How can we determine the cost of each box that Ramesh bought if he sold one at a profit of 20% and the other at a loss of 12%, given that both boxes were sold for the same price?

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Let’s assume Ramesh bought two boxes for a total of Rs 1300. We can denote the cost price of the first box as x and the cost price of the second box as y.

According to the problem:

  • The total cost of both boxes is: x + y = 1300 (1)
  • The first box is sold at a profit of 20%, making the selling price of the first box: SP1 = x + 0.2x = 1.2x
  • The second box is sold at a loss of 12%, making the selling price of the second box: SP2 = y – 0.12y = 0.88y
  • Since both selling prices are equal, we can set up the equation: 1.2x = 0.88y (2)

Now, we can solve equations (1) and (2) together:

From equation (1), we can express y in terms of x:

y = 1300 - x

Now, substitute y in equation (2):

1.2x = 0.88(1300 - x)

Next, distribute 0.88:

1.2x = 1144 - 0.88x

Now, combine like terms:

1.2x + 0.88x = 1144

This simplifies to:

2.08x = 1144

To find x, divide both sides by 2.08:

x = 550

Now that we have x, we can find y using equation (1):

y = 1300 - 550 = 750

Thus, the cost price of the boxes are:

  • Cost of the first box (x): Rs 550
  • Cost of the second box (y): Rs 750

In conclusion, Ramesh bought the first box for Rs 550 and the second box for Rs 750.

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