Question

The cost of 4 chairs and 5 tables is Rs 6600 and the cost of 5 chairs and 3 tables is Rs 5000 at the same prices. What are the prices of a table and a chair? ​

Answer 1

Answer :

Cost of a chair = Rs 400

Cost of a table = Rs 1000

Step-by-step explanation :

Given,

• The cost of 4 chairs and 5 tables is Rs 6600
• the cost of 5 chairs and 3 tables is Rs 5000

Let

• cost of 1 chair be Rs x
• cost of 1 table be Rs y

The cost of 4 chairs and 5 tables is Rs 6600

               4x + 5y = Rs 6600 --- [ 1 ]

The cost of 5 chairs and 3 tables is Rs 5000

               5x + 3y = Rs 5000

Multiply equation [1] with 5,

 5(4x + 5y) = 5(Rs 6600)

  20x + 25y = Rs 33000 --- [ 3 ]

Multiply equation [2] with 4,

  4(5x + 3y) = 4(Rs 5000)

  20x + 12y = Rs 20000 --- [ 4 ]

Subtract equation [4] from equation [3],

 equation [3] - equation [4]

20x + 25y - (20x + 12y) = Rs (33000 - 20000)

20x + 25y - 20x - 12y = Rs 13000

          13y = Rs 13000

              y = Rs 13000/13

              y = Rs 1000

Substitute y = Rs 1000 in equation [1],

  4x + 5y = Rs 6600

 4x + 5(1000) = Rs 6600

 4x + 5000 = Rs 6600

  4x = Rs (6600 - 5000)

  4x = Rs 1600

    x = Rs 1600/4

    x = Rs 400

Therefore,

Cost of a chair = Rs 400

Cost of a table = Rs 1000

Verification:

• The cost of 4 chairs and 5 tables is Rs 6600

4(Rs 400) + 5(Rs 1000) = Rs 6600

 Rs 1600 + Rs 5000 = Rs 6600

   Rs 6600 = Rs 6600

• the cost of 5 chairs and 3 tables is Rs 5000

5(Rs 400) + 3(Rs 1000) = Rs 5000

 Rs 2000 + Rs 3000 = Rs 5000

     Rs 5000 = Rs 5000

Hence verified!