Math worksheet with ratio and proportion word problems for students to solve.

Let’s solve each problem step by step.

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Problem 1: Carbon in steel

We’re told:
→ 15 g of carbon is in every 1 kg (which is 1000 g) of steel.

a. How much carbon in 10 kg of steel?

If 1 kg has 15 g → then 10 kg has 15 × 10 = 150 g

✔ Answer for 1a: 150 g

b. How much steel from 600 g of carbon?

We know: 15 g carbon → makes 1000 g steel
So, how many “15 g” groups are in 600 g?
→ 600 ÷ 15 = 40

Each group makes 1000 g steel → so 40 × 1000 = 40,000 g
That’s 40 kg — but since the question doesn’t specify units, we can leave it as grams or convert. Let’s check context: original was in g and kg. Since input was 600 g, output in g is fine unless asked otherwise. But 40,000 g = 40 kg — probably better to write as 40 kg for clarity.

Wait — let’s double-check:

Ratio: carbon : steel = 15g : 1000g = 3:200

So if carbon = 600g, then steel = (200/3) × 600 = 200 × 200 = 40,000 g = 40 kg

✔ Answer for 1b: 40 kg

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Problem 2: Class going to Alton Towers

Total children = 36
Ratio boys : girls = 5 : 4

Total parts = 5 + 4 = 9 parts

Each part = 36 ÷ 9 = 4 children

Boys = 5 parts → 5 × 4 = 20 boys

✔ Answer for 2a: 20

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Problem 3: Dan and Tom share prize money

Ratio Dan : Tom = 4 : 9
Dan got smaller amount = £120 → that’s his 4 parts

So 4 parts = £120 → 1 part = 120 ÷ 4 = £30

a. Total amount won?

Total parts = 4 + 9 = 13
Total = 13 × £30 = £390

✔ Answer for 3a: £390

b. How much did Tom get?

Tom = 9 parts → 9 × £30 = £270

✔ Answer for 3b: £270

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Problem 4: Fruit picking

Ratio Leanne : Emma : Debbie = 4 : 3 : 1
Leanne picked 12 kilos → her 4 parts = 12 kg

So 1 part = 12 ÷ 4 = 3 kg

a. How much did Emma pick?

Emma = 3 parts → 3 × 3 = 9 kg

✔ Answer for 4a: 9 kg

b. Total fruit picked?

Total parts = 4 + 3 + 1 = 8
Total = 8 × 3 = 24 kg

✔ Answer for 4b: 24 kg

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Problem 5: Aeroplane passengers

Total people = 390
Adults : Children = 9 : 4

Total parts = 9 + 4 = 13

Each part = 390 ÷ 13 = 30

a. Adults?

9 parts → 9 × 30 = 270 adults

✔ Answer for 5a: 270

b. Children?

4 parts → 4 × 30 = 120 children

✔ Answer for 5b: 120

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Problem 6: Simplify ratio 91 : 63

Find greatest common factor (GCF) of 91 and 63.

Factors of 63: 1, 3, 7, 9, 21, 63
Factors of 91: 1, 7, 13, 91
Common factors: 1, 7 → GCF = 7

Divide both by 7:

91 ÷ 7 = 13
63 ÷ 7 = 9

So simplified ratio = 13 : 9

✔ Answer for 6: 13 : 9

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Final Answer:
1a. 150 g
1b. 40 kg
2a. 20
3a. £390
3b. £270
4a. 9 kg
4b. 24 kg
5a. 270
5b. 120
6. 13 : 9