Solve Profit and Loss Related Questions

Profit, loss and discount questions have started to appear more frequently on the CAT quant section. Approximately 3-4 questions are based on the fundamental ideas of profit and loss, either directly or indirectly. To answer these questions, a variety of fast formulas and methods are employed.
Converting ratios to percentages and vice versa is extremely useful for simplifying situations.

Profit loss and discount are examples of different types of inquiries. Many of the questions have a straightforward formula or trick. Learn how to employ them as needed.

Simple Methods can be employed to Solve Profit and Loss Related Questions in CAT Exam

1. One can generate a profit only if selling price>cost price.
2. One generates a loss when selling price<cost price.
3. Profit = Selling Price – Cost Price
4. Loss = Cost Price – Selling Price
5. Sale price = if there is a profit of P%,

Cost Price =C

Then SP = {100+P / 100}×C

6. A shady trader claims to offer his items at cost price, but he uses a lighter weight. Determine his gain percentage.

Gain %=True weight – false weight / False Weight×100

7. A shopkeeper makes an x % profit on an item while using a y % lighter weight. Calculate his total profit.

Gain %=Profit % + % less in weight / 100 – %less in Weight×100

Types of Profit and Loss Questions for CAT exam

1. I sell 16 sheep at a profit of 12.5% and another 20 at a profit of a particular percentage. How much of a gain did I make on the latter figure if I gained 25% on the whole?
2. 240 cows are purchased by a farmer. He sells some of them for a 20% Profit and the rest for a 30% profit. If he makes a total profit of 28%, how many units did he sell at a 20% profit?
3. A merchant makes a 25% profit by selling a horse for Rupees400. He sells a second horse for a 10% loss and ends up with no profit or loss in total. How much did the second horse set him back?
4. A and B are the two horses I purchase. A is Rupees50. More expensive than B. I get a 16% profit on A and a 7% profit on 13. I made a total profit of Rupees100. What was the initial cost of  8?
5. How many toffees must be sold for a rupee to gain 20% if they are purchased at 18 for a rupee?

Solved examples of profit and loss problems

Q1. A vendor bought 6 oranges for Re 10 and sold them at 4 for Re 6. Find his loss or gain percent.

Ans. Suppose, number of orange bought = LCM of 6 and 4=12

∴CP=Re 10 / 6*12=Re20 and SP=Re 6 / 4*12=Re 18

∴Loss%=2 / 20*100%=10%

Q2. One obtains the selling price of 11 metres by selling 33 metres of cloth. Determine the gain percentage.

Ans.  SP of 33m–CP of 33m=Gain=SP of 11m

∴SP of 22m=CPof 33m

Let CP of each meter be Re 1. Then, CP of 22m=Re 22.

Hence SP of 22m=Re 33.

∴%Gain=11 / 22*100

=50%

Q3. A kilogramme of pure ghee costs Re 100. A shopkeeper makes a 20% profit by mixing vegetable oil that costs Re 50 per kg and selling it at Re 96 per kg. In what proportion does he combine pure ghee and vegetable oil?

Ans. Mean Cost price = Re 100 / 120*96=Re 80 per kg

Apply rule of allegation,

Therefore; Required ratio =30:20=3:2

Conclusion

Questions on profit loss and discount have become more common in the CAT quant area. Approximately 3-4 questions are directly or indirectly dependent on the fundamental concepts of profit and loss. A variety of quick formulas and approaches are used to solve these questions. Different forms of enquiries include profit loss and discount. Many of the questions follow a simple formula or trick. Learn how to use them when necessary.