Actual Prices of T.V. and Fridge
Video Explanation
Question
On selling a T.V. at 5% gain and a fridge at 10% gain, the shopkeeper gains Rs 2000. But if he sells the T.V. at 10% gain and the fridge at 5% loss, he gains Rs 1500. Find the actual prices of the T.V. and fridge.
Solution
Step 1: Let the Variables
Let the cost price of T.V. = Rs \(x\)
Let the cost price of fridge = Rs \(y\)
Step 2: Form the Equations
First condition:
\[ 5\% \text{ of } x + 10\% \text{ of } y = 2000 \]
\[ 0.05x + 0.10y = 2000 \quad (1) \]
Second condition:
\[ 10\% \text{ of } x – 5\% \text{ of } y = 1500 \]
\[ 0.10x – 0.05y = 1500 \quad (2) \]
Step 3: Remove Decimals
Multiply equations (1) and (2) by 100:\[ 5x + 10y = 200000 \quad (3) \]
\[ 10x – 5y = 150000 \quad (4) \]
Simplify equation (3) by dividing by 5:\[ x + 2y = 40000 \quad (5) \]
Simplify equation (4) by dividing by 5:\[ 2x – y = 30000 \quad (6) \]
Step 4: Solve by Elimination Method
Multiply equation (6) by 2:\[ 4x – 2y = 60000 \quad (7) \]
Add equations (5) and (7):\[ (x + 2y) + (4x – 2y) = 40000 + 60000 \]
\[ 5x = 100000 \]
\[ x = 20000 \]
Step 5: Find the Value of y
Substitute \(x = 20000\) in equation (6):\[ 2(20000) – y = 30000 \]
\[ 40000 – y = 30000 \]
\[ y = 10000 \]
Conclusion
Cost price of T.V.:
\[ \boxed{Rs\; 20000} \]
Cost price of fridge:
\[ \boxed{Rs\; 10000} \]
Final Answer (For Exam)
Cost price of T.V. = Rs 20,000
Cost price of fridge = Rs 10,000