CAT Quant Profit, Loss and Discount: Formulas, Assumption Method and Examples

Profit, Loss and Discount is a key topic in CAT Quant Arithmetic. Questions usually test how well you understand CP, SP, MP and percentage bases rather than complex calculations.

The three core relationships are simple: CP + Profit = SP, CP − Loss = SP and MP − Discount = SP. Once you understand these and the assumption method, you can solve most questions quickly and avoid common percentage traps.

CAT Quant Profit, Loss and Discount is about reading the question carefully and using three simple relationships: CP + Profit = SP, CP − Loss = SP and MP − Discount = SP. Most mistakes happen when students pick the wrong base for percentages.cracku+2

What Are CP, SP and MP?

Three prices appear in these questions. CP (Cost Price) is the price at which the seller buys the item. SP (Selling Price) is the price at which the seller sells it. MP (Marked Price) is the price shown on the product before any discount.

MP can appear under other names, such as MRP, tag price, list price, catalogue price, printed price or quoted price. Learn these, as questions may use any of them.

There are three core relationships, one for each family:

• SP = CP + Profit

• SP = CP − Loss

• SP = MP − Discount

To identify the case, compare SP and CP. If SP is more than CP, it is a profit. If SP is less than CP, it is a loss. The profit is SP − CP, and the loss is CP − SP.

Which Base Is Used for Profit, Loss and Discount Percentages?

Using the wrong base is the most common mistake. The table below gives the default rule.

If a question clearly says profit or loss is calculated on SP, follow that. If the question says nothing, use CP for profit and loss.

For example, a product is marked at Rs. 2,000 and a 40% discount is given. The discount is 40% of 2,000, which is Rs. 800. So the seller receives Rs. 1,200.

How Does the Assumption Method Work in Profit and Loss?

Many students make a mistake here. An item is sold for Rs. 150 at a 20% profit. Taking 20% of 150 gives 30, and 150 − 30 = 120. This is wrong because profit is on CP, not SP.

The assumption method fixes this. Assume CP = 100 when the CP is unknown.

1. Assume CP = 100.

2. Add the profit (or subtract the loss) to get the assumed SP. For a 20% profit, SP = 120.

3. Compare it with the real SP. Here, 120 matches Rs. 150.

4. Use the unitary method: if 120 is Rs. 150, then 100 is 150 × 100 ÷ 120 = Rs. 125.

So the CP is Rs. 125, not Rs. 120.

For a loss, the same steps work. If CP = 100 and the loss is 10%, the assumed SP is 90. Suppose the real SP is Rs. 200. Then 90 matches Rs. 200, so CP = 200 × 100 ÷ 90, which is about Rs. 222.22.

You can also use it in reverse to find the actual profit or loss in rupees when CP or SP is known.

Moving from Loss to Profit

The method also handles a change from one result to another. Suppose a seller sells at a 10% loss, and selling at a 10% profit would give Rs. 7.80 more.

• With CP = 100, a 10% loss gives SP = 90. A 10% profit gives SP = 110.

• The gap in the assumed values is 110 − 90 = 20.

• The real gap is Rs. 7.80, so 20 matches Rs. 7.80.

• Then CP = 100 matches 7.80 × 100 ÷ 20 = Rs. 39.

You can solve changes from one profit percentage to another in the same way.

How Do You Calculate Profit and Loss Percentage?

When the question asks for the percentage directly, use these formulas:

• Profit % = Profit ÷ CP × 100

• Loss % = Loss ÷ CP × 100

Always put the thing you want the percentage of in the numerator, and the base in the denominator. So for profit %, profit goes on top and CP goes below.

Sometimes the profit is given in disguise. For example, a question says the profit is Rs. 360 and also says it is 20% of CP. Then 20% matches Rs. 360. To find the SP, first find CP, which is Rs. 1,800, and then SP = 1,800 + 360 = Rs. 2,160. Read the last line of a question carefully, as it tells you what to give as the answer.

Why Must Quantities Be on the Same Basis?

Always compare like with like: per item with per item, per dozen with per dozen and total with total. The table below shows the chocolate example.

A dozen costs Rs. 9, but a dozen chocolates sells for 12 × Rs. 1 = Rs. 12. So the profit is Rs. 3 on Rs. 9, which is 3 ÷ 9 × 100 = 33.33%. You can also use the total of 240 chocolates, but it takes more time. The percentage will be the same whichever basis you use, so pick the shortest one.

How Does Discount Work with Marked Price?

Discount is always on MP unless the question says otherwise. So when MP is unknown, assume MP = 100.

An article is sold for Rs. 150 after a 20% discount. Many students take 20% of 150, which is wrong. Instead:

1. Assume MP = 100. The discount is 20, so the assumed SP is 80.

2. 80 matches Rs. 150.

3. So MP = 150 × 100 ÷ 80 = Rs. 187.50.

The formula for discount percentage is Discount % = Discount ÷ MP × 100.

For quantity-based questions, convert the quoted price into the same quantity first. For example, if 12 pairs of gloves sell at Rs. 72 after a discount, one pair costs Rs. 6. So Rs. 24 buys 4 pairs.

How Do You Solve Mixed Questions with CP, Profit, MP and Discount?

Split the information into the three families. Then build the real SP on one side and the assumed SP on the other.

Example. The CP is Rs. 174. The seller wants a 25% profit and gives a 25% discount. Find the MP.

• Real SP = 174 + 25% of 174 = 174 + 43.5 = Rs. 217.50.

• Assume MP = 100. After a 25% discount, the assumed SP = 75.

• 75 matches Rs. 217.50, so MP = 217.50 × 100 ÷ 75 = Rs. 290.

Example with known MP. An item costs Rs. 400 and is marked up by 80%. Then a 15% discount is given. Find the real profit percentage.

• MP = 400 + 320 = Rs. 720.

• Discount = 15% of 720 = Rs. 108. So SP = Rs. 612.

• Profit = 612 − 400 = Rs. 212.

• Profit % = 212 ÷ 400 × 100 = 53%.

The 80% markup is only on paper. The real profit is lower because the discount reduces the final SP.

What Are Some Advanced Question Types?

Two sellers, different bases. Seller 1 earns 20% profit on CP. Seller 2 earns 20% profit on SP. They differ by Rs. 160 in profit. Assume the same SP of 120 for both.

• Seller 1: CP = 100, so profit = 20.

• Seller 2: profit = 20% of 120 = 24.

• The gap is 4 in the assumed world, and Rs. 160 in the real world.

• So 120 matches 120 × 160 ÷ 4 = Rs. 4,800.

Parts of stock at different profits. Choose a total quantity that suits every fraction. Say 1/5 of the goods are sold at 25% profit, 1/4 at 30% and the rest at 20%. Take 20 items at Rs. 100 each, so the total value is Rs. 2,000.

The table above gives a total assumed profit of Rs. 470. If the real profit is Rs. 94, then 470 matches Rs. 94, and the real total value is 2,000 × 94 ÷ 470 = Rs. 400.

Quick Summary of Profit, Loss and Discount Rules

The table below gives the key points for revision.

Practise CAT PYQs on this topic. First write down CP, SP and MP, and then decide which family each belongs to.

Profit, Loss and Discount gets easier once you have practised the assumption method on a few questions. You can practice it with other CAT Quant Arithmetic notes, the CAT Quant Mixture and Alligation guide and the CAT Quant Averages guide. A few CAT Quant mock tests and the  PW CAT online course can help you check your speed.