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a father’s age is three times the sum of the ages of his children. after 5 years, his age will be two times the sum of their ages. find the present age of the father.

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Father's age is three times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

Click here👆to get an answer to your question ✍️ Father's age is three times the sum of ages of his two children. After 5 years his age will be twice the sum of ages of two children. Find the age of father.

Question

A

B

C

D

Father's age =88 years

Medium Open in App Solution Verified by Toppr

Correct option is B)

Let the age of father =x years

The sum of the age of 2 children =y years

According to the first condition

⇒x=3y.....eq1 After 5 years ⇒ Father's age =x+5

⇒ The sum of ages of his two children =y+10

According to the second condition

⇒x+5=2(y+10)⇒x+5=2y+20

⇒x−2y=15....eq2

Put the value of x from eq1

⇒3y−2y=15⇒y=15 Put  y=15 in eq1 ⇒x=3×15⇒x=45

Hence, father age =45 years

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A father's age is three times the sum of the ages of his two children. After 5 years, his age will be two times the sum of their ages. Find the present age of the father.

A father's age is three times the sum of the ages of his two children. After 5 years, his age will be two times the sum of their ages. Find the present age of the father.

Method of Substitution to Find the Solution of a Pair of Linear Equations

A father's ag... Question

A father's age is three times the sum of the ages of his two children. After 5 years, his age will be two times the sum of their ages. Find the present age of the father.

Open in App Solution

Let the age of first son be x and of second son be y.

Then, the father's present age be 3(x + y).

According to the question,

After 5 years, the father's age will be two times the sum of the ages of his two children.

3x+y+5=2x+5+y+5

⇒3x+3y+5=2x+10+2y+10

⇒3x+3y-2x-2y=20-5 ⇒x+y=15 ⇒3x+y=45

Hence, the present age of the father is 45 years.

Suggest Corrections 42

SIMILAR QUESTIONS

Q.

Father's age is 3 times the sum of Ages of his two children . after 5 years his age will be twice the sum of Ages of two children find the age of father

Q. The present age of a father is equal to the sum of the ages of his

5 children. 12

years hence, the sum of the ages of his children will be twice the age of their father. Find the present age of the father.

Q. The age of the father is twice the sum of the ages of his two children . After 20 years , his age will be eual to the sum of the ages of his children . Find the age of the father.

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स्रोत : byjus.com

Father's age is three times the sum of ages of his two children. After 5 years, his age will be twice the sum of ages of two children. Find the age of father.

Q.31 of chapter 3, 3. Pair of Linear Equations in Two Variables - KC Sinha - Mathematics book. Father's age is three times the sum of ages of his two children. After 5 years, his age will be twice the sum of ages of two children. Find the age of father.

Book: KC Sinha - Mathematics

Q. No. 31 of Exercise 3.5

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

31

Father's age is three times the sum of ages of his two children. After 5 years, his age will be twice the sum of ages of two children. Find the age of father.

Let the age of two children be x and y

So, the father’s present age = 3(x + y)

After five years,

Age of two children = (x + 5) + (y + 5) years

= ( x + y + 10) years

So, the age of father after five years = 3(x + y) + 5

= 3x + 3y + 5

According to the question,

3x + 3y + 5 = 2(x + y + 10)

⇒ 3x + 3y + 5 = 2x + 2y + 20

⇒ 3x – 2x + 3y – 2y = 20 – 5

⇒ x + y = 15

So, the age of two children = 15 years

And the age of father = 3(15) = 45years

Hence, the age of father is 45 years and the age of his two children is 15 years.

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Mohammed 14 day ago

Guys, does anyone know the answer?