Home
Class 14
MATHS
A person bought an item and sold it at a...

A person bought an item and sold it at a loss of 5%. If he had bought it for 10% less and sold it for ₹ 170 more, he would have had a profit of 20%, Find the cost price of this item. (nearest to ₹1)

A

₹1440

B

₹1308

C

₹1300

D

₹1500

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will define the cost price (CP) of the item and analyze the two conditions given in the question. ### Step 1: Define the Cost Price Let the cost price of the item be \( CP = x \). ### Step 2: Calculate Selling Price with 5% Loss If the item is sold at a loss of 5%, then the selling price (SP) can be calculated as: \[ SP_1 = CP - (5\% \text{ of } CP) = x - 0.05x = 0.95x \] ### Step 3: Calculate New Cost Price with 10% Less If the person had bought the item for 10% less, the new cost price would be: \[ CP_{new} = CP - (10\% \text{ of } CP) = x - 0.10x = 0.90x \] ### Step 4: Calculate Selling Price with 20% Profit If he sold it for ₹170 more than the previous selling price and made a profit of 20%, the new selling price can be calculated as: \[ SP_2 = CP_{new} + (20\% \text{ of } CP_{new}) = 0.90x + 0.20(0.90x) = 0.90x + 0.18x = 1.08x \] ### Step 5: Set Up the Equation According to the problem, the new selling price is also equal to the previous selling price plus ₹170: \[ SP_2 = SP_1 + 170 \] Substituting the expressions we found: \[ 1.08x = 0.95x + 170 \] ### Step 6: Solve for x Now, we will isolate \( x \): \[ 1.08x - 0.95x = 170 \] \[ 0.13x = 170 \] \[ x = \frac{170}{0.13} \approx 1307.69 \] ### Step 7: Round to the Nearest Rupee Rounding \( 1307.69 \) to the nearest rupee gives us: \[ CP \approx 1308 \] ### Final Answer Thus, the cost price of the item is approximately **₹1308**. ---
Promotional Banner

Similar Questions

Explore conceptually related problems

A businessman bought an article and sold it at a loss of 5%. If he had bought it for 10% less and sold it for 33 more, he would have had a profit of 30%. Find the cost price of this article.

A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.55 more,he would have had a profit of 40%. The cost price of the article is

A person bought an article and sold it at a loss of 20%. If he had bought it for 10% less and sold it for 55% more, then he would have made a profit of 50%. The C.P. of the article is

A man bought an article and sold it at a gain of 10% If the had bought it at 20% less and sold it for Rs 10 more, he would have made a profit of 40%. The cost price of the article is :

A man bought and article and sold it at a gain of 10%. If he had bought it at 20% less and sold it for Rs 10 more, he would have made a profit of 40%. Find the C.P. of the article?

A man bought an article and sold it at a gain of 5%. If he had bought it at 5% less and sold it for Rs. 1 less, he would have made a profit of 10%. The Cost Price(C.P.) of an article was

A person sold a table at a gain of 15% .Had he bought it for 25% less and sold it for Rs 60 less,he would have made a profit of 32%. The cost price of table was