Moderate Level Worksheet Questions
Interactive Comparing Quantities Using Proportion Worksheet
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
Proportion and ratio are essential mathematical tools for comparing quantities, solving practical problems, and understanding relationships between different measures. These concepts form the foundation for percentage calculations, scaling, and real-world problem solving.
Let's start with fundamental ratio and proportion concepts.
1. Write the ratio of ₹5 to ₹8.
Perfect! The ratio is written as first quantity : second quantity = 5:8.
2. Express 75% as a ratio.
Excellent! 75% = 75/100 = 3/4, which gives ratio 3:4.
3. The ratio of length to breadth of a rectangle is 5 : 3. If the breadth is 9 cm, find its length.
If 1 part of breadth =
Then Length =
Great! Using ratio scaling: if 3 parts = 9 cm, then 5 parts = 15 cm.
4. Find the value of x: 7 : x = x : 28.
To find the value of x wwe need to do
Cross multiply:
Therefore x =
Perfect! In continued proportion, the middle term is the geometric mean.
5. Express 0.6 as a percentage.
Correct! 0.6 = 6/10 = 60/100 = 60%.
6. If 8 pens cost ₹40, find the cost of 1 pen.
Excellent! Cost per pen = ₹40 ÷ 8 = ₹5.
7. In a ratio 4 : 7, what part is the second term of the sum of the terms?
Sum of terms = 4 + 7 =
Second term's part =
Perfect! The second term (7) is 7/11 of the total.
8. A sum of ₹600 is divided between A and B in the ratio 1 : 2. Find A's share.
Step 1: Total parts = 1 + 2 =
Step 2: A's share = (1/3) × 600 =
Great! A gets 1 part out of 3 total parts.
9. Write the first term of the ratio 18 : 24 in its simplest form.
Step 1: GCD of 18 and 24 =
Step 2: Simplest form: 18:24 = 3:4, so first term =
Excellent! Dividing both terms by 6 gives the simplest form 3:4.
10. If the ratio of speed of two vehicles is 3 : 5, find the ratio of their times taken to cover the same distance.
Logic: Speed ∝ 1/Time, so if speed ratio is 3:5, time ratio is
Perfect! Speed and time are inversely proportional for the same distance.
Drag each concept to its correct category:
Part B: Short Answer Questions (2 Marks Each)
1. If the income of A and B are in the ratio 7 : 9, and their total income is ₹48,000, find each income.
Step 1: Find total parts
Total parts = 7 + 9 =
Step 2: Calculate individual incomes
A's income =
B's income =
Perfect! A gets 7/16 and B gets 9/16 of the total income.
2. A map is drawn to the scale 1 cm : 50 km. Find the actual distance represented by 6 cm on the map.
Step 1: Apply the scale
If 1 cm represents 50 km, then 6 cm represents:
Excellent! Scale problems use direct proportion: 1:50 = 6:300.
3. If 12 men can complete a work in 8 days, how many men are required to complete it in 6 days?
Step 1: Calculate total work
Total work = 12 men
Men required for 6 days =
Great! This is inverse proportion: more men means less time.
4. A recipe requires sugar and flour in ratio 2 : 5. If 250 g of sugar is used, find quantity of flour needed.
Step 1: Find value of one part
If sugar = 2 parts = 250 g, then 1 part =
Step 2: Calculate flour quantity
Flour = 5 parts =
Perfect! Using ratio scaling to find the required quantity.
Part C: Long Answer Questions (4 Marks Each)
1. A sum of ₹72,000 is divided between A, B, and C in the ratio 5 : 7 : 9. Find each share.
Step 1: Find total parts
Total parts = 5 + 7 + 9 =
Step 2: Calculate each share
A's share =
B's share =
C's share =
Outstanding! Each person gets their proportional share of the total amount.
2. A mixture of milk and water contains milk and water in ratio 7 : 3. If 15 litres of water is added, ratio becomes 7 : 5. Find original quantity of milk.
Step 1: Set up initial conditions
Let original milk = 7x litres, original water = 3x litres
Step 2: Set up new conditions
After adding 15 litres: milk =
New ratio: 7x : (3x + 15) = 7 : 5
Step 3: Cross multiply and solve
Solving x =
Step 4: Find original milk quantity
Original milk = 7 × 7.5 =
Excellent! The original mixture had 52.5 litres of milk.
3. Two numbers are in ratio 3 : 4. If their LCM is 120, find the numbers.
Step 1: Express numbers in terms of x
Let the numbers be 3x and 4x
Step 2: Use LCM property
Since gcd(3,4) = 1, the numbers 3x and 4x have gcd =
LCM = (3x × 4x) ÷ x =
Step 3: Solve for x
Given: LCM =
So 12x = 120
Therefore x =
Step 4: Find the numbers
First number = 3 × 10 =
Second number = 4 × 10 =
Perfect! The numbers 30 and 40 are in ratio 3:4 with LCM 120.
4. A sum of ₹2,100 is divided among three friends in ratio 2/3 : 1/4 : 1/5. Find each share.
Step 1: Convert to whole numbers
LCM of 3, 4, 5 =
2/3 : 1/4 : 1/5 = 40/60 : 15/60 : 12/60 =
Step 2: Find total parts
Total parts = 40 + 15 + 12 =
Step 3: Calculate each share
First share = (40/67) × 2100 =
Second share = (15/67) × 2100 =
Third share = (12/67) × 2100 =
Outstanding! Converting fractional ratios to whole numbers makes calculation easier.
Test your understanding with these multiple choice questions:
For each question, click on the correct answer:
1. Which of the following is equal to 0.25?
(a) 1/4 (b) 25% (c) 25 : 100 (d) All of these
Correct! 0.25 = 1/4 = 25% = 25:100. All represent the same value.
2. If a : b = 3 : 5, then b : a =
(a) 3 : 5 (b) 5 : 3 (c) 1 : 1 (d) None
Correct! The inverse ratio flips the terms: if a:b = 3:5, then b:a = 5:3.
3. The ratio of 2 m to 150 cm is:
(a) 4 : 3 (b) 3 : 4 (c) 2 : 3 (d) 3 : 2
Correct! 2 m = 200 cm, so 200:150 = 4:3 (dividing by 50).
4. Which ratio is in the simplest form?
(a) 12 : 16 (b) 15 : 25 (c) 8 : 14 (d) 9 : 16
Correct! 9:16 has no common factors (9 and 16 are coprime).
5. If 12 workers can build a wall in 8 days, then 8 workers will build it in:
(a) 6 days (b) 8 days (c) 12 days (d) 15 days
Correct! Total work = 12×8 = 96 man-days. So 8 workers need 96÷8 = 12 days.