Question

The radio of present age of Ramesh and Mahesh is 5 : 7. After 4 years the ratio of their age will be 3 : 4. Find out their present age​

Answer 1

Answer:

Ramesh age is 20 years and Mahesh age is 28 years.

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Answer 2

GivEn:

• Ratio of present age of Ramesh and Mahesh is 5:7.
• After 4 years, the ratio of their age will be 3 : 4.

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To find:

• Present age of Ramesh and Mahesh

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SoluTion:

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${\underline{\bf{\bigstar\; According\;to\;question\;:}}}$

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Ratio of present age of Ramesh and Mahesh is 5:7

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• Let Present age of Ramesh be 5x.
• And Present age of Mahesh be 7x.

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After 4 years,

The ratio of their age will be 3 : 4.

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Their ages after four year,

• Age of Ramesh = 5x + 4 years
• Age of Mahesh = 7x + 4 years

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Therefore,

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$:\implies\sf \dfrac{5x + 4}{7x + 4} = \dfrac{3}{4}$

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$:\implies\sf 4(5x + 4) = 3(7x + 4)$

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$:\implies\sf 20x + 16 = 21x + 12$

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$:\implies\sf 20x - 21x = 12 - 16$

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$:\implies\sf - x = - 4$

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$:\implies{\underline{\boxed{\sf{\purple{x = 4}}}}}\;\bigstar$

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Putting value of x in their assumed age 5x + 4 and 7x + 4,

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Therefore,

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• Present age of Ramesh = 5 × 4 = 20 years
• Present age of Mahesh = 7 × 4 = 28 years

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Verification:

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★ Ratio of their present age = 5:7

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$:\implies\sf 20:28 = 5:7$

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$:\implies\sf \dfrac{20}{28} = \dfrac{5}{7}$

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$:\implies\sf \cancel{ \dfrac{20}{28}} = \dfrac{5}{7}$

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$:\implies\sf \dfrac{5}{7} = \dfrac{5}{7}$

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$:\implies\bf 5:7 = 5:7$

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After 4 years,

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• Age of Ramesh = 20 + 4 = 24 years
• Age of Mahesh = 28 + 4 = 32 years

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★ After 4 years, Ratio of their ages = 3:4

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$:\implies\sf 24:32 = 3:4$

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$:\implies\sf \dfrac{24}{32} = \dfrac{3}{4}$

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$:\implies\sf \cancel{ \dfrac{24}{32}} = \dfrac{3}{4}$

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$:\implies\sf \dfrac{3}{4} = \dfrac{3}{4}$

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$:\implies\bf 3:4 = 3:4$

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$\therefore$ Hence Verified