- 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-3.7
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.8
- RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.9
- 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-3.7 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.8 |
RD Chapter 3- Pair of Linear Equations in Two Variables Ex-3.9 |
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 cost of 1 pen = ₹ x

and cost of 1 pencil = ₹ y

According to the conditions,

5x + 6y = 9 ….(i)

3x + 2y = 5 …(ii)

Multiplying (i) by 1 and (ii) by 3, we get

Cost of one pen = ₹ 32

and cost of one pencil = ₹ 14

**Answer
2** :

Let the cost of 1 audio cassette = ₹ x

and cost of 1 video cassette = ₹ y

According to the condition,

7x + 3y= 1110 ….(i)

5x + 4y = 1350 ….(ii)

Multiplying (i) by 4 and (ii) by 3,

**Answer
3** :

Let number of pens = x

and number of pencils = y

x + y = 40 ….(i)

In second case,

number of pens = x – 5

and number of pencils = y + 5

(y + 5) = 4 (x – 5) => y + 5 = 4x – 20

4x – y = 5 + 20 => 4x – y = 25 ….(ii)

Adding (i) and (ii)

5x = 65 => x = 13 [From (i) ]

13 + y = 40 => y = 40 – 13 = 27

Hence number of pens = 13

and number of pencils = 27

**Answer
4** :

Let cost of 1 table = ₹ x

and cost of 1 chair = ₹ y

According to the conditions,

4x + 3y = 2250 ….(i)

3x + 4y= 1950 ….(ii)

Multiplying (i) by 4 and (ii) by 3, we get

**Answer
5** :

Let cost of 1 bag = ₹ x

and cost of 1 pen = ₹ y

According to the conditions,

3x + 4y = 257 ….(i)

4x + 3y = 324 ….(ii)

Multiplying (i) by 3 and (ii) by 4, we get

**Answer
6** :

Let the cost 1 book = ₹ x

and cost of 1 pen = ₹ y

Now according to the conditions,

5x + 7y = 79 ….(i)

7x + 5y = 77 ….(ii)

Multiplying (i) by 5 and (ii) by 7, we get

Substituting the value of x in (i)

5 x 6 + 7y = 79

=> 30 + 7y = 79

=> 7y = 79 – 30 = 49

y = 7

Cost of 1 book and 2 pens = 6 + 2 x 7 = 6 + 14 = 20

**Answer
7** :

Let the cost price of the table be ₹ x

and the cost price of the chair by ₹ y.

The selling price of the table, when it is sold at a profit of 10%

110x + 125y = 105000

and 125x + 110y = 106500

On adding and subtracting these equations, we get

235x + 235y = 211500

and 15x – 15y= 1500

i.e., x + y = 900 …(iii)

and x – y = 100 …(iv)

Solving equation (iii) and (iv), we get

2x = 1000

x = 500

500 + y = 900

=> y = 900 – 500

y = 400

x = 500, y = 400

So, the cost price of the table is ₹ 500 and the cost price of the chair is ₹ 400.

Susan invested certain amount of money in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. She received ₹ 1860 as annual interest. However, had she interchanged the amount of investment in the two schemes, she would have received 720 more as annual interest. How much money did she invest in each scheme?

[NCERT Exemplar]

**Answer
8** :

Let the amount of investments in schemes A and B be ₹ x and ₹ y, respectively.

Case I:

Interest at the rate of 8% per annum on scheme A + Interest at the rate of 9% per annum on scheme B = Total amount received

Case II:

Interest at the rate of 9% per annum on scheme A + Interest at the rate of 8% per annum on scheme B = ₹ 20 more as annual interest

**Answer
9** :

Let cost of 1 bat = ₹ x

and cost of 1 ball = ₹ y

According to the conditions,

7x + 6y = 3800 ….(i)

3x + 5y = 1750 ….(ii)

Multiplying (i) by 5 and (ii) by 6, we get

**Answer
10** :

Let the fixed charge for the book = ₹ x

and let extra charge for each day = ₹ y

According to the given conditions,

x + 4y = 27 ….(i)

x + 2y = 21 ….(ii)

Subtracting,

2y = 6 => y = 3

Substituting the value of y in (i)

x + 4 x 3 = 27

=> x + 12 = 27

=> x = 27 – 12 = 15

Amount of fixed charge = ₹ 15

and charges for each extra day = ₹ 3

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