Profit, Loss, Interest and Discount — CLAT Quantitative Techniques

A caselet describes "an article marked 40% above cost and sold at a 25% discount." CLAT asks for the profit percentage. Commercial arithmetic — profit-loss, discount, and interest — is standard fare, and every question reduces to a few clean formulas. The one discipline that matters: percentages are taken on the right base — profit on cost, discount on the marked price. This chapter fixes those bases and the interest formulas.

1. Profit and loss — always on cost price

$\text{profit\%}=\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100,\text{loss\%}=\frac{\text{CP}-\text{SP}}{\text{CP}}\times 100$

• CP ₹200, SP ₹250: profit $=50$, so $\frac{50}{200}\times 100=25\%$.
• CP ₹800, SP ₹680: loss $=120$, so $\frac{120}{800}\times 100=15\%$.

The base is always CP. Profit and loss percentages are computed on the cost price, never the selling price.

2. Recovering CP from SP

When SP and profit% are given, divide by the factor.

$\text{SP}=\text{CP}\left(1+\frac{\text{profit\%}}{100}\right)\Rightarrow \text{CP}=\frac{\text{SP}}{1+\frac{\text{profit\%}}{100}}$

• SP ₹360 at 20% profit: $\text{CP}=\frac{360}{1.20}=300$, i.e. ₹300.

3. Marked price and discount

A discount is a reduction on the marked price (MP), not the cost.

$\text{SP}=\text{MP}\left(1-\frac{\text{discount\%}}{100}\right)$

• MP ₹500 at 10% discount: $\text{SP}=500\times 0.90=450$, i.e. ₹450.
• Chaining MP, discount and profit: cost 100, marked 40% above → MP 140, then 25% discount → SP $=140\times 0.75=105$, so profit 5%.

Keep the two bases separate: mark-up is on cost, discount is on marked price. Mixing them is the classic error.

4. Simple interest

$\text{SI}=\frac{P\times R\times T}{100}$

• ₹1,000 at 5% p.a. for 2 years: $\text{SI}=\frac{1000\times 5\times 2}{100}=100$, i.e. ₹100.
• Simple interest is the same every year — it does not build on itself.

5. Compound interest

Interest is added to the principal each period, so it grows on itself.

$A=P{\left(1+\frac{R}{100}\right)}^T,\text{CI}=A-P$

• ₹1,000 at 10% p.a. for 2 years: $A=1000\times (1.1{)}^2=1210$, so $\text{CI}=210$, i.e. ₹210 (versus ₹200 simple).

6. The CI–SI difference (2 years)

A frequently tested shortcut: over 2 years, the extra that compounding gives over simple interest is

$\text{CI}-\text{SI}=P{\left(\frac{R}{100}\right)}^2$

• If this difference is ₹50 at 10% p.a.: $P\times (0.1{)}^2=50\Rightarrow 0.01P=50\Rightarrow P=5000$, i.e. ₹5,000.

7. Exam protocol

1. Take profit and loss on cost price — always.
2. Recover CP by dividing SP by $\left(1+\frac{p}{100}\right)$.
3. Apply discount on the marked price, mark-up on cost — keep the bases apart.
4. Use $\text{SI}=\frac{PRT}{100}$; simple interest is flat each year.
5. Use $A=P{\left(1+\frac{R}{100}\right)}^T$ for compound interest.
6. Remember the 2-year gap: $\text{CI}-\text{SI}=P{\left(\frac{R}{100}\right)}^2$.