By selling 32 orange in a dollar, a man loses 40%. How many orange

Hi anceer,

You can use the relation between Cost Price & Selling Price to get to your answer.

Given
We are given that a person sells 32 oranges for a dollar to make a loss of 40%. We are asked to find the number of oranges he must sell in a dollar to make a profit of 20%

Approach
We know that Selling Price = Cost Price *( 1 - Loss%) and Selling Price = Cost Price ( 1 + Profit%) Since we know the selling price and the loss%, we can find out the cost price.

Once we know the cost price and we know that the person needs to make a profit of 20%, we can find the selling price which would give us the number of oranges he needs to sell to make 20% profit.

Working Out
The person sells 32 oranges in 1 dollar. So, his SP for 1 orange = \(\frac{1}{32}\). Since he has made a loss of 40%, we can write

SP = CP *(1 - 0.4) i.e. CP for one orange = \(\frac{1}{32* 0.6}\)

For the person to make 20% profit, he would need to have his SP = CP (1 + 0.2) = 1.2*CP. Since we know the CP of 1 orange, we can write

SP for one orange to make a profit of 20% = \(1.2 * \frac{1}{32*0.6}\) = \(\frac{1}{16}\) i.e. selling price of 1 orange to make a profit of 20% is \(\frac{1}{16}\) dollars. So he needs to sell 16 oranges for a dollar to make a profit of 20%.

In such questions avoid calculating numbers at each point as the numbers taken together will cancel out to give the final answer.

Hope this helps

Regards
Harsh