Question

Five years ago, Ajay was thrice as old as Sonu. Ten years later, Ajay will be twice as old as Sonu. How old are Ajay and Sonu?
Solve it by graphical method...​

Answer 1

Answer:

Step-by-step explanation:

Given :-

• Five years ago, Ajay was thrice as old as Sonu.
• Ten years later, Ajay will be twice as old as Sonu.

To Find :-

• Both of them's ages

Solution :-

Let the present age of Ajay be = x                  

And  the present age of Sonu be = y                  

According to the Question,                

⇒ (x - 5) = 3(y - 5)                  

⇒ x - 3y = - 10 ... (i)                  

⇒ (x + 10y) = 2(y + 10)                  

⇒ x - 2y = 10 ... (ii)                

Subtracting equation (i) from equation (ii), we get                  

⇒ y = 20 ... (iii)                  

Putting this value in equation (i), we get                  

⇒ x - 60 = - 10                  

⇒ x = 50                  

Hence, age of Ajay = 50 years and age of Sonu = 20 years.

Answer 2

Answer :-

$\:$

• Present age of Ajay is 50 years

• Present age of Sonu is 20 years

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Explanation :-

$\:$

$\underline{\underline{\sf{\:\:\:Given\:\:\:}}}$

$\:$

• Five years ago, Ajay was thrice as old as Sonu.

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• Ten years later, Ajay will be twice as old as Sonu.

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$\underline{\underline{\sf{\:\:\:To\:Find\:\:\:}}}$

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• How old are Ajay and Sonu?

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$\underline{\underline{\sf{\:\:\:Solution\:\:\:}}}$

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• Let present age of Ajay be m years

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• And present age of Sonu be n years

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• Therefore, age of Ajay before 5 years = (m - 5) years

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• And age of Sonu before 5 years = (n - 5) years

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• Also, age of Ajay after 10 years = (m + 10) years

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• And age of Sonu after 10 years = (n + 10) years

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ㅤ★ According to the Question :-ㅤ

$\:$

➝ㅤㅤ(m - 5) = 3(n - 5)

$\:$

➝ㅤㅤm - 5 = 3n - (5 × 3)

$\:$

➝ㅤㅤm - 5 = 3n - 15

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➝ㅤㅤm - 3n = - 15 + 5

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➝ㅤㅤm - 3n = -10 ㅤㅤ– – – – (1)

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Also,

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➝ㅤㅤ(m + 10) = 2(n + 10)

$\:$

➝ㅤㅤm + 10 = 2n + (10 × 2)

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➝ㅤㅤm + 10 = 2n + 20

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➝ㅤㅤm - 2n = 20 - 10

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➝ㅤㅤm - 2n = 10 ㅤㅤ– – – – (2)

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ㅤ★ Subtracting (1) from (2) :-ㅤ

$\:$

➝ㅤㅤ(m - 2n) - (m - 3n) = 10 - (-10)

$\:$

➝ㅤㅤm - 2n - m + 3n) = 10 + 10

$\:$

➝ㅤㅤm - m - 2n + 3n) = 20

$\:$

➝ㅤㅤn = 20

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ㅤ★ Putting value of 'n' in (2) :-ㅤ

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➝ㅤㅤm - 2(20) = 10

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➝ㅤㅤm - 40 = 10

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➝ㅤㅤm = 10 + 40

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➝ㅤㅤm = 50

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• Therefore, Ajay is 50 years old and Sonu is 20 years old.

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