Basic Percentage Word Problems - Free Printable

Let’s solve each of the 8 percentage word problems step by step, and then identify the impossible/trick problem as requested.

---

Problem 1:

> A bike costs $200 but is reduced by 35% in a sale.
> How much is the bike reduced by?
> What does it cost in the sale?

- Reduction amount: 35% of $200 = 0.35 × 200 = $70
- Sale price: $200 - $70 = $130

✔ Answer: Reduced by $70, costs $130 in sale.

---

Problem 2:

> A bag contains some red, blue and yellow balls. 32% of the balls are blue and 44% are red. If there are 50 balls in the bag, how many are yellow?

- Total % accounted for: 32% (blue) + 44% (red) = 76%
- So yellow = 100% - 76% = 24%
- Number of yellow balls = 24% of 50 = 0.24 × 50 = 12

✔ Answer: 12 yellow balls

---

Problem 3:

> I toss a coin more than 60 times. It comes down tails 45% of the time. How many heads did I toss?

- Let total tosses = T (T > 60)
- Tails = 45% of T → Heads = 55% of T
- But we don’t know the exact number of tosses — only that it’s “more than 60”.

⚠️ Problem: We can’t compute an exact number of heads without knowing T. For example:
- If T = 61 → heads = 55% of 61 = 33.55 → not possible (can’t have half a head!)
- If T = 100 → heads = 55 → possible
- But since T must be such that 45% of T is a whole number (tails must be whole), T must be a multiple of 20 (since 45% = 9/20).

So possible values: T = 80 → tails = 36, heads = 44
T = 100 → tails = 45, heads = 55
But the problem says “more than 60” — so smallest possible is 80.

BUT — the question asks “How many heads did I toss?” implying a unique answer. Since T isn’t specified, this problem cannot be solved uniquely without assuming a value.

✘ This is likely the trick/impossible problem!
*(We’ll confirm after checking others.)*

---

Problem 4:

> A piece of hematite contains 72% iron. If the hematite weighed 150g, how much iron would there be?

- Iron = 72% of 150g = 0.72 × 150 = 108g

✔ Answer: 108 grams of iron

---

Problem 5:

> In a basketball game, Sally is the top scorer with 35% of the team’s points. If the team scored 120 points in total, how many points did Sally score?

- Sally’s points = 35% of 120 = 0.35 × 120 = 42

✔ Answer: 42 points

---

Problem 6:

> A survey of 250 trees in a small wood showed that 32% were oak trees, 26% were birch trees and the remainder were pine trees. How many pine trees were there?

- Oak: 32% of 250 = 0.32 × 250 = 80
- Birch: 26% of 250 = 0.26 × 250 = 65
- Pine = Total - (Oak + Birch) = 250 - (80 + 65) = 250 - 145 = 105

✔ Answer: 105 pine trees

---

Problem 7:

> A toy helicopter costs $64 before sales tax. If the sales tax is 10%, how much would it cost to buy?

- Tax = 10% of $64 = 0.10 × 64 = $6.40
- Total cost = $64 + $6.40 = $70.40

✔ Answer: $70.40

---

Problem 8:

> In a school survey of 300 pupils, 63% walk to school regularly. How many children is this?

- 63% of 300 = 0.63 × 300 = 189

✔ Answer: 189 children

---

## ✔ Final Answer:

All problems except Problem 3 have clear, unique numerical answers.

🚫 The Impossible/Trick Problem is: Problem 3

> *“I toss a coin more than 60 times. It comes down tails 45% of the time. How many heads did I toss?”*

Why it’s impossible/tricky:

- The number of tosses is not given — only that it’s “more than 60”.
- 45% of the total tosses must be a whole number (you can’t have 0.5 tails).
- So total tosses must be a multiple of 20 (since 45% = 9/20).
- Smallest possible total tosses > 60 that satisfies this is 80.
- Then tails = 36, heads = 44.
- But the problem doesn’t specify that total tosses is 80 — it could be 100, 120, etc., giving different numbers of heads.
- Therefore, without knowing the exact number of tosses, we cannot give a unique answer.

This makes it the trick/impossible problem.

---

## ✔ Final Summary:

| Problem | Answer |
|---------|--------|
| 1 | Reduced by $70; Sale price $130 |
| 2 | 12 yellow balls |
| 3 | ❗ Impossible / Trick Problem — No unique answer without knowing exact number of tosses |
| 4 | 108g iron |
| 5 | 42 points |
| 6 | 105 pine trees |
| 7 | $70.40 |
| 8 | 189 children |

---

✔ Did you manage to find the impossible problem?
→ Yes! It’s Problem 3.