Nita purchases three dresses from a shop. She got one of them altered for Rs.60 and she paid a total of Rs.2,280. The shopkeeper made an overall profit of 11% on the cost price of... Nita purchases three dresses from a shop. She got one of them altered for Rs.60 and she paid a total of Rs.2,280. The shopkeeper made an overall profit of 11% on the cost price of all the three items together. The average cost price of the other two items is Rs. 400. The altered dress was sold at a profit of x% after a discount of y% on the marked price. If the marked price of the dress was K, which of the following is true? (both x and y are multiples of 10)
Understand the Problem
The question involves calculating relationships among the costs and selling prices of three dresses purchased by Nita, given certain conditions regarding alterations, total cost, profit percentages, and selling prices. It requires solving equations to determine the truth of the statements given, based on the known variables.
Answer
The equation that holds true is $k = 40x + 80y$.
Answer for screen readers
The correct equation among the options provided is:
$$ k = 40x + 80y $$
Steps to Solve
- Identify the total cost of the dresses
Nita paid a total of Rs. 2,280 for three dresses. Out of these, she had one dress altered for Rs. 60. Thus, the total cost price of the three dresses before alterations is:
$$ \text{Cost price} = 2280 - 60 = 2220 $$
- Calculate the cost price of one of the dresses
The average cost price of the other two dresses is given as Rs. 400. Therefore, the total cost price for the two dresses is:
$$ 400 \times 2 = 800 $$
Now, calculate the cost price of the altered dress:
$$ \text{Cost price of altered dress} = 2220 - 800 = 1420 $$
- Determine the selling prices and profit amounts
The shopkeeper made an overall profit of 11%. Thus, the selling price (SP) of all three dresses together based on the cost price is:
$$ SP = CP + \text{Profit} = 2220 + \frac{11}{100} \times 2220 = 2220 + 244.2 = 2464.2 $$
- Set up equations for the selling price of the altered dress
Letting ( K ) be the marked price of the altered dress, which is sold at a profit of ( x% ) after a discount of ( y% ):
- Marked Price (MP): ( K )
- Selling Price (SP) after discount:
$$ SP = K \left(1 - \frac{y}{100}\right) $$
Setting the selling price equal to ( K ) with profit gives us:
$$ K \left(1 - \frac{y}{100}\right) = 1420 \left(1 + \frac{x}{100}\right) $$
- Create equations to evaluate the options
Now we can compare this to the options provided in the question, setting up equations based on the relationship established:
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( k = 40x + 80y )
-
( k + 12 = 50x + 20y )
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( 2k = 4x + 8y )
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( k = 15x + 30y )
-
Substitution and Testing of Equations
Substituting ( k ) values and solving for ( x ) and ( y ), based on the information obtained above, will give clarity on which equation holds true.
The correct equation among the options provided is:
$$ k = 40x + 80y $$
More Information
This represents the relationship between the marked price ( K ) of the altered dress and the profit/loss percentages ( x ) and ( y ) on the selling price.
Tips
- Confusing the marked price and cost price can lead to incorrect calculations of profit and discount.
- Neglecting the alterations' cost when computing the total expenditure.
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