 6)$

$\sf \: 27x + 54 = 32x + 24$

$\sf \: 32x - 27x = 54 - 24$

$\sf \: 5x = 54 - 24$

$\sf \: 5x = 30$

$\sf \: x \: = \cancel\dfrac{30}{6}$

$\sf \: \:x = 6 \: years$

Present ages are

A = 8(6) = 48 years

B = 3(6) = 18 years