Cost Price of Table and Chair

Video Explanation

Question

Jamila sold a table and a chair for ₹1050, thereby making a profit of 10% on the 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.

Solution

Step 1: Let the Variables

Let the cost price of the table = ₹\(x\)

Let the cost price of the chair = ₹\(y\)

Step 2: Form the First Equation

Selling price of table at 10% profit:

\[ 1.10x \]

Selling price of chair at 25% profit:

\[ 1.25y \]

Total selling price:

\[ 1.10x + 1.25y = 1050 \quad (1) \]

Step 3: Form the Second Equation

Selling price of table at 25% profit:

\[ 1.25x \]

Selling price of chair at 10% profit:

\[ 1.10y \]

Total selling price:

\[ 1.25x + 1.10y = 1065 \quad (2) \]

Step 4: Remove Decimals

Multiply both equations by 20:

\[ 22x + 25y = 21000 \quad (3) \]

\[ 25x + 22y = 21300 \quad (4) \]

Step 5: Solve by Elimination Method

Multiply equation (3) by 25:

\[ 550x + 625y = 525000 \]

Multiply equation (4) by 22:

\[ 550x + 484y = 468600 \]

Subtract:

\[ 141y = 56400 \]

\[ y = 400 \]

Step 6: Find the Value of x

Substitute \(y = 400\) in equation (3):

\[ 22x + 25(400) = 21000 \]

\[ 22x + 10000 = 21000 \]

\[ 22x = 11000 \]

\[ x = 500 \]

Conclusion

Cost price of the table:

\[ \boxed{₹500} \]

Cost price of the chair:

\[ \boxed{₹400} \]