Reasoning/Problem Solving Maths Worksheets for Year 6 (age 10-11 ... - Free Printable

Let’s solve each problem one by one, step by step.

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1. Karina had a roll of ribbon 4.8 m long. She cut off a piece 58 cm long. How much was left?

First, convert everything to the same unit — let’s use centimeters (cm).

- 4.8 meters = 4.8 × 100 = 480 cm
- She cut off 58 cm

Now subtract:
480 – 58 = 422 cm

You can also write it as 4.22 meters if you want, but since the question doesn’t specify, either is fine. We’ll go with cm for now.

✔ Answer: 422 cm

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2. A cup holds 0.2 litres. How many times can it be filled from a 4.2 litre pot of drink?

We divide total amount by cup size:

4.2 ÷ 0.2 = ?

Think: 0.2 goes into 4.2 how many times?

Multiply both numbers by 10 to make it easier:
42 ÷ 2 = 21

✔ Answer: 21 times

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3. A tablespoon holds 22 ml of liquid. How many tablespoons can be filled from a one litre bottle of medicine?

1 litre = 1000 ml

Divide: 1000 ÷ 22

Let’s calculate:

22 × 45 = 990 → that’s close!

1000 – 990 = 10 ml left over → not enough for another full tablespoon.

So, 45 full tablespoons

✔ Answer: 45

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4. An inch is approximately 2.54 cm. How many centimetres are there in one foot (12 inches)?

Multiply: 12 × 2.54

Break it down:

10 × 2.54 = 25.4
2 × 2.54 = 5.08
Add them: 25.4 + 5.08 = 30.48

✔ Answer: 30.48 cm

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5. A kilogram is approximately 2.2 pounds. Which is heavier: 10 pounds or 5 kilograms?

Convert 5 kg to pounds:
5 × 2.2 = 11 pounds

Compare: 11 pounds vs 10 pounds → 11 is heavier.

So, 5 kilograms is heavier

✔ Answer: 5 kilograms

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6. A small swimming pool holds 70,000 litres of water. The pool is filled with a hosepipe that supplies 1,750 litres an hour. How long does it take to fill the pool?

Divide total volume by rate per hour:

70,000 ÷ 1,750

Simplify: Divide numerator and denominator by 10 → 7,000 ÷ 175

Still big? Let’s try dividing 70,000 ÷ 1,750 directly.

Note: 1,750 × 40 = 70,000 → because 1,750 × 4 = 7,000 → so ×40 = 70,000

✔ Answer: 40 hours

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7. Change this list of ingredients to metric units:

Original:
- 4 oz sugar
- 1/2 oz flour
- 2 oz margarine
- 3 eggs
- 2 teaspoons of orange juice

Use approximate conversions:

- 1 ounce ≈ 28 grams (we’ll use 28 for simplicity)
- 1 teaspoon ≈ 5 millilitres

So:

→ Sugar: 4 oz × 28 = 112 g
→ Flour: 0.5 oz × 28 = 14 g
→ Margarine: 2 oz × 28 = 56 g
→ Eggs: still 3 eggs (no change needed)
→ Orange juice: 2 tsp × 5 ml = 10 ml

✔ Answer:
- 112 g sugar
- 14 g flour
- 56 g margarine
- 3 eggs
- 10 ml orange juice

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8. A model car has a volume of 90 millilitres. Another car is five and a quarter times as big. What is the volume of the big car?

Five and a quarter = 5.25

Multiply: 90 × 5.25

Break it down:

90 × 5 = 450
90 × 0.25 = 22.5
Add: 450 + 22.5 = 472.5

✔ Answer: 472.5 millilitres

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9. Josephine cycled 8.03 kilometres, then ran 4.2 kilometres and finally walked 2,000 metres. How far did she travel altogether? Give your answer in kilometres and metres.

First, convert all to metres:

- 8.03 km = 8,030 m
- 4.2 km = 4,200 m
- 2,000 m = 2,000 m

Add: 8,030 + 4,200 = 12,230; + 2,000 = 14,230 metres

Now convert back to km and m:

14,230 m = 14 km and 230 m

✔ Answer: 14 kilometres and 230 metres

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10. How many millilitres of soup needs to be added to 4.56 litres to make 5 litres?

Subtract: 5 – 4.56 = 0.44 litres

Convert to millilitres: 0.44 × 1000 = 440 ml

✔ Answer: 440 millilitres

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Final Answer:
1. 422 cm
2. 21 times
3. 45
4. 30.48 cm
5. 5 kilograms
6. 40 hours
7. 112 g sugar, 14 g flour, 56 g margarine, 3 eggs, 10 ml orange juice
8. 472.5 millilitres
9. 14 kilometres and 230 metres
10. 440 millilitres