# 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

## 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.

**A**

## Father's age =75 years

**B**

## Father's age =45 years

**C**

## Father's age =66 years

**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.

Byju's Answer Standard X Mathematics

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.

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

Standard X Mathematics

## 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

### Chapter: 3. Pair of Linear Equations in Two Variables

### Subject: Maths - Class 10th

### 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.

## Chapter Exercises

### Exercise 3.2

### Exercise 3.3

### Exercise 3.4

### Exercise 3.5

### Exercise 3.1

## More Exercise Questions

1

The sum of the two numbers is 18. The sum of their reciprocals is 1/4. Find the numbers.

2

The sum of two numbers is 15 and sum of their reciprocals is . Find the numbers.

3

Two numbers are in the ratio of 5 : 6. If 8 is subtracted from each of the numb, they become in the ratio of 4 : 5. Find the numbers.

4

The sum of two numbers is 16 and the sum of their reciprocals is 1/3. Find the numbers.

5

Two positive numbers differ by 3 and their product is 54. Find the numbers.

6

Two numbers are in the ratio of 3 : 5. If 5 is subtracted from each of the number they become in the ratio of 1 : 2. Find the numbers.

7

Two numbers are in the ratio of 3 : 4. If 8 is added to each number, they become in the ratio of 4 : 5. Find the numbers.

8

Two numbers differ by 2 and their product is 360. Find the numbers.

9

Two numbers differ by 4 and their product is 192. Find the numbers.

10

Two numbers differ by 4 and their product is 96. Find the numbers.

11

The monthly incomes of A and B are in the ratio of 5 : 4 and their monthly expenditures are in the ratio of 7 : 5. If each saves Rs. 3000 per month, find the monthly income of each.

12

Scooter charges consist of fixed charges and the remaining depending upon the distance travelled in kilometres. If a person travels 12 km, he pays Rs. 45 and for travelling 20 km, he pays Rs. 73. Express the above statements in the form of simultaneous equations and hence, find the fixed charges and the rate per km.

13

A part of monthly hostel charges in a college is fixed and the remaining depend on the number of days one has taken food in the mess. When a student A, takes food for 22 days, he has to pay Rs. 1380 as hostel charges, whereas a student B, who takes food for 28 days, pays Rs. 1680 as hostel charges. Find the fixed charge and the cost of food per day.

14

Taxi charges in a city consist of fixed charges per day and the remaining depending upon the distance travelled in kilometers. If a person travels 110 km, he pays Rs. 690, and for travelling 200 km, he pays Rs. 1050. Find the fixed charges per day and the rate per km.

15

A part of monthly hostel charges in a college are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25 days, he has to pay Rs. 1750 as hostel charges whereas a student a d who takes food for 28 days, pays Rs. 1900 as hostel charges. Find the fixed charges and the cost of the food per day.

16

The total expenditure per month of a household consists of a fixed rent of the house and the mess charges, depending upon the number of people sharing the house. The total monthly expenditure is Rs. 3,900 for 2 people and Rs. 7,500 for 5 people. Find the rent of the house and the mess charges per head per month.

17

The car rental charges in a city comprise a fixed charge together with the charge for the distance covered. For a journey of 13 km, the charge paid is Rs. 96 and for a journey of 18 km, the charge paid is Rs. 131. What will a person have to pay for travelling a distance of 25 km?

18

The sum of a two - digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.

19

A two - digit number is 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

20

A number consists of two digits. When it is divided by the sum of its digits, the quotient is 6 with no remainder. When the number is diminished by 9, the digits are reversed. Find the number.

21

The sum of the digits of a two - digit number is 12. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.

22

A two - digit number is 3 more than 4 times the sum of its digits. If 18 is added to the number, the digits are reversed. Find the number.

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