Question

A shopkeeper sold a TV set for Rs. 17940 (price inclusive of a discount of 8%) and gained 19.6%. If no discount is allowed, then what will be his gain per cent?

Answer 1

Hint: First remove the discount and find the original price of the TV set. This will be the original selling price. Now using the profit percentage and given selling price find the cost price of Tv set. From this cost price and calculated selling price find the profit. Which is the required result in this case.

Complete step-by-step answer:
Given selling price in the question with discount is:
SP = 17940
Given discount on this TV set as given in the question is:
Discount= 8%
Gained profit with this SP selling prices is given as: 19.6%
By basic knowledge the relation between profits, cost price (CP), selling price (SP), Profit(P) is given byis given by:
$CP=100\times \dfrac{SP}{100+P}............(i)$
By substituting the given values, we get the cost prices as:
$CP=100\times \dfrac{17940}{100+19.6}$
By simplifying the value of denominator, we get it as:
$CP=\dfrac{100\times 17940}{119.6}$
By simplifying the numerator of the above value we get:
$CP=\dfrac{1794000}{119.6}$
By simplifying the whole term, we get value of CP as:
CP=15000 …(ii)
The cost price remains constant In both cases:
Now, we need the value of selling price without discount. The discount is given as 8%. So, if x is the original selling price we can write:
x=8% of x= given selling price.
By definition of percentage we can find the value of second term as:
$8%\,of\,x=\dfrac{8}{100}\times x$
By simplifying the term above, we can write it as:
$\dfrac{8x}{100}$
By substituting this into equation, we get it as follows:
$x-\dfrac{8x}{100}=17940$
By taking least common multiple and cross multiplication, we get:
92x=1794000
By dividing with 92 on both sides, we get it as:
X=19500
As the original price is 19500 and cost price is 15000,
By substituting these into equation (i) we get it as:
$15000=100\times \dfrac{19500}{100+P}$
By cross multiplying and simplification, we can get it as:
100+P=130
By subtracting 100 on both sides, we get it as:
P=130-100
By simplifying the above equation, we get value of P as:
P=30
Therefore option (d) is the correct answer.

Note: Be careful while calculating the cost price. The whole answer depends on it. Do not substitute P as P/100 it is already considered as P%. so, you can directly substitute 19.6 generally students confuse and substitute 0.196 which will lead you to wrong results.