Question

Five years ago,anu thrice as old as sonu after ten years ,Anu will be twice as old as sonu .how old are anu and sonu,please sent only correct answer.​

Answer 1

Given :

• Five years ago,anu thrice as old as sonu.
• After ten years ,Anu will be twice as old as sonu .

To find :

• The age of Anu's and Sonu's =?

Step-by-step explanation :

Let, the present age of Anu =x year

Then, the present age of Sonu =y year

Five years ago Anu's age = x – 5years

Five years ago Sonu's age = y–5years

It is Given that,

Anu was thrice as old as Sonu,

As per question,

x − 5 = 3 (y – 5)

x – 5 = 35 – 15

x – 3y = −15 + 5

x – 3y = −10 ....(1)

Now,

After 10 years Anu's age will, x + 10 years

After 10 years Sonu's age will be = y + 10 years

It is Given that,

Anu will be twice as old as Sonu,

As per question,

x + 10 = 2( y + 10)

x + 10 = 2y + 20

x – 2y = 10 …..(2)

x – 3y = −10 …..(1)

Subtracting equation (1) from equation (2), we get,

x - 3y - (x - 2y) = 10 - (-10)

x - x - 3y + 2y = 10 + 10

y = 20

On putting the value of y = 20 in equation (1) we get

x − 3 × 20 = −10

x = 60 – 10

x = 50

Therefore, age of Anu =50 years and age of Sonu = 20 years respectively.

Answer 2

$\underline {\rule{261}{2}}$

$\star\;\;{\underline{\underline{\frak \pink{Given:-}}}}$

• Five years ago,anu thrice as old as sonu after ten years ,Anu will be twice as old as sonu.

$\star\;\;{\underline{\underline{\frak \pink{To\;Find:-}}}}$

• Present age of sonu and anu.

$\star\;\;{\underline{\underline{\frak \purple{Solution:-}}}}$

• Let the present age of Anu be x years.
• Let the present age of sonu be y years.

★ According to question:-

5 years ago,

Age of Anu = ( x - 5 ) years

Age of sonu = ( y - 5 ) years

Anu was thrice as old as sonu.

$\dashrightarrow$ x - 5 = 3(y - 5)

$\dashrightarrow$ x - 5 = 3y - 15

$\dashrightarrow$ x - 3y = -15 + 5

$\dashrightarrow$ x - 3y = -10 ---(1)

$\rule{200}3$

After ten years,

Age of Anu = x + 10

Age of sonu = x + 10

Anu will be twice as old as sonu.

$\rightdasharrow$ x + 10 = 2(y + 10)

$\dashrightarrow$ x + 10 = 2y + 20

$\dashrightarrow$ x - 2y = 20 - 10

$\dashrightarrow$ x - 2y = 10 ---(2)

$\rule{200}3$

★ Using elimination method:-

Substract eq(2) from eq(1) :-

Then we get,

$\dashrightarrow$ 0x - y = -20

$\dashrightarrow$ ${\underline{\underline{\boxed{\sf{\red{y = 20}}}}}}$

Putting value of y in eq(1) :-

$\dashrightarrow$ x - 3(20) = -10

$\dashrightarrow$ x - 60 = -10

$\dashrightarrow$ x = -10 + 60

$\dashrightarrow$ ${\underline{\underline{\boxed{\sf{\red{x = 50}}}}}}$

Hence,

The present age of Anu = x = 20 years.

The present age of Sonu = y = 50 years.

$\underline {\rule{261}{2}}$