Vardaan
Class 7 Maths • Chapter 08

Comparing Quantities

Vardaan Learning Institute • Detailed Notes with Practice Questions

📊 1. Ratio and Proportion (Review)

Ratio: Comparison of two quantities of the same type by division. Ratio of a to b = a:b = a/b

Proportion: Two ratios are equal: a:b = c:d → a×d = b×c (cross-multiplication)
E.g., Is 3:4 = 9:12? → 3×12 = 36 and 4×9 = 36 ✓ Yes, they are in proportion.

💯 2. Percentages — Conversions

Fraction → %
Multiply by 100%
% → Fraction
Divide by 100
Decimal → %
Multiply by 100
% of a number
= (% / 100) × Number
Examples:
• 3/4 = 3/4 × 100 = 75%
• 0.36 = 0.36 × 100 = 36%
• 30% of 250 = 30/100 × 250 = 75
• 120 is what % of 400? → (120/400) × 100 = 30%

📈 3. Profit and Loss

Term Formula When?
Profit Profit = SP − CP (when SP > CP) Selling price more than cost price
Loss Loss = CP − SP (when CP > SP) Cost price more than selling price
Profit % (Profit/CP) × 100 Always calculated on CP
Loss % (Loss/CP) × 100 Always calculated on CP
SP (if profit % known) SP = CP × (100 + Profit%)/100 Finding selling price
SP (if loss % known) SP = CP × (100 − Loss%)/100 Finding selling price
CP (if SP and Profit% known) CP = SP × 100/(100 + Profit%) Finding cost price
Solved Examples:
1. CP = ₹600, SP = ₹750. Profit = 750−600 = ₹150. Profit% = (150/600)×100 = 25%
2. CP = ₹800, Loss% = 10%. SP = 800 × (100−10)/100 = 800 × 90/100 = ₹720
3. SP = ₹1200, Profit% = 20%. CP = 1200 × 100/120 = ₹1000

🏦 4. Simple Interest (SI)

SI = (P × R × T) / 100    |    Amount = P + SI
Symbol Meaning Common units
P Principal (original sum borrowed/invested) Rupees (₹)
R Rate of Interest per annum % per year (p.a.)
T Time period Years (convert months: T = months/12)
SI Simple Interest earned/paid Rupees (₹)
A Amount = Principal + SI Rupees (₹)
Find P
P = (SI × 100) / (R × T)
Find R
R = (SI × 100) / (P × T)
Find T
T = (SI × 100) / (P × R)
Find A
A = P + SI = P(1 + RT/100)
Examples:
1. P=₹5000, R=8% p.a., T=3 yrs. SI = (5000×8×3)/100 = ₹1200. Amount = 5000+1200 = ₹6200
2. SI=₹600, P=₹4000, T=2 yrs. R = (600×100)/(4000×2) = 7.5% p.a.
3. A=₹7000, P=₹5000, R=10% p.a. SI=2000. T = (2000×100)/(5000×10) = 4 years
✏️ Practice Questions — Comparing Quantities (30 Questions)

Section A — Percentage Basics Easy

Q1. Convert 3/5 to percentage
Q2. Convert 0.085 to percentage
Q3. Find 15% of 320
Q4. 48 is what % of 200?
Q5. Increase 400 by 25%
Q6. Decrease 600 by 15%
Q7. 30% of a number is 90. Find the number.
Q8. A class has 40% boys. Total students = 50. How many girls?

Section B — Profit and Loss Medium

Q9. CP=₹450, SP=₹540. Find Profit%
Q10. CP=₹1200, Loss%=5%. Find SP.
Q11. SP=₹924, Profit%=12%. Find CP.
Q12. A toy costs ₹250. At what price must it be sold to earn 20% profit?
Q13. A TV costing ₹15000 is sold at a loss of 8%. Find SP.
Q14. A shopkeeper buys 10 pens for ₹80 and sells 8 of them for ₹80. Find profit or loss %.
Q15. Sheena bought a dress for ₹800 and sold it for ₹680. Find her loss%.
Q16. A phone sells for ₹6300 after a 10% discount on the marked price. Find marked price.

Section C — Simple Interest Medium

Q17. P=₹3000, R=6%, T=2 yr. Find SI and Amount.
Q18. P=₹8000, R=5.5%, T=3 yr. Find SI.
Q19. SI=₹810, P=₹4500, T=3 yr. Find Rate.
Q20. A=₹5500, P=₹5000, R=10%. Find Time.
Q21. In how many years will ₹1500 double itself at 10% SI?
Q22. Find principal that earns SI=₹720 in 4 years at 6%.
Q23. Sita deposited ₹10000 for 6 months at 8% p.a. Find SI. (T = 6/12 = 0.5 yr)
Q24. P=₹6000 at 7% for 2.5 years. Find Amount.

Section D — Mixed / Challenge Hard

  1. Q25. A shopkeeper marks up by 30% on cost and then gives 10% discount. Find overall Profit%.
  2. Q26. Ramesh invested ₹12000. Half at 8% and rest at 6% SI. Find total interest in 2 years.
  3. Q27. A bookseller sells 2 books at ₹480 each. On one he gains 20% and on other he loses 20%. Find overall profit or loss % and total. (Hint: Find CPs first.)
  4. Q28. Reena scored 72 out of 80 in Maths, 65 out of 75 in Science. In which subject did she perform better (use percentage)?
  5. Q29. A sum of money triples itself in 20 years at SI. What is the rate of interest per annum?
  6. Q30. By selling 25 articles, a trader earns a profit equal to the SP of 5 articles. Find the Profit%.
✅ Key Answers: Q1:60% | Q3:48 | Q4:24% | Q5:500 | Q6:510 | Q7:300 | Q9:20% | Q10:₹1140 | Q11:₹825 | Q12:₹300 | Q17:SI=₹360, A=₹3360 | Q19:6% | Q21:10 yrs | Q25:17% profit | Q28:Maths=90%, Sci≈86.7%, Maths better | Q29:10%

📝 Quick Revision

  1. Ratio a:b = a/b. In proportion a:b = c:d, ad = bc (cross multiply)
  2. Fraction to % → multiply by 100. % to fraction → divide by 100
  3. Profit/Loss % always calculated on COST PRICE (CP)
  4. SP = CP × (100 ± P or L%) / 100. CP = SP × 100 / (100 ± P or L%)
  5. SI = PRT/100. Amount = P + SI. Always check time in YEARS
  6. Discount is always on MARKED PRICE. Profit/Loss on COST PRICE