Ratio Word Problems Worksheets - Free Printable

Let’s go step by step through each question. We’ll start with the first setup and build from there.

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Initial Setup:
Captain Salamander puts 2 white balls and 4 black balls in a bag.

Total balls = 2 + 4 = 6 balls

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1) What is the ratio of white balls to black balls?

White : Black = 2 : 4

→ Answer: 2 : 4

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2) Write this ratio in its simplest form

We can divide both numbers by 2:

2 ÷ 2 = 1
4 ÷ 2 = 2

So, simplest form is 1 : 2

→ Answer: 1 : 2

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He shakes the bag and picks out a ball at random.

Total balls still = 6 (2 white, 4 black)

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3) What is the probability that it is white?

Probability = (number of white balls) / (total balls) = 2/6

Simplify: 2 ÷ 2 = 1, 6 ÷ 2 = 3 → 1/3

→ Answer: 1/3

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4) What is the probability that it is black?

Black balls = 4, total = 6 → 4/6

Simplify: 4 ÷ 2 = 2, 6 ÷ 2 = 3 → 2/3

→ Answer: 2/3

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He puts the ball back and adds 4 more white balls into the bag and shakes it.

Now:
- White balls: original 2 + 4 new = 6 white
- Black balls: still 4 black
- Total balls = 6 + 4 = 10

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5) What is the ratio of white to black balls now?

White : Black = 6 : 4

We can leave it like this for now — but let’s check if they want simplest form? The instruction says “write your ratio answers in the form __ : __” — doesn’t specify simplest unless asked. But since Q2 asked for simplest, maybe we should simplify here too? Let’s see context.

Actually, looking at Q7 later, it asks for a 3-part ratio — so probably they accept unsimplified unless specified. But to be safe, let’s give both and pick what fits.

Wait — Q5 just says “ratio”, not “simplest”. So 6:4 is fine. But often in math, we simplify ratios unless told otherwise. Let me check the pattern.

In Q1 and Q2, they separated “what is the ratio” and then “simplest form”. So for Q5, since they didn’t ask for simplest, maybe 6:4 is acceptable. But actually, in most school problems, you simplify ratios automatically. Hmm.

Looking ahead — Q7 will have red:white:black — likely unsimplified. To avoid confusion, I’ll write 6:4, but note that it simplifies to 3:2. However, since the problem didn’t say “simplest”, and Q2 specifically did, I think 6:4 is okay. But let me double-check standard practice.

Actually, no — in ratio problems, unless stated otherwise, you usually present in simplest form. For example, if you have 6:4, it’s better as 3:2. And since Q2 taught us to simplify, I think we should do it here too.

But wait — the instruction says: “Write your ratio answers in the form __ : __.” It doesn’t say “simplest”, but in math class, ratios are typically simplified. Also, in Q2 they made a point to ask for simplest, implying that sometimes you don’t — but for consistency, let’s look at the next part.

Actually, let’s proceed with 6:4 for now, and if needed adjust. But I think the expected answer is 3:2. Let me calculate:

6 white : 4 black → divide by 2 → 3:2

Yes, that’s simpler and standard.

→ Answer: 3 : 2

*(I’ll go with simplified because it’s good practice and matches Q2’s intent.)*

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6) What is the probability that a ball chosen at random will be black?

Black balls = 4
Total balls = 10
Probability = 4/10 = 2/5 (simplified)

→ Answer: 2/5

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Now Captain Salamander adds 2 red balls into the bag.

Current before adding red:
- White: 6
- Black: 4
- Add 2 red → now red = 2

Total balls = 6 + 4 + 2 = 12

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7) What is the ratio of red balls to white balls to black balls?

Red : White : Black = 2 : 6 : 4

Can we simplify? Divide all by 2 → 1 : 3 : 2

Again, since they didn’t specify “simplest”, but in ratio problems, we usually simplify. Also, 2:6:4 reduces nicely.

→ Answer: 1 : 3 : 2

*(If they wanted unsimplified, it would be 2:6:4, but 1:3:2 is better.)*

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8) What is the probability that a ball chosen at random will be red?

Red balls = 2
Total = 12
Probability = 2/12 = 1/6

→ Answer: 1/6

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9) What is the probability that a ball chosen at random will not be white?

Not white means black or red.

Black = 4, Red = 2 → total not white = 6
Total balls = 12
Probability = 6/12 = 1/2

Alternatively: P(not white) = 1 - P(white) = 1 - (6/12) = 1 - 1/2 = 1/2

→ Answer: 1/2

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Captain Salamander now empties the bag, and then refills it with red and white balls in the ratio of 2 red balls for every 3 white balls.

So new ratio: Red : White = 2 : 3

This means for every 2 red, there are 3 white.

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10) If he puts in 6 red balls, how many white balls would there be?

Ratio Red : White = 2 : 3

If red = 6, which is 2 × 3, then white = 3 × 3 = 9

Because 2 parts → 6, so 1 part = 3, so 3 parts = 9.

→ Answer: 9

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11) If he puts in 18 white balls, how many red balls would there be?

Ratio Red : White = 2 : 3

White = 18 → which is 3 parts → so 1 part = 18 ÷ 3 = 6

Then red = 2 parts = 2 × 6 = 12

→ Answer: 12

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Now, let’s compile all final answers clearly.

Final Answer:
1) 2 : 4
2) 1 : 2
3) 1/3
4) 2/3
5) 3 : 2
6) 2/5
7) 1 : 3 : 2
8) 1/6
9) 1/2
10) 9
11) 12