- 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-3.8
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.9
- 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-3.8 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.9 |
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 first number = x

and second number = y

x + y = 8 ….(i)

and x + y = 4 (x – y)

=> 4 (x – y) = 8

=> x – y = 2 ….(ii)

Adding (i) and (ii),

2x = 10 => x = 5

Subtracting (ii) from (i),

2y = 6 => y = 3

Numbers are 5, 3

**Answer
2** :

Let unit’s digit = x

and ten’s digit = y

Number = x + 10y

Now according to the condition

x + y = 13 ….(i)

Number after interchanging their digits,

y + 10x

Now y + 10x – x – 10y = 45

9x – 9y = 45

=> x – y = 5

x – y = 5 ….(ii)

Adding (i) and (ii),

2x = 18 => x = 9

subtracting 8

2y = 8 => y = 4

Number = x + 10y = 9 + 4 x 10 = 9 + 40 = 49

**Answer
3** :

Let units digit = x

and ten’s digit = y

Number = x + 10y

and number by reversing their digits = y+ 10x

Now according to the conditions,

x + y = 5 ….(i)

and y + 10x = x + 10y + 9

=> y + 10x – x – 10y = 9

=> 9x – 9y = 9x – y = 1 ….(ii)

(Dividing by 9)

Adding we get:

2x = 6 => x = 3

and subtracting,

2y = 4 => y = 2

Number = x + 10y = 3 + 10 x 2 = 3 + 20 = 23

**Answer
4** :

Let the ones digit = x

and tens digit = y

Number = x + 10y

and number by reversing the order of digits = y +10x

According to the conditions,

x + y = 15 ….(i)

y + 10x = x + 10y + 9

=> y + 10x – x – 10y = 9

=> 9x – 9y = 9

=>x – y = 1 ……..(ii)

(Dividing by 9)

Adding (i) and (ii)

2x = 16

x = 8

and subtracting, 2y = 14 => y = 7

Number = x + 10y = 8 + 10 x 7 = 8 + 70 = 78

**Answer
5** :

Sum of two-digit number and number formed by reversing its digits = 66

Let units digit = x

Then tens digit = x + 2

Number = x + 10 (x + 2) = x + 10x + 20 = 11x + 20

and by reversing its digits

Unit digit = x + 2

and tens digit = x

Number = x + 2 + 10x = 11x + 2

11x + 20 + 11x + 2 = 66

=> 22x + 22 = 66

=> 22x = 66 – 22 = 44

=> x = 2

Number = 11x + 20 = 11 x 2 + 20 = 22 + 20 = 42

and number by reversing its digits will be 11x + 2 = 11 x 2 + 2 = 22 + 2 = 24

Hence numbers are 42 and 24

**Answer
6** :

Let first number = x

and second number = y

x + y = 1000 ……..(i)

**Answer
7** :

Let the unit’s digit of the number = x

and ten’s digit = y

Number = x + 10y

By reversing the digits, the new number will be = y +10x

According to the condition,

x + 10y + y + 10x = 99

=> 11x + 11y = 99

=> x + y = 9 ….(i)

and x – y = 3 ….(ii)

Adding we get,

2x = 12

x = 6

and subtracting, 2y = 6

y= 3

Number = x + 10y = 6 + 10 x 3 = 6 + 30 = 36

**Answer
8** :

Let the unit digit of the number = x

and tens digit = y

Number = x + 10y

and number after reversing the order of digits = y + 10x

According to the conditions,

x + 10y = 4 (x + y)

=> x + 10y = 4x + 4y

=> 4x + 4y – x – 10y = 0

=> 3x – 6y = 0

=> x – 2y = 0

=> x = 2y ….(ii)

and x + 10y + 18 = y + 10x

=> x + 10y – y – 10x = -18

=> – 9x + 9y = -18

=> x – y = 2 ….(ii)

(Dividing by – 9)

=> 2y – y = 2 {From (i}

=> y = 2

x = 2y = 2 x 2 = 4

Number = x + 10y = 4 + 10 x 2 = 4 + 20 = 24

**Answer
9** :

Let unit digit of the number = x

and ten’s digit = y

Number = x + 10y

and number after reversing the digits = y + 10x

According to the conditions,

x + 10y = 4 (x + y) + 3

=> x + 10y = 4x + 4y + 3

=> x + 10y – 4x – 4y = 3

=> -3x + 6y = 3

=> x – 2y = -1 ….(i)

(Dividing by -3)

and x + 10y + 18 = y + 10x

=> x + 10y – y – 10x = -18

=> -9x + 9y = -18

=>x – y = 2 ….(ii)

(Dividing by 9)

Subtracting (i) from (ii)

y = 3

x – 3 = 2

=>x = 2 + 3 = 5 {From (ii)}

Number = x + 10y = 5 + 10 x 3 = 5 + 30 = 35

**Answer
10** :

Let units digit of the number = x

and ten’s digit = y

then number = x + 10y

The number by reversing the digits = y+ 10x

According to the condition given,

x + 10y = 6 (x + y) + 4

=> x + 10y = 6x + 6y + 4

=> x + 10y – 6x – 6y = 4

=> -5x + 4y = 4 ….(i)

and x + 10y – 18 = y + 10x

=> x + 10y – y – 10x = 18

=> -9x + 9y = 18

=> x – y = -2 ….(ii)

(Dividing by 9)

=> x = y – 2

Substituting in (i),

-5 (y – 2) + 4y = 4

-5y + 10 + 4y = 4

-y = 4 – 10 = – 6

y = 6

Number = x + 10y = 4 + 10 x 6 = 4 + 60 = 64

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