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By Selling 20 Umbrellas for Rs. 2400, A man losses 20%, How many should he sell for Rs. 7200 to gain 20%?
1. 34
2. 31
3. 40
4. 42

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Correct Answer - Option 3 : 40

Given:

Selling Price of 20 Umbrellas = 2400.

Loss = 20%

Concept:

If an item is sold at a profit of x%, and the CP = y

Then, SP = [(100 + x)/100] × y

Similarly, 

If an item is sold at a loss of a%, and the CP = y

Then, SP = [(100 - a)/100] × y

Calculation:

Let the number of umbrellas to be sold be x

Now, the unit SP = 2400/20 = Rs.120

Hence, the unit CP is obtained as:

120 = [(100 - 20)/100] × CP

⇒ Unit CP = Rs.150

Now, for a profit of 20%, the SP of the each umbrellas has to be:

7200/x = [(100 + 20)/100] × 150

⇒ 7200/x = 180

⇒ x = 40

∴ The number of umbrellas to be sold is 40

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