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A shopkeeper sell a T.V for `3000 and makes a profit of15%, he sells a different T.V at a loss of 10%. Over all, he neither gains nor loses. What is cost price of the second T.V?
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A shopkeeper sell a T.V for `3000 and makes a profit of15%, he sells a...
Problem:

A shopkeeper sells a T.V for `3000 and makes a profit of 15%. He sells a different T.V at a loss of 10%. Over all, he neither gains nor loses. What is the cost price of the second T.V?

Solution:

Let's assume the cost price of the first TV (which was sold at a profit of 15%) is CP1, and the cost price of the second TV (which was sold at a loss of 10%) is CP2.

Given that the profit percentage on the first TV is 15%, we can calculate its selling price (SP1) as follows:
SP1 = CP1 + Profit
SP1 = CP1 + (15/100)*CP1
SP1 = 1.15*CP1

Similarly, the selling price of the second TV (SP2) can be calculated as follows:
SP2 = CP2 - Loss
SP2 = CP2 - (10/100)*CP2
SP2 = 0.9*CP2

Now, we are given that the shopkeeper neither gains nor loses over all, which means that the total selling price of both TVs is equal to their total cost price. Mathematically, we can represent this as follows:
SP1 + SP2 = CP1 + CP2

Substituting the values of SP1 and SP2 from the above calculations, we get:
1.15*CP1 + 0.9*CP2 = CP1 + CP2

Simplifying the above equation, we get:
0.15*CP1 = 0.1*CP2
CP1/CP2 = 2/3

Therefore, the cost price of the second TV is (2/3) times the cost price of the first TV. Since we are given that the cost price of the first TV is `3000, we can calculate the cost price of the second TV as follows:
CP2 = (3/2)*CP1
CP2 = (3/2)*`3000
CP2 = `4500

Hence, the cost price of the second TV is `4500.
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A shopkeeper sell a T.V for `3000 and makes a profit of15%, he sells a different T.V at a loss of 10%. Over all, he neither gains nor loses. What is cost price of the second T.V?
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