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प्रश्न
A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.
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उत्तर
\[\text { Let the C . P of the article be Rs . x }. \]
\[\text { Original S . P = x } + \frac{25}{100}x\]
\[ = Rs . \frac{5x}{4}\]
\[\text { If he purchased it at 20 % less }, \]
\[\text { C . P = x } - \frac{20}{100}x\]
\[ = \text {Rs} . \frac{4x}{5}\]
\[\text { He sold the article at Rs 36 . 75 less } . \]
\[\text { So, the selling price = Rs }. \frac{5x}{4} - 36 . 75\]
\[\text { Given that he would have gained 30 % selling at that price } . \]
\[\text { Therefore, gain % } = \frac{S . P - C . P}{C . P} \times 100\]
\[S . P - C . P = \frac{5x}{4} - 36 . 75 - \frac{4x}{5}\]
\[ = \frac{5x}{4} - \frac{4x}{5} - 36 . 75\]
\[ = \frac{25x - 16x}{20} - 36 . 75\]
\[ = \frac{9x}{20} - 36 . 75\]
\[\text { So, gain % } = \frac{S . P - C . P}{C . P} \times 100\]
\[30 = \frac{\frac{9x}{20} - 36 . 75}{\frac{4x}{5}} \times 100\]
\[ = \left( \frac{9x}{20} - 36 . 75 \right) \times \frac{5}{4x} \times 100\]
\[ = \frac{9x - 735}{16x} \times 100\]
\[30 = \frac{9x - 735}{16x} \times 100\]
\[\frac{225x - 18375}{4x} = 30\]
\[225x - 18375 = 120x\]
\[105x = 18375\]
\[x = \frac{18375}{105}\]
\[ = 175\]
\[\text { So, the cost price of the article is Rs . 175 } .\]
संबंधित प्रश्न
The cost of an article was Rs 15,500. Rs 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article
A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs 300, find his profit percent.
A tradesman marks his goods at such a price that after allowing a discount of 15%, he makes a profit of 20%. What is the marked price of an article whose cost price is Rs 170?
Sambhajirao bought a machine from a factory for Rs. 80000. He paid the octroi tax of Rs. 1600 and spent Rs. 800 on transport besides Rs. 300 on porterage. He sold the machine for one lakh rupees. How much was his profit?
Some articles are bought at 2 for ₹ 15 and sold at 3 for ₹ 25. Find the gain percentage
What is the marked price of a hat which is bought for ₹ 210 at 16% discount?
A bicycle is purchased for ₹ 1800 and is sold at a profit of 12%. Its selling price is ______.
Sonal bought a bed sheet for ₹ 400 and sold it for ₹ 440. Her ______ % is ______.
Match the entries in Column I with the appropriate entries in Column II:
| Column I | Column II |
| (i) 3:5 | (A) ₹ 54 |
| (ii) 2.5 | (B) ₹ 47 |
| (iii) 100% | (C) ₹ 53 |
| (iv) `2/3` | (D) ₹ 160 |
| (v) `6 1/4%` | (E) 60% |
| (vi) 12.5% | (F) 25% |
| (vii) SP when CP = ₹ 50 and loss = 6 % | (G) `1/16` |
| (viii) SP when CP = ₹ 50 and profit = ₹ 4 | (H) 250% |
| (ix) Profit% when CP = ₹ 40 and SP = ₹ 50 | (I) ₹ 159 |
| (x) Profit% when CP = ₹ 50 and SP = ₹ 60 | (J) `66 2/3%` |
| (xi) Interest when principal = ₹ 800, Rate of interest = 10% per annum nd period = 2 years |
(K) 20% |
| (xii) Amount when principal = ₹ 150, Rate of interest = 6% per annum and period = 1 year |
(L) 0.125 |
| (M) 3 : 2 | |
| (N) ₹ 164 | |
| (O) 3 : 3 |
