Question

the ages of Hari and Harry are in the ratio of 5:7 . four years from now, the ratio of their ages will be 3:4 . find their present ages.​

Answer 1

$\huge\sf\pink{Answer}$

☞ Their present ages are 21 & 28

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$\huge\sf\blue{Given}$

✭ Ratio of the ages of Har and Harry is 5:7

✭ After four years their ages will be of the ratio 3:4

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$\huge\sf\gray{To \:Find}$

◈ Their Present ages?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Let}}$

• Hari's Age = 5x
• Harry's Age = 7x

So after 4 years their ages will be

• Hari's Age = 5x+4
• Harry's Age = 7x+4

☯ $\large\underline{\sf As \ Per \ the \ Question}$

After four years their ratio will be 3:4 so,

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

«« Cross Multiply »»

➝ $\sf 4(5x+4) = 3(7x+4)$

➝ $\sf 20x+16 = 21x+12$

➝ $\sf 20x-21x = 12-16$

➝ $\sf -x = -4$

➝ $\sf \red{x = 4}$

So now their present ages will be,

⪼ $\sf Hari = 5x = 5\times 4 = \orange{20 \ yrs}$

⪼ $\sf Harry = 7x = 7\times 4 = \orange{28 \ yrs}$

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Answer 2

Given :

• Hari and Harry's age are in the ratio of 5:7
• Four years from now the ratio of their ages will be 3:4

To find :

• Their present ages

According to the question,

Let,

The age of Hari is 5x &

Age of Harry is 7x

Now,after four years their age will be

• Hari 5x + 4
• Harry 7x + 4

So,the equation will be

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

$\sf{ \: \: : \implies3(7x + 4) = 4(5x + 4) }$

$\sf{ \: \: : \implies21x + 12 = 20x + 16 }$

$\sf{ \: \: : \implies21x - 20x = 16 - 12 }$

$\sf{ \: \: : \implies \: x = 4} \: \orange\bigstar$

___________....

So,

Present age of Hari = 5x = 5 × 4 = 20 years

Present age of Harry = 7x = 7 × 4 = 28 years...