the marked price of a ceiling fan is rs.3500.the discount allowed on it is 15%. the shopkeeper offers an additional discount of 5% due to the change in season.what would be the loss if it cost rs.3000 to the shopkeeper.
Answers
Assume the original cost price as x and the selling price including GST as y. Now, in the first step find the net marked price by including the GST of Rs. 3500 in it. To do this add 3500 and 12% of 3500. In the next step consider the discount of 20% on this overall price obtained to get the selling price and therefore the value of y. Now, use the formula profit% = (y−xx)×100% and substitute the obtained value of y and given profit% to calculate the value of x.
Complete step by step solution:
Here we have been provided with the marked price of an article with the rate of GST as 12% and we are asked to find the original cost price and the selling price including the GST if the discount provided by the shopkeeper is 20% and he is making a profit of 10%.
Let us assume the original cost price as x and the selling price including GST as y. Now, the marked price including the GST will be the sum of Rs. 3500 and 12% of Rs. 3500. So we have,
⇒ Net price of the article = 3500+(12100×3500)
⇒ Net price of the article = Rs. 3920
Considering the discount of 20% provided by the shopkeeper on this net price we get the selling price of the article including the GST, so we get,
⇒y=3920−20100×3920⇒y=3920−15×3920
⇒ y = Rs. 3136
Therefore the selling price including the GST is Rs. 3136.
Now, it is given that the shopkeeper makes a profit of 10% on this selling price. We know that the profit% = profitcost price×100% where profit = selling price – cost price, so substituting the obtained and the given values we get,
⇒10%=y−xx×100%⇒110=3136x−1⇒110+1=3136x
On simplifying we get,
⇒x=3136×1011
⇒ x = Rs. 2850.9
Therefore, the original cost price is nearly Rs. 2851
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