Ratio and Proportion Problems worksheet with five word problems for students to solve.

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

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Problem 1:
There are 600 pupils in a school. The ratio of boys to girls is 3:5. How many girls and how many boys are in this school?

Step 1: Understand the ratio.
Boys : Girls = 3 : 5
That means for every 3 boys, there are 5 girls.

Step 2: Add the parts of the ratio.
3 + 5 = 8 parts total.

Step 3: Divide total pupils by total parts to find value of one part.
600 ÷ 8 = 75 → So each “part” is 75 pupils.

Step 4: Multiply to find boys and girls.
Boys = 3 × 75 = 225
Girls = 5 × 75 = 375

Check: 225 + 375 = 600 ✔

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Problem 2:
The perimeter of a rectangle is 280m. The ratio of its length to its width is 5:2. Find the area of the rectangle.

Step 1: Recall perimeter formula for rectangle:
Perimeter = 2 × (length + width)

Step 2: Let length = 5x, width = 2x (because ratio is 5:2)

Step 3: Plug into perimeter formula:
2 × (5x + 2x) = 280
2 × 7x = 280
14x = 280
x = 280 ÷ 14 = 20

Step 4: Find actual length and width.
Length = 5x = 5 × 20 = 100 m
Width = 2x = 2 × 20 = 40 m

Step 5: Area = length × width = 100 × 40 = 4000 m²

Check: Perimeter = 2×(100+40)=2×140=280 ✔

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Problem 3:
A jar is filled with pennies and nickels in the ratio of 5:3. If there are 30 nickels in the jar, how many pennies are there?

Step 1: Ratio Pennies : Nickels = 5 : 3

Step 2: We know nickels = 30, which corresponds to 3 parts.

So, 3 parts = 30 → 1 part = 30 ÷ 3 = 10

Step 3: Pennies = 5 parts = 5 × 10 = 50

Check: 50 pennies : 30 nickels = 5:3 ✔

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Problem 4:
The scale on a map is 1:20,000. What actual distance does a length of 8cm on the map represent?

Step 1: Scale 1:20,000 means 1 cm on map = 20,000 cm in real life.

Step 2: So 8 cm on map = 8 × 20,000 = 160,000 cm

Step 3: Convert to meters or kilometers if needed.
160,000 cm = 1,600 meters (since 100 cm = 1 m)
Or 1.6 km (since 1000 m = 1 km)

But since question doesn’t specify unit, we can leave as 160,000 cm — but better to convert to more practical units.

Actually, let’s write it as 1,600 meters or 1.6 km — both are correct. But perhaps best to give in meters since 160,000 cm is large.

Wait — let’s check:
8 cm × 20,000 = 160,000 cm
160,000 cm ÷ 100 = 1,600 m
1,600 m ÷ 1,000 = 1.6 km

We’ll go with 1,600 meters unless specified otherwise. But actually, in map problems, often they expect km. Let me see — 1.6 km is cleaner.

But to be precise, let’s state both? No — pick one. Since 8cm is small, 1.6km makes sense.

Actually, let’s stick to meters: 1,600 m. Or maybe the problem expects cm? No — that’s too big.

Standard practice: convert to meters or kilometers. I’ll use meters.

Final: 1,600 meters.

But wait — let’s double-check calculation:
8 × 20,000 = 160,000 cm → yes
160,000 / 100 = 1,600 m → yes

✔

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Problem 5:
If 6 copies of a book cost $9, calculate the cost of 8 books.

Step 1: Find cost of one book.
$9 ÷ 6 = $1.50 per book

Step 2: Multiply by 8.
$1.50 × 8 = $12.00

Check: 6 books = $9 → 1 book = $1.50 → 8 books = $12 ✔

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Now, compiling all answers:

Final Answer:
1. Boys: 225, Girls: 375
2. 4000 m²
3. 50 pennies
4. 1600 meters (or 1.6 km)
5. $12