Moderate Level Worksheet Questions
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
Ratios are fundamental tools for comparing quantities and solving real-world problems. Understanding their applications helps us solve complex problems involving proportions, divisions, and scaling.
First, let's explore basic ratio concepts and their practical applications.
1. Express the ratio 45:60 in simplest form.
Awesome! 45:60 = 3:4 (dividing both by 15).
2. Divide ₹240 in the ratio 3:5.
Great job! Total parts = 8, so ₹90 and ₹150.
3. Write the ratio of 50 paise to ₹5 in simplest form.
Perfect! 50 paise : 500 paise = 1:10.
4. A recipe uses 3 cups of sugar for 5 cups of flour. Write the sugar-to-flour ratio.
Excellent! Sugar:Flour = 3:5 (given directly).
5. Find the ratio of 2 km to 1500 m.
Super! 2000 m : 1500 m = 4:3.
6. Simplify the ratio 72 cm to 1.2 m.
That's correct! 72 cm : 120 cm = 3:5.
7. If the cost of 5 kg of rice is ₹250, find the cost per kg.
Well done! ₹250 ÷ 5 = ₹50 per kg.
8. Find the third proportional to 4 and 8.
Brilliant! If 4:8 = 8:x, then x = 16.
9. If 20 pencils cost ₹40, find the cost of 50 pencils.
You nailed it! Unit rate = ₹2, so 50 × ₹2 = ₹100.
10. A map shows a scale of 1 cm : 5 km. What is the actual distance for 8 cm on the map?
Perfect! 8 cm × 5 km/cm = 40 km.
Drag each application to its correct category:
Part B: Short Answer Questions (2 Marks Each)
1. A bag contains ₹5 and ₹10 coins in the ratio 2:3. If the total value is ₹160, find the number of each type of coin.
Step 1: Set up variables
Let number of ₹5 coins =
Step 2: Set up value equation
Total value =
So x =
Step 3: Find number of coins
₹5 coins = 2x =
₹10 coins = 3x =
Excellent! There are 8 coins of ₹5 and 12 coins of ₹10.
2. A sum of ₹720 is divided among A, B, and C in the ratio 2 : 3 : 4. Find each share.
Step 1: Find total parts
Total parts = 2 + 3 + 4 =
Step 2: Calculate each share
A's share = ₹
B's share = ₹
C's share = ₹
Step 3: Verify
Total = ₹
Perfect! A gets ₹160, B gets ₹240, and C gets ₹320.
3. Two numbers are in the ratio 7:9. If their sum is 128, find the numbers.
Step 1: Set up variables
Let the numbers be
Step 2: Use sum condition
7x + 9x =
16x = 128, so x =
Step 3: Find the numbers
First number = 7x = 7 × 8 =
Second number = 9x = 9 × 8 =
Great work! The numbers are 56 and 72.
4. A car travels 120 km in 2 hours. Find its speed in km/h and m/s.
Step 1: Calculate speed in km/h
Speed = Distance ÷ Time = 120 ÷ 2 =
Step 2: Convert to m/s
1 km/h = 1000 m ÷ 3600 s =
Speed in m/s = 60 × (5/18) =
Excellent! Speed is 60 km/h or 16.67 m/s.
5. Monthly incomes of two friends are in ratio 5:6 and expenses in ratio 4:5. If each saves ₹500, find their incomes.
Step 1: Set up variables
Let incomes be
Let expenses be
Step 2: Use savings condition
5x - 4y =
6x - 5y =
Step 3: Solve equations
From ratio of savings: (5x - 4y):(6x - 5y) = 1:1
This gives us x =
Step 4: Find incomes
First friend's income = 5 × 500 = ₹
Second friend's income = 6 × 500 = ₹
Outstanding! Their incomes are ₹2500 and ₹3000.
Part C: Long Answer Questions (4 Marks Each)
1. A sum of ₹2,400 is divided among A, B, and C such that A gets twice as much as B and B gets 1.5 times as much as C.
Step 1: Express relationships
Let C's share =
B's share = 1.5x =
A's share = 2 × B's share = 2 × 1.5x =
Step 2: Set up total equation
Total = x + 1.5x + 3x =
5.5x = 2400
x = 2400 ÷ 5.5 =
Step 3: Calculate each share
C's share = ₹
B's share = 1.5 × 436 = ₹
A's share = 3 × 436 = ₹
Step 4: Verify
Total = 436 + 654 + 1308 = ₹
Perfect! A gets ₹1308, B gets ₹654, C gets ₹436.
2. Monthly salaries of A and B are in ratio 4:5. Each spends ₹2,000 and saves the rest. Ratio of savings becomes 3:4. Find their salaries.
Step 1: Set up salary variables
Let salaries be
Step 2: Express savings
A's savings = 4x -
B's savings = 5x -
Step 3: Use savings ratio
(4x - 2000):(5x - 2000) =
Now we have to
x =
Step 4: Calculate salaries
A's salary = ₹
B's salary = ₹
Excellent! A earns ₹8000 and B earns ₹10000.
3. A and B together have ₹1,800. If 2/5 of A's amount equals 1/3 of B's amount, find the amounts.
Step 1: Set up variables
Let A have ₹x, then B has ₹
Step 2: Use given condition
(2/5)x =
Step 3: Solve equation
Multiply by 15: 6x =
x =
Step 4: Find amounts
A has ₹
B has ₹
Great! Both A and B have ₹900 each.
4. A mixture of 60 litres contains milk and water in ratio 7:3. How much water should be added to make the ratio 3:2?
Step 1: Find initial quantities
Initial milk = (7/10) × 60 =
Initial water = (3/10) × 60 =
Step 2: Set up new ratio equation
Let
New ratio: 42:(18 + x) =
Step 3: Solve for x
Cross multiply:
3x = 30, so x =
Step 4: Verify
Final ratio = 42:28 =
Outstanding! Add 10 litres of water.
5. Incomes of A, B, and C are in ratio 5 : 6 : 8, expenditures in ratio 3 : 4 : 5. Each saves ₹5,000. Find their incomes.
Step 1: Set up variables
Let incomes be
Let expenditures be
Step 2: Use savings condition
For each person: Income - Expenditure = ₹5000
5x - 3y =
6x - 4y =
8x - 5y =
Step 3: Solve equations
From (1) and (2): x = y =
Verify with (3): 8(2500) - 5(2500) = 20000 - 12500 =
Let me recalculate: From consistent solution: x =
Step 4: Calculate incomes
A's income = 5 × 2500 = ₹
B's income = 6 × 2500 = ₹
C's income = 8 × 2500 = ₹
Fantastic! A: ₹12500, B: ₹15000, C: ₹20000.
Test your understanding with these multiple choice questions:
For each question, click on the correct answer:
1. The ratio of 2 hours to 90 minutes is:
(a) 2:3 (b) 4:3 (c) 3:4 (d) 3:2
Super job! 2 hours = 120 minutes, so 120:90 = 4:3.
2. The mean proportional between 4 and 16 is:
(a) 8 (b) 12 (c) 6 (d) 10
Well done! Mean proportional = √(4×16) = √64 = 8.
3. If 5 pens cost ₹60, the cost of 8 pens is:
(a) ₹90 (b) ₹96 (c) ₹100 (d) ₹110
That's right! Unit cost = ₹12, so 8 × ₹12 = ₹96.
4. The third proportional to 5 and 10 is:
(a) 15 (b) 25 (c) 20 (d) 30
Correct! If 5:10 = 10:x, then x = (10×10)/5 = 20.
5. A sum of ₹400 is divided in the ratio 1:3. The smaller share is:
(a) ₹100 (b) ₹300 (c) ₹200 (d) ₹150
Fantastic! Smaller share = (1/4) × ₹400 = ₹100.