Samreen sells a keyboard for ₹1,260 at a profit of 25%, and another keyboard for ₹1,440 at a loss of 10%. What is her total gain or loss percentage?

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Accepted Answer

Step 1: Calculate the cost price of the first keyboard.
Selling Price (SP1) = ₹1260, Profit = 25%
Profit% = (SP - CP)/CP * 100
Let CP1 be the cost price of the first keyboard.
25 = (1260 - CP1)/CP1 * 100
=> 25/100 = (1260 - CP1)/CP1
=> 1/4 = (1260 - CP1)/CP1
=> CP1/4 = 1260 - CP1
=> CP1 + CP1/4 = 1260
=> (5/4)CP1 = 1260
=> CP1 = (1260 * 4)/5 = ₹1008

Step 2: Calculate the cost price of the second keyboard.
Selling Price (SP2) = ₹1440, Loss = 10%
Loss% = (CP - SP)/CP * 100
Let CP2 be the cost price of the second keyboard.
10 = (CP2 - 1440)/CP2 * 100
=> 10/100 = (CP2 - 1440)/CP2
=> 1/10 = (CP2 - 1440)/CP2
=> CP2/10 = CP2 - 1440
=> CP2 - CP2/10 = 1440
=> (9/10)CP2 = 1440
=> CP2 = (1440 * 10)/9 = ₹1600

Step 3: Calculate total cost price and total selling price.
Total CP = CP1 + CP2 = 1008 + 1600 = ₹2608
Total SP = SP1 + SP2 = 1260 + 1440 = ₹2700

Step 4: Calculate total gain or loss.
Total Gain = Total SP - Total CP = 2700 - 2608 = ₹92

Step 5: Calculate gain percentage.
Gain% = (Gain / Total CP) * 100 = (92 / 2608) * 100
= (92 * 100) / 2608
= 9200 / 2608
= 3.527% approximately

Convert 0.527% to fraction:
0.527 * 163 ≈ 86
So, gain% = 3 86/163 %

Therefore, Samreen has a total gain of 3 86/163 %.

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