Exercise 5.2 — Discounts and GST
Discounts, profit and loss, Goods and Service Tax.
Exercise 5.2 – Comparing Quantities Using Proportion (Profit, Loss, Discount & GST)
Exercise 5.2 of Class 8 Mathematics (CBSE, Telangana & Andhra Pradesh syllabus) brings together everything you've learned about percentages and applies it to real-life money situations: profit and loss, discount, VAT, and GST (Goods and Services Tax). Every problem in this exercise is essentially the same percentage formula applied in a different shopping, business, or billing context.
Once you understand the core relationships between Cost Price (C.P.), Selling Price (S.P.), Marked Price (M.P.), and the percentage change, all 16 questions in this exercise become a matter of identifying which formula to use and substituting the correct values.
Key Formulas You Must Know
These four formula groups cover every single problem in Exercise 5.2. Keep this table handy while solving — almost every question is a direct application of one of these.
| Concept | Formula | Used In |
|---|---|---|
| Discount | Discount = (Discount % ÷ 100) × Marked Price | Q5, Q13 |
| Selling Price (with discount) | S.P. = M.P. × (100 − discount %) ÷ 100 | Q5, Q13 |
| Profit | Profit = S.P. − C.P. (when S.P. > C.P.) | Q7, Q8, Q12 |
| Loss | Loss = C.P. − S.P. (when C.P. > S.P.) | Q8, Q11 |
| Profit % | Profit % = (Profit ÷ C.P.) × 100 | Q7, Q8, Q12 |
| Loss % | Loss % = (Loss ÷ C.P.) × 100 | Q8, Q11 |
| S.P. from Profit % | S.P. = C.P. × (100 + profit %) ÷ 100 | Q8, Q9, Q10 |
| C.P. from S.P. and Profit % | C.P. = S.P. × 100 ÷ (100 + profit %) | Q9, Q10 |
| Original Price from GST-included Bill | Original Price = Bill Amount × 100 ÷ (100 + GST %) | Q14 |
| GST Amount | GST = (GST % ÷ 100) × Original Price | Q15 |
In 2012, there were 36.4 crore internet users worldwide. Over the next ten years, this number was estimated to increase by 125%. We need to find the estimated number of users in 2022.
A 125% increase means the new value is 225% of the original (100% original + 125% increase = 225%). So we multiply 36.4 crore by 225/100.
New Value = Original Value × (100 + % increase) / 100
The monthly rent of a house is ₹2500, and it increases by 5% at the end of each year. We need the rent after 2 years. The key idea here is that the second year's increase is calculated on the already increased rent — this is the same logic as compound interest.
Step 1: Rent After 1 Year
Step 2: Rent After 2 Years
A company's share price was ₹7.50 on Monday. It changed by different percentages on three consecutive days: +6% on Tuesday, −1.5% on Wednesday, and −2% on Thursday. Each day's change is applied to the previous day's closing price, not the original Monday price.
Tuesday (increase by 6%)
Wednesday (decrease by 1.5%)
Thursday (decrease by 2%)
Reshma has a drawing measuring 2 cm by 4 cm and sets the photocopier to 150% to enlarge it. Setting a copier to 150% means every dimension of the original becomes 150% of its original value — this is a direct "percentage of a quantity" calculation applied to both the width and the length.
A book's printed (marked) price is ₹150 and the shop offers a 15% discount. We need the actual amount the customer pays — this is a direct application of the selling price formula for discounts.
S.P. = Marked Price × (100 − discount %) / 100
A gift item marked at ₹176 was sold for ₹165. This time we are given the actual discount in rupees implicitly (the difference between marked and selling price) and asked to express it as a percentage of the marked price.
A shopkeeper bought 200 bulbs at ₹10 each, but 5 bulbs got fused (became scrap and unsellable). The remaining 195 bulbs were sold at ₹12 each. The trick here is that the Cost Price is based on all 200 bulbs (the shopkeeper paid for all of them), but the Selling Price only comes from the 195 bulbs actually sold.
This question gives a table with five rows, each row missing different values (Selling Price, Profit, Loss, Profit %, or Loss %). Each row tests a different rearrangement of the same core profit/loss formulas. The "Expenses" column (repairs, transport, etc.) must always be added to the Cost Price before any calculation.
| Row | Cost Price + Expenses | Total C.P. | S.P. | Profit / Loss | Profit % / Loss % |
|---|---|---|---|---|---|
| 1 | ₹750 + ₹50 | ₹800 | ₹880 | Profit = ₹80 | Profit % = 10% |
| 2 | ₹4500 + ₹500 | ₹5000 | ₹4000 | Loss = ₹1000 | Loss % = 25% |
| 3 | ₹46,000 + ₹4000 | ₹50,000 | ₹60,000 | Profit = ₹10,000 | Profit % = 20% |
| 4 | ₹300 + ₹50 | ₹350 | ₹392 | Profit = ₹42 | Profit % = 12% (given) |
| 5 | ₹330 + ₹20 | ₹350 | ₹315 | Loss = ₹35 | Loss % = 10% (given) |
Row 1: Finding S.P. and Profit % (C.P. and Profit Given)
Row 2: Finding S.P. and Loss % (C.P. and Loss Given)
Row 3: Finding Profit and Profit % (C.P. and S.P. Given)
Row 4: Finding S.P. and Profit (C.P. and Profit % Given)
Row 5: Finding S.P. and Loss (C.P. and Loss % Given)
A table was sold for ₹2142 at a gain of 5%. We're asked at what price it should be sold to gain 10% instead. This requires a two-step approach: first work backward from the given S.P. and profit % to find the C.P., then use the C.P. to find the new S.P. for the desired profit %.
Step 1: Find the Cost Price
Step 2: Find New S.P. for 10% Gain
Gopi sold a watch to Ibrahim at a 12% gain. Ibrahim then sold it to John at a 5% loss. John paid ₹1330. We need to find how much Gopi sold it for. The key insight is that Ibrahim's selling price to John equals John's cost price, and working backward gives us Ibrahim's cost price — which is also Gopi's selling price.
Gopi --(12% gain)--> Ibrahim --(5% loss)--> John pays ₹1330
Step: Find Ibrahim's Cost Price (= Gopi's Selling Price)
Madhu and Kavitha bought a house for ₹3,20,000 and had to sell it for ₹2,80,000 due to financial difficulties. We need both the actual loss amount and the loss percentage.
A showroom owner bought a second-hand car for ₹1,50,000 and spent ₹20,000 on repairs and painting before selling it for ₹2,00,000. As with Question 7, the repair cost must be added to the cost price before finding profit or loss.
Lalitha's hotel bill was ₹1450, already including 5% VAT. The hotel owner then gave her an 8% discount on the total bill amount. We don't need to remove the VAT first — the discount is applied directly to the final billed amount of ₹1450.
When a bill shows the final amount with GST already added, you must work backward to find the original (pre-tax) price. The formula divides by (100 + GST%) instead of multiplying — because the bill amount represents 100% + GST% of the original price.
Original Price = Bill Amount × 100 / (100 + GST %)
| Item | GST % | Bill Amount (₹) | Original Price (₹) |
|---|---|---|---|
| (i) Diamond | 3% | 10,300 | 10,000 |
| (ii) Pressure Cooker | 12% | 3,360 | 3,000 |
| (iii) Face Powder | 28% | 256 | 200 |
(i) Diamond — 3% GST, Bill ₹10,300
(ii) Pressure Cooker — 12% GST, Bill ₹3,360
(iii) Face Powder — 28% GST, Bill ₹256
Unlike Question 14, this is a forward GST problem. A cellphone company fixes the price at ₹4500, and a dealer pays 12% GST additionally on top of this. We need both the GST amount and the total purchase price the dealer pays.
This is a Higher Order Thinking Skills (HOTS) problem. A Super Bazaar prices items in rupees and paise, and after adding 4% sales tax, the final amount must come out to exactly 'n' rupees (a whole number) with no rounding. We need the smallest such 'n'.
Let the original price be ₹x. Adding 4% tax gives the final amount n:
Common Mistakes to Avoid in Exercise 5.2
- Calculating percentage on the wrong base: Profit %, Loss %, and Discount % are always calculated on the Cost Price or Marked Price, never on the Selling Price (unless explicitly stated otherwise).
- Forgetting additional expenses: Repairs, transport, or other costs (as in Q7, Q8 Row 1-2, and Q12) must be added to the Cost Price before any profit/loss calculation.
- Confusing GST-included vs GST-additional problems: If the bill already includes GST (Q14), divide by (100 + GST%). If GST is charged on top of a fixed price (Q15), multiply by GST% and add it separately.
- Using the original value for successive percentage changes: In problems like Q2 and Q3, each new percentage change applies to the most recent value, not the original starting value.
- Ignoring shape/scenario-specific properties: In chain transactions (Q10), carefully track who is the buyer and who is the seller at each stage — the same number can be both an S.P. and a C.P. depending on perspective.
What Exercise 5.2 Prepares You For
The percentage-based reasoning in this exercise — increase, decrease, reverse calculation, and successive changes — forms the foundation for earlier topics in Comparing Quantities Using Proportion as well as more advanced applications later. The "successive percentage change" idea from Questions 2 and 3 directly leads into compound interest calculations, while the algebraic approach in Question 16 is a stepping stone toward forming and solving linear equations.
Strong command over profit, loss, discount, and GST is also extremely useful for Class 9 algebraic expressions, where similar real-world relationships are expressed and manipulated using variables instead of fixed numbers.