ICSE Class 10 Maths: Ratio and Proportion Word Problems

Ever wondered why your favourite snack pack seems to double when you share it with a friend? That’s ratio in action, and the math behind it shows up everywhere – even in your exams.

💡 In Simple Words: A ratio tells you how many parts of one thing match parts of another. A proportion says two ratios are equal. Solve a word problem by turning the story into a proportion, then find the missing number.

Maths Ratio and Proportion Word Problems – Quick Overview

When the exam asks for a "ratio word problem" it’s really testing two skills: reading a real‑life situation and translating it into a clean mathematical statement. The same idea works for "6th grade math ratio and proportion word problems" and even for the GED – the steps don’t change.

What is a Ratio?

A ratio is just a way of comparing two quantities. Think of it like a recipe: 2 cups of flour for every 3 cups of sugar means the flour‑to‑sugar ratio is 2:3. You can write it with a colon (2:3), a fraction (2/3), or the word "to" (2 to 3). The important part is that the two numbers stay together as a pair.

What is a Proportion?

A proportion says two ratios are the same. If you double the recipe, you get 4 cups of flour for every 6 cups of sugar – that’s 4:6, which simplifies back to 2:3. So 2:3 = 4:6 is a proportion. In symbols we write a/b = c/d. Once you set up a proportion, you can cross‑multiply (multiply across the equals sign) to find the missing piece.

Step‑by‑Step Process for Solving Ratio Word Problems

Here’s the recipe most teachers love:

• Read the problem carefully – highlight the numbers and what they’re comparing.
• Identify the two quantities that form a ratio.
• Write the given ratio in simplest form.
• Set up a proportion using the unknown quantity.
• Cross‑multiply and solve for the unknown.
• Check the answer makes sense in the original context.

Want a visual? Below is a tiny flowchart that walks you through these steps.

Worked Example 1 – Simple Sharing

Problem: A juice mix uses orange juice and water in the ratio 3:5. If you have 12 L of orange juice, how many litres of water do you need?

Solution:

1. Ratio orange : water = 3 : 5.
2. Let the amount of water be w litres.
3. Set up the proportion: 3/5 = 12/w.
4. Cross‑multiply: 3·w = 5·12 → 3w = 60.
5. Divide both sides by 3: w = 20 L.
6. Check: 12 L orange to 20 L water = 12/20 = 3/5 – correct!

Worked Example 2 – Mixed Ages (GED style)

Problem: In a class, the ratio of boys to girls is 4:7. If there are 28 girls, how many boys are there?

Solution:

1. Given ratio boys : girls = 4 : 7.
2. Let boys be b. Girls are 28.
3. Proportion: 4/7 = b/28.
4. Cross‑multiply: 4·28 = 7·b → 112 = 7b.
5. Divide by 7: b = 16.
6. Check: 16 boys to 28 girls simplifies to 4:7 – perfect.

Common Mistakes to Dodge

• Mixing up which quantity goes on which side of the proportion.
• Forgetting to simplify the given ratio first – it can lead to bigger numbers and more arithmetic errors.
• Skipping the “check” step – a quick sanity check catches swapped numbers.

Quick Comparison Table

📝 Likely Exam Questions

1. Question: The ratio of red to blue marbles in a bag is 2:3. If there are 45 blue marbles, how many red marbles are there?
   Answer: Set up 2/3 = r/45 → 2·45 = 3r → 90 = 3r → r = 30.
2. Question: A recipe calls for sugar and flour in the ratio 1:4. If you use 5 kg of sugar, how much flour is needed?
   Answer: 1/4 = 5/f → 1·f = 4·5 → f = 20 kg.
3. Question: In a school, the student‑teacher ratio is 20:1. If there are 600 students, how many teachers are there?
   Answer: 20/1 = 600/t → 20t = 600 → t = 30 teachers.
4. Question: A map uses a scale of 1 cm : 5 km. If two cities are 12 cm apart on the map, what is the real distance?
   Answer: 1/5 = 12/x → x = 12·5 = 60 km.
5. Question: The ratio of the ages of A and B is 5:3. Five years ago, A was twice as old as B. Find their present ages.
   Answer: Let ages be 5k and 3k. Five years ago: 5k‑5 = 2(3k‑5). Solve: 5k‑5 = 6k‑10 → k = 5. Ages now: A = 25, B = 15.