ICSE Class 10 Maths: Ratio and Proportion Word Problems Guide

Why ratio and proportion word problems matter

Ever wondered why recipes, sports scores, or even movie ticket prices can be written as simple fractions? That's the magic of ratios and proportions, and they pop up in every exam question you’ll face.

💡 In Simple Words: A ratio compares two quantities, like how many apples to oranges you have. A proportion says two ratios are equal, like saying 2 apples for every 3 oranges is the same as 4 apples for every 6 oranges. When a word problem gives you a situation, you turn it into a ratio or proportion and solve for the missing number.

What are ratio and proportion word problems?

In a word problem, the story hides numbers that relate to each other. Your job is to spot the relationship, write it as a ratio (a:b) or a proportion (a:b = c:d), and then find the unknown piece.

Key terms explained

• Ratio: a way to compare two amounts, like 3:5 means for every 3 of the first thing there are 5 of the second.
• Proportion: an equation that says two ratios are equal, such as 3:5 = 6:10.
• Cross‑multiply: a quick trick to solve a proportion. Multiply the top left number by the bottom right, and the top right by the bottom left, then set the products equal.

How to solve ratio word problems step‑by‑step

Most ICSE questions follow the same pattern. Follow these four moves and you’ll be set.

Step 1 – Read the problem

Highlight the numbers and the words that show comparison: "for every", "each", "times as many", "in the ratio of".

Step 2 – Identify the known ratio

Write the ratio in its simplest form. If the problem says 12 red balls and 8 blue balls, the ratio red:blue is 12:8, which simplifies to 3:2.

Step 3 – Set up a proportion

Replace the unknown part with a variable, usually x. If the question asks how many blue balls there would be if there are 15 red balls, write 3:2 = 15:x.

Step 4 – Cross‑multiply and solve

Multiply across: 3·x = 2·15, so 3x = 30, giving x = 10. That means 10 blue balls.

Worked example – a classic ICSE question

Problem: A school library has fiction and non‑fiction books in the ratio 4:3. If there are 280 fiction books, how many non‑fiction books are there?

Solution:

1. Known ratio = 4 (fiction) : 3 (non‑fiction).
2. Set up proportion: 4/3 = 280 / x.
3. Cross‑multiply: 4·x = 3·280 → 4x = 840.
4. Divide: x = 840 / 4 = 210.

So the library holds 210 non‑fiction books.

Common tricks for ICSE exams

• Always simplify the given ratio first – it keeps numbers small.
• If the problem involves “times as many”, turn it into a multiplication before forming the proportion.
• Check units. A ratio of distance to time is a speed, so make sure you’re not mixing kilometres with metres.
• When two ratios are given, you can set them equal directly if they compare the same pair of things.

Quick reference table

📝 Likely Exam Questions

1. Question: The ratio of boys to girls in a class is 5:4. If there are 27 girls, how many boys are there?
   Answer: 5/4 = x/27 → 5·27 = 4x → x = 33.5, but students must be whole, so the data is inconsistent – likely a typo. In a correct problem with 28 girls, x = 35 boys.
2. Question: A recipe calls for sugar and flour in the ratio 2:5. If you use 300 g of flour, how much sugar do you need?
   Answer: 2/5 = x/300 → 2·300 = 5x → x = 120 g.
3. Question: Two trains start from the same station. Train A travels twice as fast as Train B. After 3 hours, Train A has covered 210 km. How far has Train B travelled?
   Answer: Speed ratio 2:1, so distance ratio also 2:1. 210 km : x = 2 : 1 → 210 = 2x → x = 105 km.
4. Question: In a garden, the number of rose bushes to tulip bulbs is 3:7. If there are 84 tulip bulbs, how many rose bushes are there?
   Answer: 3/7 = x/84 → 3·84 = 7x → x = 36.
5. Question: A company’s profit to loss ratio is 4:1. If the loss this year is ₹25,000, what is the profit?
   Answer: 4/1 = profit/25,000 → profit = 4·25,000 = ₹100,000.