Question

. The ages of Simmy and Jimmy are in the ratio 6:8. Five years from now the ratio of their
ages will be 4:5. Find their present ages.

Answer 1

❍ Let the present ages of Simmy and Jimmy be 6x and 8x respectively.

— After five years, their ages

• Simmy's age = (6x + 5)
• Jimmy's age = (8x + 5)

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$\underline{\bigstar\:\boldsymbol{According\;to\:the\;given\: Condition\; :}}$

⠀

• Five years from now, the ratio of their ages (Jimmy's and Simmy's age) will be 4: 5. By making equation.

⠀

Therefore,

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$:\implies\sf \dfrac{(6x + 5)}{(8x + 5)} = \dfrac{4}{5} \\\\\\:\implies\sf 5(6x + 5) = 4(8x + 5) \\\\\\:\implies\sf 30x + 25 = 32x + 20\\\\\\:\implies\sf 32x - 30x = 25 - 20\\\\\\:\implies\sf 2x = 5\\\\\\:\implies{\underline{\boxed{\frak{\purple{x = \dfrac{5}{2}}}}}}\:\bigstar$

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Hence,

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• Simmy's age = 6x = 6 (⁵⁄₂) = 3(5) = 15 years.

• Jimmy's age = 8x = 8 (⁵⁄₂) = 4(5) = 20 years.

$\therefore{\underline{\sf{Hence,\; present\:ages\;of\;Simmy\;and\;Jimmy\:are\; \bf{15\:years\;\&\;20\;years }.}}}$

Answer 2

Given :-

The  ages of Simmy and Jimmy are in the ratio 6:8 five years from now the ratio of their ages will be 4:5

To Find :-

Present ages

Solution :-

Let the present age of Simmy be 6y and Jimmy be 8y

After 5 years

[6y + 5]/[8y + 5] = 4/5

• We Need to do cross multiplication

5(6y + 5) = 4(8y + 5)

$\sf (5 \times 6y) + (5\times 5)=(4 \times 8y)+(4 \times 5)$

30y + 25 = 32y + 20

32y - 30y = 25 - 20

2y = 5

y = 5/2

Or,

y = 5

Age of simmy

$\sf 6 \times 2.5$

15 years

Age of Jimmy

$\sf 8 \times 2.5$

20 years