1.a cloth merchant on selling 27 metres of cloth obtains a profit equal to the selling price of 9 metres of the same cloth . find the profit percent.
2. by selling cloth at rupees 9 per metre a shopkeeper loses 10% . at what rate should it be sold so as to gain 15%.
To solve these problems, we need to understand the concepts of profit and loss percentage.
1. Let's solve the first problem:
The cloth merchant sells 27 meters of cloth, which gives him a profit equal to the selling price of 9 meters of the same cloth.
To find the profit percentage, we need to determine the profit earned by the merchant. The selling price of 9 meters of cloth is equal to the profit.
Let's assume the cost price (CP) of 1 meter of cloth is 'x' rupees.
Profit earned = Selling price (SP) of 9 meters of cloth = 9x rupees
Since the profit earned is equal to the selling price, we can conclude that the selling price (SP) is twice the cost price (CP) of 9 meters of cloth.
SP = 2 * CP
9x = 2 * CP
CP = (9x / 2)
Profit Percentage = (Profit / Cost Price) * 100
Profit Percentage = ((2 * CP - CP) / CP) * 100
Profit Percentage = ((CP) / CP) * 100
Profit Percentage = 100
Therefore, the profit percentage is 100%.
2. Let's solve the second problem:
The shopkeeper sells cloth at 9 rupees per meter, resulting in a loss of 10%.
To find the selling price (SP) at which the shopkeeper can gain 15%, we'll use the formula:
Selling Price (SP) = (100 + Gain Percentage) / 100 * Cost Price (CP)
Let's assume the cost price (CP) of 1 meter of cloth is 'x' rupees.
Given: Loss Percentage = 10%
Profit Percentage = 15%
Loss in selling price = (Loss Percentage / 100) * CP
Loss in selling price = (10 / 100) * CP = 0.10 * CP
The selling price at a loss = CP - Loss in selling price
SP = CP - 0.10 * CP = 0.90 * CP
To calculate the selling price to gain 15%:
SP = (100 + 15) / 100 * CP = 1.15 * CP
To gain 15%, the selling price should be 1.15 times the cost price.
Therefore, we have:
0.90 * CP = 1.15 * CP
Solving for CP:
0.90 * CP - 1.15 * CP = 0
-0.25 * CP = 0
CP = 0
It implies that the cost price of the cloth is 0 rupees, which is not possible.
Hence, there is a mistake or inconsistency in the given information.