Question

4 tables and 3 chairs cost rs 2100 and 5 tables and 2 chairs cost rs 1750. find the cost of 1 table and 1 chair

Answer 1

Let us assume, the cost of table is Rs t and cost of chairs is Rs c

Given:

4t + 3c = 2100 ----------------1

and 

5t + 2c = 1750 -----------------2

Multiply equation 1 by 2 and equation 2 by 3

8t + 6c = 4200 ----------------3

and

15t + 6c = 5250 ------------------4

Subtract equation 3 from equation 4

7t = 1050

t = Rs 150

Substitute the value of c in equation 1

4 * 150 + 3c = 2100

600 + 3c = 2100

3c = 1500

c = Rs 500

Therefore, the cost of a table is Rs 150 and the cost of a chair is Rs 500

Answer 2

Given data : 4 chairs and 3 tables cost Rs 2100 and 5 chairs and 2 tables cost Rs 1750.

Solution : Let, the cost of one chair be x and the cost of one table be y.

Now, according to the given data;

• 4x + 3y = 2100 ----{1}

• 5x + 2y = 1750 ----{2}

Now, multiply eq. {1} by 2

• 8x + 6y = 4200 ----{3} and similarly,

Multiply eq. {2} by 3

• 15x + 6y = 5250 ----{4}

Now, subtract eq. {3} from eq. {4}

15x + 6y = 5250

- (8 + 6y) = 4200

______________

7x = 1050

x = 1050/7

x = 150

Now, put value of x in eq. {1}

➜ 4x + 3y = 2100

➜ 4*(150) + 3y = 2100

➜ 600 + 3y = 2100

➜ 3y = 2100 - 600

➜ 3y = 1500

➜ y = 1500/3

➜ y = 500

Answer : Hence, the cost of one chair is Rs 150 and the cost of one table is Rs 500.

[Verification : Put vale of x and y in eq. {1}

➜ 4x + 3y = 2100

➜ 4*(150) + 3*(500) = 2100

➜ 600 + 1500 = 2100

➜ 2100 = 2100

Hence, it's verified]