Question

A shopkeeper sold a mobile phone for Rs. 12000. Had he offered a discount of 10% on the selling price, there would be a loss of 4%. What is the cost price of that Mobile phone?

Answer 1

Hint: It is said that the mobile phone was sold for Rs. 12000, so this is our selling price (SP). Similarly a discount% of 10% is given for a second case along with the loss% of 4%. Calculate Discount using the formula \[D=\left( \dfrac{discount\%}{100} \right)\cdot SP\] and then calculate a new selling price SP after subtracting discount the initial SP and find the correct answer.

Complete step-by-step answer:
The price for which any goods are bought for is the cost price (CP) and the price at which they are sold is called the selling price (SP).
By following the above said statement we conclude the selling price (SP) of the mobile phone is 12000 rupees.
If we assume the shopkeeper gave a discount of 10% then the loss percentage would be 4%. This implies the discount% = 10% of SP and loss% = 4%.
We can find the exact discount by using the formula discount \[D=\left( \dfrac{discount\%}{100} \right)\cdot SP\].
Applying the above formula we get,
\[D=\left( \dfrac{10}{100} \right)\cdot 12000\]
Dividing 10 by 100 we get,
\[D=\left( 0.01 \right)\cdot 12000\]
On multiplying 0.01 by 12000 we get the discount as,
D = 1200
After a discount of 1200 the new selling price (SP) would then be the difference of initial SP and the discount.
The above statement can be expressed mathematically as,
SP = 12000 – 1200
Subtracting 1200 from 12000 we get,
SP = 10800
We know the relation for cost price and loss\% is given as \[CP=\left( \dfrac{100}{100-loss\%} \right)\cdot SP\].
Applying the above mentioned formula to calculate cost price (CP) of the mobile phone,
\[CP=\left( \dfrac{100}{100-4} \right)\cdot 10800\]
Subtracting 4 from 100 in the denominator of the fraction,
\[CP=\left( \dfrac{100}{96} \right)\cdot 10800\]
On dividing 100 by 96 we get,
\[CP=\left( 1.04 \right)\cdot 10800\]
Multiplying 1.04 by 10800 to get the CP,
CP = 11250
Hence the cost price of the mobile phone is 11250 rupees.

Note: The possible error that you may encounter could be that you might have not taken the discount into consideration and solved it directly which would result in an incorrect answer. Another thing to take care of is the calculation of discount. After calculating the discount of 1200 rupees it must be subtracted from the selling price SP to find the new SP for the mobile phone in the case of the discount.