Question

Jamila sold a table and a chair for ₹ 1050, thereby making a profit of 10% on a table and 25% on the chair. If she had taken a profit of 25% on the table and 10% on the chair she would have got ₹ 1065. Find the cost price of each.

Answer 1

Given: Jamila sold a table and a chair together for ₹ 1050, making 10% profit on the table and 25% on the chair. If instead she had taken 25% on the table and 10% on the chair, the total would be ₹ 1065.

Step-wise calculation:

1. Let the cost price (CP) of the table = x and of the chair = y.

2. From the first scenario (10% on table, 25% on chair):

1.10x + 1.25y = 1050   ...(Equation 1)

3. From the second scenario (25% on table, 10% on chair):

1.25x + 1.10y = 1065   ...(Equation 2)

4. Subtract Equation 1 from Equation 2:

(1.25x – 1.10x) + (1.10y – 1.25y) = 1065 – 1050

0.15x – 0.15y = 15

0.15(x – y) = 15 

⇒ x – y = 100

So x = y + 100.

5. Substitute x = y + 100 into Equation 1:

1.10(y + 100) + 1.25y = 1050

1.10y + 110 + 1.25y = 1050

2.35y + 110 = 1050

2.35y = 940

`y = 940/2.35`

y = 400

6. Then x = y + 100

= 400 + 100

= 500

Cost price of the table = ₹ 500.

Cost price of the chair = ₹ 400.