Let's solve this problem step-by-step:
Given that Hitesh sells an article at \(\frac{4}{13}\) of its marked price and incurs a loss of 30%. Let the marked price be \(M\).
Thus, the selling price (SP) at a loss of 30% is:
\(\text{SP}_1 = \frac{4}{13} \times M\)
Let the cost price (CP) of the article be \(C\). Given a loss of 30%, we have:
\(\text{SP}_1 = C - \frac{30}{100} \times C = 0.7 C\)
Equating the two SP expressions, we get:
\(\frac{4}{13} \times M = 0.7 \times C\)
From this, we find the relationship between \(M\) and \(C\):
\(C = \frac{4M}{13 \times 0.7}\)
Now, if the article is sold at 60% of its marked price, we find the new selling price \(\text{SP}_2\):
\(\text{SP}_2 = 0.6 \times M\)
The profit percentage can be calculated using the formula:
\(\text{Profit \%} = \left( \frac{\text{SP}_2 - C}{C} \right) \times 100\)
Substitute \(\text{SP}_2\) and \(C = \frac{4M}{13 \times 0.7}\) into this formula:
\(\text{Profit \%} = \left( \frac{0.6M - \frac{4M}{13 \times 0.7}}{\frac{4M}{13 \times 0.7}} \right) \times 100\)
Simplify the expression:
\(\text{Profit \%} = \left( \frac{0.6M - \frac{4M}{9.1}}{\frac{4M}{9.1}} \right) \times 100\)
\(= \left( \frac{0.6M \times 9.1 - 4M}{4M} \right) \times 100\)
\(= \left( \frac{5.46M - 4M}{4M} \right) \times 100\)
\(= \left(\frac{1.46}{4}\right) \times 100\)
\(= 36.50\%\)
Therefore, when Hitesh sells the article at 60% of its marked price, he makes a profit of 36.50%. Thus, the correct answer is 36.50%.
Important Questions from Successive Selling
A dealer sold an article at a loss of 2%. Had he sold it for Rs. 44 more, he would have gained 20%. Find the cost price of the article
Radha purchased a Computer table for Rs. 10000 and a Centre table for Rs. 5000. She sold Computer table with 8% profit. With what profit percent should she sell the Centre table so as to gain 10% on the whole transaction.
If selling price of 75 articles is equal to cost price of 60 articles, then the approximate loss or gain percent is :
A.T.V. is sold at 8% gain. Had it been sold for Rs.2553 less; there would have been loss of 15%. To gain 18%, the selling price (in Rs.) of T.V. would be:
Some fruits are bought at 15 for Rs. 140 and an equal number of fruits at 10 for Rs. 120. If all the fruits are sold at Rs. 132 per dozen, then what is the profit percent in the entire transaction?
