# A piece of cloth is sold for rs85.80 at a profit of 30%. if it had been sold at rs 7.50 per m ,the profit would have been rs 16.50.the length of the piece is ?

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x = 11

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## To find the length of the cloth, we can set up a proportion using the information given:

Let "x" be the length of the cloth in meters.

According to the problem, if the cloth is sold at Rs. 7.50 per meter, the profit would be Rs. 16.50.

Profit = Selling Price - Cost Price
16.50 = (7.50 * x) - Cost Price

We also know that the cloth is sold for Rs. 85.80 at a profit of 30%.

Profit = Selling Price - Cost Price
0.30 * Cost Price = 85.80 - (7.50 * x)

Now we can solve the two equations simultaneously:

0.30 * Cost Price = 85.80 - (7.50 * x) ...(1)
16.50 = (7.50 * x) - Cost Price ...(2)

Let's solve equation (1) for the Cost Price:

0.30 * Cost Price = 85.80 - (7.50 * x)
Cost Price = (85.80 - (7.50 * x)) / 0.30

Substitute the Cost Price into equation (2):

16.50 = (7.50 * x) - [(85.80 - (7.50 * x)) / 0.30]

Now, we can solve for "x" by simplifying the equation:

16.50 = (7.50 * x) - [286 - (30 * x)] / 0.30
16.50 = (7.50 * x) - [2860 - 30 * x] / 0.30
16.50 = (7.50 * x) - (9533.33 - 37.5 * x)
16.50 = 7.50 * x - 9533.33 + 37.5 * x
16.50 = 45 * x - 9533.33
16.50 + 9533.33 = 45 * x
9549.83 = 45 * x
x = 9549.83 / 45
x ≈ 212.22

Therefore, the length of the piece of cloth is approximately 212.22 meters.

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## To find the length of the piece of cloth, we can set up an equation based on the given information.

Let's assume the length of the cloth is 'L' meters.

Given that the cloth is sold at a profit of 30%, the selling price can be calculated as follows:
Selling price = Cost price + Profit
85.80 = Cost price + (30% of cost price)

To find the cost price, we can calculate:
Cost price = Selling price - Profit
Cost price = 85.80 - (30% of 85.80)

Now, let's calculate the cost price:

Cost price = 85.80 - (30/100 * 85.80)
Cost price = 85.80 - 25.74
Cost price = 60.06

Now we have the cost price of the cloth.

Next, we are given that if the cloth was sold at rs 7.50 per meter, the profit would be rs 16.50.

Considering the length of the cloth to be 'L' meters, the selling price would be:
Selling price = 7.50 * L

Using the same formula as before, we can set up an equation to find the cost price at rs 7.50 per meter:

Cost price = Selling price - Profit
60.06 = 7.50 * L - 16.50

Now, let's solve the equation for 'L', which will give us the length of the piece:

60.06 + 16.50 = 7.50 * L
76.56 = 7.50 * L

Dividing both sides by 7.50, we get:
L = 76.56 / 7.50

Therefore, the length of the piece of cloth is L = 10.208 meters (rounded to three decimal places).

So, the length of the cloth is approximately 10.208 meters.