Question

4 chairs and 3 tables cost₹21000 and 5 chairs and 2 tables cost₹17500 .find the cost of a chair and a table separately?

Answer 1

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 = 21000 ----{1}

• 5x + 2y = 17500 ----{2}

Now, multiply eq. {1} by 2

• 8x + 6y = 42000 ----{3} and similarly,

Multiply eq. {2} by 3

• 15x + 6y = 52500 ----{4}

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

15x + 6y = 52500

- (8 + 6y) = 42000

______________

7x = 10500

x = 10500/7

x = 1500

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

➜ 4x + 3y = 21000

➜ 4*(1500) + 3y = 21000

➜ 6000 + 3y = 21000

➜ 3y = 21000 - 6000

➜ 3y = 15000

➜ y = 15000/3

➜ y = 5000

Answer : Hence, the cost of one chair is Rs 1500 and the cost of one table is Rs 5000.

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

➜ 4x + 3y = 2100

➜ 4*(1500) + 3*(5000) = 2100

➜ 6000 + 1500 = 21000

➜ 21000 = 21000

Hence, it's verified]