The price (P) of a block of rectangular marble varies directly as the cube of its length (l cm). Mr Chan spends $400 on a block of marble. He cuts it into two blocks of equal length. He then sells these two blocks of marble.how to find mr chan's profit or lose and his porfit% or loss%

To solve this problem, we need to understand the concept of direct variation and how it applies to this situation. Here are the steps:

1. Since the price of the marble varies directly as the cube of its length, we can express this relationship as P = kl^3, where k is the constant of variation.

2. Mr. Chan spends $400 on a block of marble. So, we can write this as 400 = kl^3.

3. When Mr. Chan cuts the block of marble into two blocks of equal length, the length of each block becomes l/2.

4. The price of each smaller block of marble would then be k*(l/2)^3 = k*l^3/8 = 400/8 = $50.

5. Therefore, the total price for the two smaller blocks of marble would be 2*$50 =$100.

6. Mr. Chan originally spent $400 and he sells the two smaller blocks for$100. Therefore, he has a loss of $400 -$100 = $300.

7. The percentage loss can be calculated as (Loss / Original price) * 100%. So, the percentage loss would be ($300 /$400) * 100% = 75%.

So, Mr. Chan has a loss of $300 and a percentage loss of 75%.