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An item is sold for ₹ 504 after allowing 20% discount and still a profit of 5% has been earned. The marked price is how much more than the cost price ?

Solution

Correct Option: 3

Let the cost price be CPCP.

The selling price after a 20% discount is 504504. Therefore, the marked price MPMP can be calculated as:

MP=50410.20=5040.80=630MP = \frac{504}{1 - 0.20} = \frac{504}{0.80} = 630.

Since a profit of 5% is earned, we have:

SP=CP+0.05CP=1.05CPSP = CP + 0.05 \cdot CP = 1.05 \cdot CP.

Setting the selling price equal to the selling price formula gives:

1.05CP=5041.05 \cdot CP = 504.

Thus,

CP=5041.05=480CP = \frac{504}{1.05} = 480.

Now, the difference between the marked price and the cost price is:

MPCP=630480=150MP - CP = 630 - 480 = 150.

The marked price is ₹ 150 more than the cost price.

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