Ratio and Proportion Worksheet featuring six math problems on ratios, proportions, and unit conversions.

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

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Problem 1:
A playschool has 63 boys and 27 girls. What will be the number of boys if there are 9 girls in the school?

→ First, find the ratio of boys to girls:
63 boys : 27 girls → Simplify by dividing both by 9 → 7 : 3

So for every 3 girls, there are 7 boys.

Now, if there are 9 girls (which is 3 × 3), then boys = 7 × 3 = 21

✔ Check: 21 boys : 9 girls → divide by 3 → 7:3 ✔️

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Problem 2:
A machine can produce 6 yards of fabric in 2 minutes. How much fabric can the machine produce in 1 hour?

→ 1 hour = 60 minutes

→ In 2 minutes → 6 yards
→ So in 1 minute → 6 ÷ 2 = 3 yards
→ In 60 minutes → 3 × 60 = 180 yards

✔ Check: 60 min ÷ 2 min = 30 sets → 30 × 6 yards = 180 ✔️

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Problem 3:
12 miles are approximately equal to 19 km. How many km (approx.) are equal to 18 miles?

→ Set up a proportion:
12 miles → 19 km
18 miles → ? km

→ Multiply 19 by (18/12) = 19 × 1.5 = 28.5 km

✔ Check: 18 is 1.5 times 12 → so 19 × 1.5 = 28.5 ✔️

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Problem 4:
80 boys are attending a picnic. There is a ratio of 3:5 for the number of girls to the number of boys. How many girls are there?

→ Ratio girls : boys = 3 : 5
Boys = 80 → which corresponds to 5 parts

→ So 1 part = 80 ÷ 5 = 16
→ Girls = 3 parts = 3 × 16 = 48

✔ Check: 48 girls : 80 boys → divide by 16 → 3:5 ✔️

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Problem 5 (first one):
The total weight of 15 boxes is 45 pounds. How much would 40 boxes weigh?

→ Weight per box = 45 ÷ 15 = 3 pounds
→ 40 boxes = 40 × 3 = 120 pounds

✔ Check: 15 boxes → 45 lbs → 40 boxes is more than double → 120 is reasonable ✔️

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Problem 5 (second one — labeled again as 5, but actually #6):
4 spoons cost $12. How much do 16 spoons cost?

→ Cost per spoon = 12 ÷ 4 = $3
→ 16 spoons = 16 × 3 = $48

✔ Check: 16 is 4 times 4 → so cost = 4 × 12 = 48 ✔️

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Final Answer:
21
180 yards
28.5 km
48
120 pounds
$48