CUET CUET General Test 2024 - 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 ? | PYQs + Solutions

CUET General Test 2024

Arithmetic

Profit & Loss

Medium

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 ?

₹ 120

₹ 135

₹ 150

₹ 160

Correct Option: 3

Let the cost price be

CP

The selling price after a 20% discount is

504

. Therefore, the marked price

MP

can be calculated as:

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

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

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

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

1.05 \cdot CP = 504

Thus,

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

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

MP - CP = 630 - 480 = 150

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