Hello,

Greetings for the day!

This question on Profit & Loss is based on a standard model, on which we will give you information in a bit. However, even if you do not know about this model, you will be able to solve this question if your basic concepts of Profit & Loss are strong.

Let us now deal with the question on hand.

Profit = Selling Price (SP) – Cost Price (CP).

Profit/Loss Percentage = [(Profit /Loss) / Cost Price] x 100.

As we know, profit/loss is always calculated as a percentage of cost price.

Method 1 – Use the standard model:If the SP of 2 articles is same and the profit and loss percentage values are same i.e. one of them is sold at let’s say x% profit and the other is sold at x% loss, then, the transaction will always be a loss. The loss percentage is given by the expression (x^2)/100.

So, as you see from the expression above, the loss percentage depends on the value of x; the SP of the two articles does not have any bearing on the answer. As such, your energies, when dealing with such a problem, should be focused on gleaning the value of x from the question.

In our question, the value of x is 20. Hence, the overall transaction is a loss of 4%.

Method 2 – Use the basic concepts of Profit & Loss:Let the SP of the new cycle and the old cycle (which is given as $Y in the question) be $600.

Then,

For the new cycle, SP = 120% of CP of new cycle (since he sold the new cycle at a profit of 20%).

Substituting the value of SP and simplifying, we get CP of new cycle = $500.

Since the SP of the new cycle is $600, the SP of the old cycle also has to be $600.

Therefore,

For the old cycle, SP = 80% of CP of old cycle (since he sold the old cycle at a loss of 20%).

Substituting the value of SP and simplifying, we get CP of old cycle = $750.

Therefore, total CP of the two cycles = $1250 and total SP of the two cycles = $1200. This means, there is a loss of $50.

Hence, percentage of loss = (50/1250) x 100 = 4%.

Although the second method appears lengthy, it is actually the simpler approach, especially if you believe in remembering only the bare minimum of concepts. Obviously, if you remember the model mentioned in Method 1, this problem just becomes a piece of cake for you and you will be able to answer this question within 10 seconds.

However, this can be an undoing of sorts if you start thinking, “ Wait! I solved this so quickly, is there something I missed reading or is this question really this easy?” and then go back and mess up your previous answer.

So, we advise you to be more confident about yourselves and not think that every problem has some trick element associated with it.

Hope this helps!

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- CrackVerbal Prep Team

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