Question

Sum of the present ages of anu and binu is 65.after five years anu's age will be four times binus age. What are their ages now?

Answer 1

Answer:

Let the ages of father and his son be x and y respectively.

Case I:- The sum of the ages of father and his son is 65 years.

age of father + age of son = 65

⇒x+y=65⟶(i)

Case II:- After 5 years, fathers age will be twice the age of his son.

Age of father = 2 (age of son)

⇒x+5=2(y+5)

⇒x+5=2y+10

⇒x=2y+5⟶(ii)

From eq

n

(i)&(ii), we have

(2y+5)+y=65

⇒3y=65−5

⇒y=20

Substituting the value of y in eq

n

(i), we have

x+20=65

⇒x=45

Hence, the present age of father and son is 45 and 20 respectively and equation (i)&(ii) are the pair of linear equations in two variables.

Answer 2

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Sum of anu and binu's age is 65
• After 5 years anu's age will be 4 times the binu's age

______________________

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

⠀⠀⠀⠀

• Present age of anu and binu = ??

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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Let anu's present age be x

Let Binu's present age be y

⠀⠀⠀⠀

Acc. to the first statement :-

⠀⠀⠀⠀

x + y = 65 --- ( i )

⠀⠀⠀⠀

___________________________________

⠀⠀⠀⠀

⠀⠀⠀⠀

After 5 years

⠀⠀⠀⠀

Anu's age = x + 5

⠀⠀

Binu's age = y + 5

⠀⠀⠀⠀

____________________________________

⠀⠀

Acc. to the second statement :-

⠀⠀⠀⠀

x + 5 = 4( y + 5 )

⠀⠀⠀⠀

x + 5 = 4y + 20

⠀⠀

x - 4y = 20 - 5

⠀⠀⠀⠀

x - 4y = 15 --- ( ii )

⠀⠀⠀⠀

• Subtracting eq ( ii ) from ( i )

⠀⠀⠀⠀

x + y - ( x - 4y ) = 65 - 15

⠀⠀

x + y - x + 4y = 65 - 15

⠀⠀⠀⠀

y + 4y = 65 - 15

⠀⠀

5y = 65 - 15

⠀⠀

5y = 50

⠀⠀

y = 50 / 5

⠀⠀⠀⠀

y = 10 ⠀

⠀⠀⠀⠀

• putting value of y in eq ( i )

⠀⠀⠀⠀

x + y = 65

⠀⠀⠀⠀

x + 10 = 65

⠀⠀

x = 65 - 10

⠀⠀⠀⠀

x = 55

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

⠀⠀

• Anu's age = 55
• Binu's age = 10