Question

Five years ago, Anu was thrice as old as Sonu. After ten years, Anu will be twice as old as Sonu. How old are Anu and Sonu?​

Answer 1

$\huge\underline\mathbb{\red S\pink {0} \purple {L} \blue {UT} \orange {1}\green {ON :}}$

$\sf\underline{\underline{\green{GIVEN \: }}}$

√ Five years ago,

Anu was thrice as old as Sonu.

√ And Ten years later,

Anu will be twice as old as Sonu.

$\sf\underline{\underline{\green{TO \: FIND \: }}}$

√ The age of Anu and the Sonu.

$\sf\underline{\underline{\green{NOW, \: }}}$

let us assumed that :-

Present ages :-

Anu = "x" year old

and

Sonu = "y" year old

Than, Five years ago :-

Age of Anu = x – 5 years

Age of Sonu = y – 5 years

Anu was thrice as old as Sonu :-

x- 5 = 3(y – 5)

x – 5 = 3y – 15

x – 3 y = - 10 ……….. ( 1 )

Now 10 years later the ages are :-

Age of Anu = x + 10

Age of Sonu = y + 10

$\sf\underline{\underline{\green{ACCORDING \: TO \: GIVEN \: CONDITION \: }}}$

we have

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

x+10=2y+20

⇒x−2y=10 -------- ( 2 )

Now,

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

y = 10−(−10)

y = 20 years

Then put the value of "y" in the 1st equation for getting the value of "x" :-

x − 3 ( 20 ) = −10

x − 60 = −10

x = 50 years

$\sf\underline{\underline{\green{HENCE, \: }}}$

$<font color =blue>$

Anu's age = x = 50 years

Sonu's age = y = 20 years.

Answer 2

Given :–

• Five years ago, the age of Anu was thrice as old as Sonu.
• After ten years, Anu will be thrice as old as Sonu.

To Find :–

• Ages of Anu and Sonu.

Solution :–

Let,

The age of Anu be x.

And the age of Sonu be y.

Five years ago, their ages will be,

→ Age of Anu = x – 5.

→ Age of Sonu = y – 5.

Anu was thrice as old as Sonu.

● Anu's age = 3(Sonu's age)

➠ x – 5 = 3(y – 5)

➠ x – 5 = 3y – 15

➠ x – 3y = – 15 + 5

➠ x – 3y = –10 ––––– (1)

Then, after 10 years later.

Their ages will be,

→ Age of Anu = x + 10.

→ Age of Sonu = y + 10.

According to the given problem,

Anu will be twice as old as Sonu.

So,

● Anu's age after 10 years = 2(Sonu's age after 10 years)

➠ (x + 10) = 2(y + 10)

➠ x + 10 = 2y + 20

➠ x – 2y = 20 – 10

➠ x – 2y = 10 ––––– (2)

Now, subtract equation (1) from equation (2),

➠ (x – 2y) – (x – 3y) = (10) – (–10)

➠ x – 2y – x + 3y = 10 + 10

➠ 0 + y = 20

➠ y = 20

Now, put the value of y in equation (1),

➠ x – 3y = –10

➠ x – 3(20) = –10

➠ x – 60 = –10

➠ x = –10 + 60

➠ x = 50

Hence,

• The age of Anu (x) is 50 years old.

• The age of Sonu (y) is 20 years old.