Exercise 5.1 is the first practice exercise of Chapter 5, Comparing Quantities Using Proportion, in Class 8 Mathematics (CBSE, Telangana & Andhra Pradesh syllabus). It puts every idea from the chapter's introduction — ratio, compound ratio, and percentage — to work in realistic situations: comparing working hours, mixing liquids of different units, splitting business profits, adjusting supermarket prices, and even a tricky ratio-based geometry problem involving points on a line.

Below is a complete, step-by-step explanation of all 14 problems in this exercise, grouped by theme so the underlying pattern in each type of question is easy to spot and reuse.

Part 1 — Finding and Simplifying Basic Ratios (Q1)

Question: Find the ratio of the following quantities, in simplest form.

Part 2 — Solving for an Unknown in a Compound Ratio (Q2, Q3, Q4)

These three problems all use the compound ratio rule — multiply the antecedents together, and multiply the consequents together — and then solve the resulting simple equation for the unknown.

Part 3 — Real-Life Ratio Word Problems (Q5, Q7, Q8)

Part 4 — Using Ratios to Compare Triangle Sides (Q6, Q10)

Part 5 — Percentage Word Problems (Q9, Q12, Q13)

Part 6 — Updating a Whole Price Table With Percentage Changes (Q11)

Question: Madhuri visits a supermarket where rice and jam/fruits have gone down in price, while oil and dal have gone up. Find every changed price below.

• Rice and Jam/Apples (fruits): price decreased by 5% (rice) and 8% (jam & apples)
• Oil and Dal: price increased by 10%

Part 7 — A Challenging Ratio-Division Problem on a Line Segment (Q14)

Question: Points P and Q lie on segment AB, on the same side of its midpoint. P divides AB in the ratio 2 : 3, and Q divides AB in the ratio 3 : 4. If PQ = 2, find the length of AB.

Common Mistakes to Avoid

• Forgetting unit conversion before forming a ratio: As in Q1(ii), litres and millilitres (or any mismatched units) must be converted to the same unit first.
• Multiplying the wrong terms in a compound ratio: Always multiply antecedent × antecedent and consequent × consequent — never antecedent × consequent.
• Forgetting to invert a ratio when asked: In Q4, the "inverse ratio of 4 : 5" is 5 : 4, not 4 : 5 — missing this flip changes the entire answer.
• Mixing up "increased by" and the final new value: Q12 and Q13 ask for the change and the new total separately — always re-read which one the question wants.
• Assuming PQ = PB + QB instead of PB − QB: In problems like Q14, carefully figure out the actual order of the points on the line before deciding whether to add or subtract two segment lengths.
• Not double-checking with cross-multiplication: Whenever a ratio equation involves an unknown (like Q2, Q3), cross-multiplying is the safest way to isolate that unknown without sign or fraction errors.

Quick Reference — All 14 Answers at a Glance

What This Exercise Prepares You For

Exercise 5.1 directly applies the formulas from the chapter introduction on ratio, proportion, compound ratio and percentage — if any step above felt unfamiliar, that's the right place to revise the underlying rule before continuing.

The percentage-change skills practised in Q11, Q12, and Q13 carry forward directly into the chapter's next exercises on profit, loss, discount, and simple interest, while the ratio-of-sides idea in Q6 and Q10 is a first taste of triangle similarity, a concept explored in much greater depth in the Triangles chapter in Class 9.