Figure it Out — Profit, Loss and Discount — Fractions in Disguise

1. 12 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 19

   If a shopkeeper buys a geometry box for ₹75 and sells it for ₹110, what is his profit margin with respect to the cost?

   Hint. Find the profit first, then express it as a percentage of the cost — not of the selling price.

   Step 1 — Find the profit. Profit = selling price − cost price = 110 − 75 = ₹35

   Step 2 — Express it as a percentage of the cost. The question says with respect to the cost, so the cost price is the base:

   profit margin = (profit ÷ cost price) × 100 = (35 ÷ 75) × 100 = 3500 ÷ 75 = 46.67%

   (Exactly, 35/75 = 7/15 = 46⅔%.)

   Why the base matters so much. The same ₹35 profit expressed against the selling price would be (35 ÷ 110) × 100 = 31.82% — a very different figure from the same transaction. So a profit percentage is meaningless unless you say what it is a percentage of.

   The chapter draws this distinction explicitly: profit margin on cost answers "how much did I gain for every rupee I spent?", while profit margin on revenue answers "how much of my sales was profit?". Shops usually quote the first when setting prices and the second when reporting results.

   Check: if the margin on cost is 46.67%, then the selling price should be 75 × 1.4667 = ₹110 ✓

   ✦ 46.67% (exactly 46⅔%), since the ₹35 profit is measured against the ₹75 cost price.

2. 22 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 19

   I am a carpenter and I make chairs. The cost of materials for a chair is ₹475 and I want a profit margin of 50%. At what price should I sell a chair?

   Hint. A 50% margin on cost means the selling price is the cost plus half the cost.

   Step 1 — Interpret the 50% margin. A profit margin of 50% on cost means the profit is half the cost price.

   Profit = 50% of 475 = 0.50 × 475 = ₹237.50

   Step 2 — Find the selling price. Selling price = cost + profit = 475 + 237.50 = ₹712.50

   The one-step version. Adding 50% to a quantity means multiplying it by 1.5: 475 × 1.5 = ₹712.50 ✓ This multiplier form is worth using, because it extends directly: a 20% margin means × 1.2, a 35% margin × 1.35.

   Check by working backwards. Profit = 712.50 − 475 = 237.50, and 237.50 ÷ 475 = 0.5 = 50% ✓

   A caution about which base is meant. If the carpenter had instead wanted profit to be 50% of the selling price, the answer would be different: SP − 475 = 0.5 × SP gives 0.5 × SP = 475, so SP = ₹950. Because "profit margin" is ambiguous in ordinary speech, always state which base you are using — here the chapter's convention is margin on cost.

   In practice the carpenter would probably round to ₹715 or ₹720, since ₹712.50 is an awkward price to charge.

   ✦ ₹712.50, since a 50% margin on a cost of ₹475 means multiplying by 1.5.

3. 33 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 19

   The total sales of a company (its revenue) was ₹2.5 crore last year, with a healthy profit margin of 25%. What was the total expenditure of the company last year?

   Hint. A profit margin quoted on revenue means the profit is that percentage of the sales figure.

   Step 1 — Identify the base. The chapter defines a company's profit margin with respect to revenue, so the 25% is 25% of the sales figure, not of the costs.

   Step 2 — Find the profit. Profit = 25% of ₹2.5 crore = 0.25 × 2.5 = ₹0.625 crore (that is, ₹62.5 lakh)

   Step 3 — Find the expenditure. Revenue = expenditure + profit, so Expenditure = revenue − profit = 2.5 − 0.625 = ₹1.875 crore (that is, ₹1 crore 87.5 lakh)

   The one-step version. If profit is 25% of revenue, then expenditure must be the other 75%: Expenditure = 0.75 × 2.5 = ₹1.875 crore ✓ This is quicker and avoids a subtraction.

   Check both conditions. Profit = 2.5 − 1.875 = 0.625, and 0.625 ÷ 2.5 = 0.25 = 25% ✓

   Why the base changes the answer. Had the 25% been a margin on cost instead, we would need expenditure × 1.25 = 2.5, giving expenditure = ₹2 crore — a difference of ₹12.5 lakh from the same words. This is exactly why financial statements always specify whether a margin is on cost or on revenue.

   ✦ ₹1.875 crore, since a 25% margin on revenue leaves 75% of the ₹2.5 crore as expenditure.

4. 42 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 19

   A clothing shop offers a 25% discount on all shirts. If the original price of a shirt is ₹300, how much will Anwar have to pay?

   Hint. A 25% discount means he pays the remaining 75%.

   Method 1 — find the discount, then subtract. Discount = 25% of 300 = 0.25 × 300 = ₹75 Amount paid = 300 − 75 = ₹225

   Method 2 — go straight to what he pays. If 25% is taken off, Anwar pays the remaining 75%: 0.75 × 300 = ₹225 ✓

   The second method is one step instead of two, and it is the one to build the habit of using — it becomes essential in the later questions where discounts and increases are chained together.

   A mental route. 25% is a quarter, so a quarter of 300 is 75, and 300 − 75 = 225 ✓

   Check: the ₹75 saved out of ₹300 is 75/300 = 0.25 = 25% ✓

   The multiplier idea, which the chapter builds on later:

   Change	Multiplier
   25% discount	× 0.75
   10% discount	× 0.90
   18% GST added	× 1.18
   35% profit added	× 1.35

   Writing every percentage change as a single multiplier is what makes chained changes manageable — a 25% discount followed by an 18% tax is just × 0.75 × 1.18, with no need to compute either amount separately.

   ✦ ₹225, since a 25% discount means paying 75% of ₹300.

5. 52 marksGanita Prakash Cl-8 Part 2, Figure it Out, page 19

   The petrol price in 2015 was ₹60 and ₹100 in 2025. What is the percentage increase in the price of petrol? (i) 50% (ii) 40% (iii) 60% (iv) 66.66% (v) 140% (vi) 160.66%

   Hint. A percentage increase is always measured against the ORIGINAL value, not the new one.

   Step 1 — Find the increase. Increase = 100 − 60 = ₹40

   Step 2 — Express it as a percentage of the original price. A percentage change is always measured against the value you started from:

   percentage increase = (increase ÷ original) × 100 = (40 ÷ 60) × 100 = 4000 ÷ 60 = 66.66%

   So the answer is option (iv).

   (Exactly, 40/60 = 2/3 = 66⅔%.)

   Why the wrong options are tempting. • (ii) 40% — treats the ₹40 rise as though it were already a percentage. • (ii)/(ii) 40% is also what you get by dividing 40 by the new price 100 — the single commonest error in the whole topic. Dividing by 100 is easy, which is exactly what makes it dangerous. • (v) 140% — this is what the new price is as a percentage of the old one (100/60 ≈ 166.7%, so not even that), or a confusion between "increased by" and "increased to".

   The rule to fix in your mind: percentage change = (change ÷ ORIGINAL) × 100 The original value is the base, always — whether the change is a rise or a fall.

   Check: increasing ₹60 by 66.66% gives 60 × 1.6666 = ₹100 ✓

   ✦ (iv) 66.66% — the ₹40 rise measured against the original ₹60, since a percentage change is always taken on the starting value.

Solutions written by the tuition.in editorial team and checked against the NCERT Class 8 Mathematics textbook Ganita Prakash Part 2, Reprint 2026-27 (hegp201.pdf), where this is Chapter 1 (pages 1-32) — the eighth chapter of the Class 8 course. The title refers to percentages being fractions in disguise, with denominator 100. IMPORTANT DIFFERENCE FROM PART 1: this PDF carries NO printed answer key, so every answer here was derived from first principles and independently recomputed in Python before being written — including all the compound-interest amounts, the two-buffalo profit-and-loss problem, the reverse-percentage car price, and the left-handed-people puzzle. FOUR ITEMS ARE FLAGGED IN PLACE where the printed figure cannot be recovered from text: the bar-model diagrams (Figure it Out 2, Q1), the runners' race picture (Q4 of the first block), the region-E area diagram and the chips-packet label, and the computer-ability bar graph. One genuine inconsistency in the book's own numbers is also flagged: 24% of 160 students is 38.4, which is not a whole number of people.. Questions are referenced from the NCERT textbook for identification.