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NCERT Solutions Ganita Prakash (Part 2) Chapter 1 –20Section 1.3 — Figure it Out

Book page 19 Updated on2026-09-05

Q1.
If a shopkeeper buys a geometry box for ₹75 and sells it for ₹110, what is his profit margin with respect to the cost?
Answer
Profit = 110 – 75 = ₹35
Profit % = 35/75 × 100 = 3500/75
= 46.67% (exactly 46⅔%)
Tip: Estimate first. ₹35 is a little less than half of ₹75, so the margin must be a little under 50%. 46.67% fits.
Q2.
I am a carpenter and I make chairs. The cost of materials for a chair is ₹475 and I want to have a profit margin of 50%. At what price should I sell a chair?
Answer
SP = CP + 50% of CP = 150% of CP
= 1.5 × 475
= ₹712.50

Equivalently: profit = half of 475 = ₹237.50, and 475 + 237.50 = ₹712.50.

Careful: A 50% margin does not mean “half the selling price is profit”. Here the profit ₹237.50 is exactly a third of the selling price ₹712.50 — because the 50% is measured against the cost, not the sale.
Q3.
The total sales of a company (also called revenue) was ₹2.5 crore last year. They had a healthy profit margin of 25%. What was the total expenditure (costs) of the company last year?
Answer

Reading “profit margin” the way this chapter has used it so far — a percentage of the cost — the revenue is 125% of the expenditure.

1.25 × expenditure = ₹2.5 crore
Expenditure = 2.5/1.25 = ₹2 crore
Profit = 2.5 – 2 = ₹0.5 crore, and 0.5/2 × 100 = 25% ✓
Why it happens: Questions 1 and 2 of this set both measure the margin against the cost, so we keep that meaning here. But the chapter also introduces a second convention — profit as a percentage of the revenue — used when a business asks “how much profit did I make on my overall revenue?”. On that reading the profit would be 25% of ₹2.5 crore = ₹0.625 crore and the expenditure ₹1.875 crore. Both are defensible arithmetic; what is not optional is saying which base you used. In business writing, “margin” usually means the second one, so always check.
Q4.
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 to buy this shirt?
Answer
He pays 100% – 25% = 75% of the marked price
= 3/4 × 300
= ₹225

Or: discount = 25% of 300 = ₹75, so he pays 300 – 75 = ₹225.

Q5.
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%
Answer

(iv) 66.66%.

Increase = 100 – 60 = ₹40
Percentage increase = increase / original × 100
= 40/60 × 100 = 200/3
= 66.66% (exactly 66⅔%)
Why it happens: Option (ii) 40% is the trap: ₹40 is the amount of the rise, not its percentage. Option (v) 140% is the second trap: the new price is 140% of the old price, but the increase is 140% – 100% = 40 percentage points on a base of 60, i.e. 66.66%. Percentage change is always measured against the original amount — the 2015 price of ₹60, not the 2025 price of ₹100.
Check it yourself: If the price had fallen back from ₹100 to ₹60, the percentage decrease would be 40/100 = 40% — a different number for the same ₹40, because the base has changed.
Q6.
Samson bought a car for ₹4,40,000 after getting a 15% discount from the car dealer. What was the original price of the car? [Printed as question 3 on page 20; the book restarts its numbering there.]
Answer
After a 15% discount he pays 85% of the original price
0.85 × original = 4,40,000
original = 4,40,000 / 0.85 = 44,00,000/8.5
= ₹5,17,647 (5,17,647.06 to the nearest paisa)

Check: 15% of 5,17,647 = ₹77,647, and 5,17,647 – 77,647 = ₹4,40,000. ✓

Why it happens: Adding 15% of ₹4,40,000 (which is ₹66,000) to get ₹5,06,000 is wrong, and it is worth seeing exactly why: the discount was 15% of the original price, a bigger number than ₹4,40,000, so 15% of it is more than ₹66,000. Whenever a percentage has already been applied and you are working backwards, divide — do not add the same percentage back.
Note: From this question onwards the book's printed numbering restarts at 3 on page 20, so its “3, 4, 5, …, 9” repeat numbers already used on page 19. The questions are numbered here continuously, Q6 to Q12.
Q7.
1600 people voted in an election and the winner got 500 votes. What percent of the total votes did the winner get? Can you guess the minimum number of candidates who stood for the election? [Printed as question 4 on page 20.]
Answer
Winner's share = 500/1600 × 100 = 5/16 × 100
= 31.25%

Minimum number of candidates: 4.

Votes left for everyone else = 1600 – 500 = 1100
No other candidate can have 500 or more (or they would not have lost)

With 3 candidates: 2 others share 1100 votes
→ at least one of them gets 1100 ÷ 2 = 550 > 500 — impossible

With 4 candidates: 3 others share 1100 votes
→ e.g. 400, 350, 350 — all below 500. Possible.
Why it happens: The winner did not get a majority — 31.25% is under half — so the other 68.75% of the votes must have been split among enough people that no one of them beat 500. Two rivals cannot split 1100 votes without one of them crossing 550. Three rivals can. This is a real feature of first-past-the-post elections: the more candidates there are, the smaller the share a winner needs.
Q8.
The price of 1 kg of rice was ₹38 in 2024. It is ₹42 in 2025. What is the rate of inflation? (Inflation is the percentage increase in prices.) [Printed as question 5 on page 20.]
Answer
Increase = 42 – 38 = ₹4
Rate of inflation = 4/38 × 100 = 400/38 = 200/19
= 10.53% (10.526…%)
Did you know? Inflation is always quoted against the earlier price, which is why the same ₹4 rise means different things at different price levels. A ₹4 rise on ₹38 rice is 10.53% inflation; the same ₹4 on ₹200 pulses would be only 2%.
Q9.
A number increased by 20% becomes 90. What is the number? [Printed as question 6 on page 20.]
Answer
Let the number be x. Increasing it by 20% makes it 120% of x
1.2x = 90
x = 90/1.2 = 900/12
= 75

Check: 20% of 75 = 15, and 75 + 15 = 90. ✓

Why it happens: Taking 20% of 90 and subtracting gives 72 — and that is wrong, as the check shows: 20% of 72 is 14.4, giving 86.4, not 90. The 20% was added to the smaller starting number, so undoing it means dividing by 1.2, not subtracting 20% of the result.
Q10.
A milkman sold two buffaloes for ₹80,000 each. On one of them, he made a profit of 5% and on the other a loss of 10%. Find his overall profit or loss. [Printed as question 7 on page 20.]
Answer

He made an overall loss of about ₹5,079, which is about 3.08%.

The two selling prices are equal, but the two cost prices are not — so work each one out first.

Buffalo 1 (5% profit): SP = 105% of CP
1.05 × CP₁ = 80,000 → CP₁ = 80,000/1.05 = ₹76,190.48

Buffalo 2 (10% loss): SP = 90% of CP
0.90 × CP₂ = 80,000 → CP₂ = 80,000/0.90 = ₹88,888.89

Total cost price = 76,190.48 + 88,888.89 = ₹1,65,079.37
Total selling price = 80,000 + 80,000 = ₹1,60,000
Loss = 1,65,079.37 – 1,60,000 = ₹5,079.37
Loss % = 5,079.37 / 1,65,079.37 × 100 = 3.08%
Why it happens: It is tempting to say “+5% and –10% average out to –2.5%”. They do not, because the two percentages sit on different bases. The buffalo sold at a loss had cost him ₹88,889 — far more than the ₹76,190 buffalo — so the 10% loss is taken on a bigger amount than the 5% profit. Percentages can only be added when they refer to the same whole; here they refer to two different cost prices.
Check it yourself: Profit on the first = 80,000 – 76,190.48 = ₹3,809.52. Loss on the second = 88,888.89 – 80,000 = ₹8,888.89. The difference, 8,888.89 – 3,809.52 = ₹5,079.37, is the overall loss.
Q11.
The population of elephants in a national park increased by 5% in the last decade. If the population of the elephants last decade is p, the population now is (i) p × 0.5 (ii) p × 0.05 (iii) p × 1.5 (iv) p × 1.05 (v) p + 1.50 [Printed as question 8 on page 20.]
Answer

(iv) p × 1.05.

Population now = p + 5% of p
= p + 0.05p
= p(1 + 0.05)
= 1.05p
Why it happens: Look at what the wrong options would mean. (ii) p × 0.05 is only the increase, 5% of p — not the new total. (i) p × 0.5 would be a 50% fall. (iii) p × 1.5 would be a 50% rise, ten times too much. (v) p + 1.50 adds a fixed 1.5 elephants, which is not a percentage at all. Growing by r means multiplying by (1 + r) — the whole plus the extra.
Q12.
Which of the following statement(s) mean the same as — “The demand for cameras has fallen by 85% in the last decade”? (i) The demand now is 85% of the demand a decade ago. (ii) The demand a decade ago was 85% of the demand now. (iii) The demand now is 15% of the demand a decade ago. (iv) The demand a decade ago was 15% of the demand now. (v) The demand a decade ago was 185% of the demand now. (vi) The demand now is 185% of the demand a decade ago. [Printed as question 9 on page 20.]
Answer

Only (iii) means the same thing.

Let the demand a decade ago be d.
Fallen by 85% → the fall is 0.85d
Demand now = d – 0.85d = 0.15d = 15% of d
StatementWhat it saysSame?
(i)now = 0.85d — a fall of only 15%No
(ii)d = 0.85 × now, so demand has risenNo
(iii)now = 0.15dYes
(iv)d = 0.15 × now, so demand has risen sharplyNo
(v)d = 1.85 × now, a fall of about 46%No
(vi)now = 1.85d, a rise of 85%No
Why it happens: Two separate traps are at work. The first is confusing “fallen by 85%” with “is 85% of” — the first leaves 15%, the second leaves 85%. The second is swapping which quantity is the base. The correct reverse statement is not (v): if now = 0.15d then d = now/0.15 = 6.67 × now, that is, the demand a decade ago was about 667% of the demand now — not 185%.
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