Moderate Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Express the ratio 24 : 36 in its simplest form.

Correct! Dividing both by 12: 24 : 36 = 2 : 3.

(2) If the ratio of boys to girls in a class is 3:4, how many girls are there if there are 12 boys?

Perfect! If boys : girls = 3 : 4, then girls = 43 × 12 = 16.

(3) Write the ratio of 15 cm to 2 m.

Excellent! 2 m = 200 cm. Ratio = 15 : 200 = 3 : 40.

(4) Find the fourth proportional to 3, 7, 14. 32233047

Great! If 3 : 7 = 14 : x, then x = (7 × 14) ÷ 3 = 983 = 32 23.

(5) If 5 pens cost ₹20, how much will 8 pens cost?

Correct! Cost per pen = ₹4. Cost of 8 pens = 8 × 4 = ₹32.

Short Answer Questions (2 Marks Each)

Answer each question clearly

(1) A recipe requires ingredients in the ratio 2 : 3 : 5. If the quantity of the first ingredient is 200 g, find the quantities of the other two ingredients.

Second ingredient: g Third ingredient: g

Excellent! If first : second : third = 2 : 3 : 5, then second = 32 × 200 = 300 g, third = 52 × 200 = 500 g.

(2) The ratio of the ages of A and B is 5:7. If A is 20 years old, find B's age.

Perfect! If A : B = 5 : 7, then B = 75 × 20 = 28 years.

(3) Divide ₹315 among three friends in the ratio 2 : 3 : 4.

First friend: ₹ Second friend: ₹ Third friend: ₹

Correct! Total parts = 2 + 3 + 4 = 9. Shares: 70, 105, 140.

(4) If 7 notebooks cost ₹84, find the cost of 10 notebooks.

Great! Cost per notebook = ₹12. Cost of 10 = 10 × 12 = ₹120.

(5) The ratio of the number of apples to oranges in a basket is 4:5. If there are 45 oranges, how many apples are there?

Perfect! If apples : oranges = 4 : 5, then apples = 45 × 45 = 36.

Long Answer Questions (4 Marks Each)

(1) A sum of money is to be divided among A, B, and C in the ratio 3 : 4 : 5. If C gets ₹150 more than A, find the total sum of money.

Total sum: ₹

Correct! Let shares be 3x, 4x, 5x. C - A = 5x - 3x = 2x = 150, so x = 75. Total = 12x = 900.

(2) A map is drawn with a scale of 1:50,000. If the distance between two towns on the map is 8 cm, find the actual distance in km.

Actual distance: km

Perfect! Actual distance = 8 × 50,000 = 4,00,000 cm = 4 km.

(3) Two numbers are in the ratio 7:9. If their sum is 128, find the numbers.

Smaller number: Larger number:

Excellent! Let numbers be 7x and 9x. Sum = 16x = 128, so x = 8. Numbers are 56 and 72.

(4) The ratio of the lengths of two rectangles is 5:6 and the ratio of their breadths is 4:5. Find the ratio of their areas.

Ratio of areas:

Great! Area ratio = (5×4) : (6×5) = 20 : 30 = 2 : 3.

(5) A school has students in the ratio of boys to girls as 7:5. If there are 140 boys, find the total number of students in the school.

Total students:

Correct! If boys : girls = 7 : 5, then girls = 57 × 140 = 100. Total = 140 + 100 = 240.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The ratio 12:18 in simplest form is:

(a) 3:4 (b) 2:3 (c) 4:6 (d) 6:9

Correct! Dividing both by 6: 12:18 = 2:3.

(2) If 5 kg of sugar costs ₹150, the cost of 8 kg is:

(a) ₹200 (b) ₹240 (c) ₹250 (d) ₹300

Correct! Cost per kg = ₹30. Cost of 8 kg = 8 × 30 = ₹240.

(3) The fourth proportional to 2, 5, 10 is:

(a) 15 (b) 20 (c) 25 (d) 30

Correct! If 2:5 = 10:x, then x = (5 × 10) ÷ 2 = 25.

(4) If the ratio of two numbers is 3:7 and their sum is 40, the smaller number is:

(a) 12 (b) 15 (c) 18 (d) 20

Correct! Let numbers be 3x and 7x. Sum = 10x = 40, so x = 4. Smaller = 12.

(5) A sum of money is divided among three friends in the ratio 1 : 2 : 3. If the total sum is ₹360, the largest share is:

(a) ₹60 (b) ₹100 (c) ₹180 (d) ₹120

Correct! Total parts = 6. Largest share = 36 × 360 = ₹180.

(6) The ratio of the number of boys to girls in a class is 2:3. If there are 24 girls, the number of boys is:

(a) 12 (b) 16 (c) 18 (d) 20

Correct! If boys:girls = 2:3, then boys = 23 × 24 = 16.

(7) Two numbers are in the ratio 5:8. If the smaller number is 25, the larger number is:

(a) 30 (b) 35 (c) 40 (d) 45

Correct! If ratio is 5:8 and smaller = 25, then larger = 85 × 25 = 40.

(8) The ratio of lengths of two rectangles is 3:4 and the ratio of their breadths is 2:3. The ratio of their areas is:

(a) 3:4 (b) 1:2 (c) 2:3 (d) 1:1

Correct! Area ratio = (3×2):(4×3) = 6:12 = 1:2.

(9) If 7 pens cost ₹28, the cost of 10 pens is:

(a) ₹36 (b) ₹38 (c) ₹40 (d) ₹42

Correct! Cost per pen = ₹4. Cost of 10 pens = 10 × 4 = ₹40.

(10) A map is drawn with a scale of 1:25,000. If two places are 6 cm apart on the map, the actual distance in meters is:

(a) 1.5 km (b) 1500 m (c) 0.15 km (d) 15 km

Correct! Actual distance = 6 × 25,000 = 1,50,000 cm = 1500 m = 1.5 km.

True or False

Determine whether these statements are True or False:

Advanced Proportion Quiz