Question

The cost of 3 chairs and 2 tables = Rs 700. The cost of 5 chairs and 3 tables =Rs 1100. A man purchased 2 chairs and 2 tables & paid Rs 700 to the shopkeeper. But the shopkeeper says its not the correct amount and returns it to the man. Find the amount returned to the man.

Answer 1

Let the cost of a chair is Rs C and cost of a table is Rs T.
Given 
3C + 2T = Rs 700 -------1
and
5C + 3T = Rs 1100.......2
 Solve these two linear equations
Multiply Eqn 1 by 5 and eqn 2 by 3
15C + 10T = Rs 3500 ---------3
and
15C + 9T = Rs 3300 ---------4
Substract eqn 4 from 3
T = 200
Substitute the value of T in Eqn 1
3C + 2 * 200 = Rs 700
3C + 400 = Rs 700
3C = 300
C= Rs 100
Cost of a Table is Rs 200 and Cost of a chair is Rs 100
Therefore cost of 2 Chair is 2 * 100 = Rs 200
and Cost of 2 Tables = 2 * 200 = Rs 400
Total Cost of the furniture is Rs 200 + Rs 400 = Rs 600
Man Paid Rs 700 to the shopkeeper.
Therefore shopkeeper returned Rs 700 - Rs 600 = Rs 100.