- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.1
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.2
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.3
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.4
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.5
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.6
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.7
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.8
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.10
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.11
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-VSAQS

RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.1 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.2 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.3 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.4 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.5 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.6 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.7 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.8 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.10 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.11 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-VSAQS |

**Answer
1** :

Let present age of father = x

and that of son = y

According to the conditions,

x = 3y ….(i)

After 12 years,

Age of father = x + 12

and age of son = y + 12

x + 12 = 2(y + 12)

x + 12 = 2y + 24

=> 3y + 12 = 2y + 24 {From (i)}

=> 3y – 2y = 24 – 12

=> y = 12

x = 3y = 3 x 12 = 36

Hence present age of father = 36 years and age of son = 12 years

**Answer
2** :

Let present age of A = x years

and age of B = y years

10 years later

A’s age will be = x + 10

and B’s age will be = y + 10

x + 10 = 2(y + 10)

=> x + 10 = 2y + 20

=> x – 2y = 20 – 10

=> x – 2y = 10 ….(i)

5 years ago,

A’s age was = x – 5 years

and B’s age was = y – 5 years

x – 5 = 3 (y – 5)

=> x – 5 = 3y – 15

=> x – 3y = 5 – 15 = -10 ….(ii)

Subtracting (ii) from (i) we get

y = 20

and x – 2 x 20 = 10

=> x = 40 + 10 = 50

A’s present age = 50 years

and B’s present age = 20 years

**Answer
3** :

Let present age of Nuri = x years

and age of Sonu = y years

5 years ago,

age of Nuri = (x – 5) years

and age of Sonu = (y – 5) years

x – 5 = 3 (y – 5) = 3y – 15

=> x = 3y – 15 + 5

=> x = 3y – 10 ….(i)

10 years later,

age of Nuri = x + 10

and age of Sonu = y + 10

x + 10 = 2 (y + 10) = 2y + 20

=> x = 2y + 20 – 10 = 2y+ 10 ….(ii)

From (i) and (ii)

3y – 10 = 2y + 10 => 3y – 2y = 10 + 10

=> y = 20

x = 3y – 10 [from (i)]

x = 3 x 20 – 10 = 60 – 10 = 50 years

and age of Sonu = 20 years

**Answer
4** :

Let present age of a man = x years

and age of his son = y years

6 years hence,

age of the man = x + 6

and age of his son = y + 6

x + 6 = 3 (y + 6)

=> x + 6 = 3y + 18

=> x – 3y = 18 – 6 = 12

=> x – 3y = 12 ….(i)

3 years ago,

the age of the man = x – 3

and age of his son = y – 3

x – 3 = 9 (y – 3)

=> x – 3 = 9y – 27

=> x – 9y = -27 + 3

=> x – 9y = -24 ….(ii)

Subtracting (ii) from (i),

6y = 36

=> y = 6

From (i), x – 3 x 6 = 12

=> x – 18 = 12

=> x = 12 + 18 = 30

Present age of man = 30 years

and age of his son = 6 years

**Answer
5** :

Let present age of father = x years

and age of his son = y years

10 years ago,

Father’s age = x – 10

and son’s age = y – 10

x – 10 = 12(y – 10)

=> x – 10 = 12y – 120

=> x – 12y = -120 + 10 = -110

=> x – 12y = -110 ….(i)

10 years hence,

Father’s age = x + 10

and his son’s age = y + 10

10y = 120

y = 12

From (ii), x – 2y = 10

x – 2 x 10 = 10

=> x – 24 = 10

=> x = 10 + 24

=> x = 34

Present age of father = 34 years

and age of his son = 12 years

**Answer
6** :

Let present age of father = x years

and age of his son = y years

x = 3y + 3 …….(i)

3 years hence,

Father’s age = (x + 3)

and his son’s age = (y + 3)

x + 3 = 2 (y + 3) + 10 = 2y + 6 + 10

x + 3 = 2y + 16

=> x = 2y + 16 – 3 = 2y + 13 ….(ii)

From (i) and (ii)

3y + 3 = 2y + 13

=> 3y – 2y = 13 – 3

=> y = 10

and x = 3y + 3 = 3 x 10 + 3 = 30 + 3 = 33

Present age of father = 33 years

and age of his son = 10 years

**Answer
7** :

Let present age of father = x years

and age of son = y years

x = 3y ………(i)

12 years hence,

Father’s age = x + 12

and son’s age = y + 12

(x + 12) = 2 (y + 12)

=> x + 12 = 2y + 24

=> x = 2y + 24 – 12 = 2y + 12 ….(ii)

From (i) and (ii)

3y = 2y + 12

=> 3y – 2y = 12

=> y = 12

x = 3y = 3 x 12 = 36

Present age of father = 36 years and

age of son = 12 years

**Answer
8** :

Let father’s present age = x years

and sum of ages of his two children = y

then x = 3y

=> y = (1/3) x ….(i)

After 5 years,

Age of father = x + 5

and sum of age of two children = y + 2 x 5 = y + 10

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

x + 5 = 2y + 20

=> x = 2y + 20 – 5

x = 2y + 15 ….(ii)

From (i)

x = 2 x (1/3) x + 15

=> x = (2/3) x + 15

=> x – (1/3) x = 15

=> (1/3) x = 15

=> x = 15 x 3 =45

Age of father = 45 years

**Answer
9** :

Let present age of father = x years

and age of his son = y years

2 years ago,

age of father = x – 2

and age of son = y – 2

x – 2 = 5(y – 2)

=> x – 2 = 5y – 10

=> x = 5y – 10 + 2

=> x = 5y – 8 ………(i)

2 years later,

age of father = x + 2

and age of son = y + 2

x + 2 = 3 (y + 2) + 8

=> x + 2 = 3y + 6 + 8

=> x = 3y + 14 – 2 = 3y + 12 ….(ii)

From,(i) and (ii)

5y – 8 = 3y + 12

=> 5y – 3y = 12 + 8

=> 2y = 20

=> y = 10

From (i)

x = 5y – 8 = 5 x 10 – 8 = 50 – 8 = 42

Present age of father = 42 years

and age of son = 10 years

**Answer
10** :

Let age of A = x years

and age of B = y years

According to the conditions,

x = y + 2

=> y = x – 2 ….(i)

Age of A’s’ father = 2x

Age of B’s sisters = y/2

2x – 2y = 40

4x – y = 80 ….(ii)

4x – (x – 2) = 80

=> 4x – x + 2 = 80

3x = 80 – 2 = 78

x = 26

A’s age = 26 years

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