A shopkeeper allows a discount of 20% on the marked price of an item and thus gains 10%. What is the ratio of the cost price to the marked price of the item?

Question

Accepted Answer

Let the marked price (MP) be Rs. 100.

Discount allowed = 20% of MP = 20% of 100 = Rs. 20
So, Selling Price (SP) = MP - Discount = 100 - 20 = Rs. 80

The shopkeeper gains 10%.
Let Cost Price (CP) = x
So, SP = CP + 10% of CP = 1.1x
But SP = Rs. 80
So, 1.1x = 80
=> x = 80 / 1.1 = 800 / 11

Now, ratio of CP to MP = (800/11) : 100 = (800/11) / 100 = 800 / 1100 = 8 / 11
But this is not matching the options. Let's check the calculation again.

Wait, let's try with the options:
Let the ratio be x : y (CP : MP)
Let MP = y, CP = x

Discount = 20% of MP = 0.2y
SP = MP - Discount = y - 0.2y = 0.8y

Given, gain = 10%
So, SP = CP + 10% of CP = 1.1x
So, 0.8y = 1.1x
=> x/y = 0.8 / 1.1 = 8 / 11

So, the correct ratio is 8:11, which matches option 1.

Therefore, the correct answer is 8:11.

Correction: The correct answer is option 1 (8:11).

Answer

Answer

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