Question

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

Let cost of 1 chair be Rs. x

cost of be table be Rs. y

According to the question,

cost of 4 chairs and 3 tables is Rs. 2100

So, 4x + 3y = 2100 ……...... (i)

Also,

cost of 5 chairs and 2 tables is Rs.1750

So 5x + 2y = 1750 ……….. (ii)

from equation (i) and (ii)

2 × (i) gives 8x + 6y = 4200 ……… (iii)

3 × (ii) gives 15x + 6y = 5250 ……….. (iV)

{(iii) - (iV)} ,

15x + 6y – 8x – 6y = 5250 – 4200

7x = 1050

x=1050/7

So, x = 150

putting the value of x in equation (ii), we get

⇒ 5(150) + 2y = 1750

⇒750 + 2y = 1750

⇒2y= 1750 – 750

⇒2y = 1000

⇒ y =1000/2

⇒ y =500

Hence, cost of each chair, x = Rs. 150

cost of each table , y = 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]