| **RATIO AND PROPORTION** |ICDS Supervisor ,RI,ARI,AMIN,SFS|

**1. If a:b = 3:5, and b:c = 4:7, what is the ratio of a to c?**

a) 6:7

b) 12:35

c) 3:4

d) 7:15

**Answer: a) 6:7**

**2. If 4x + 6y = 18, and 2x + 3y = 9, what is the ratio of x to y?**

a) 2:3

b) 3:2

c) 1:2

d) 2:1

**Answer: a) 2:3**

**3. The ratio of boys to girls in a class is 2:3. If there are 25 students in the class, how many are girls?**

a) 10

b) 15

c) 20

d) 25

**Answer: b) 15**

**4. If the ratio of the side lengths of two similar triangles is 3:5, and the area of the smaller triangle is 27 square units, what is the area of the larger triangle?**

a) 45 square units

b) 75 square units

c) 81 square units

d) 125 square units

**Answer: b) 75 square units**

**5. A recipe calls for a mixture of sugar and flour in the ratio 2:5. If the total mixture weighs 280 grams, how much flour is needed?**

a) 100 grams

b) 140 grams

c) 175 grams

d) 200 grams

**Answer: c) 175 grams**

**6. If a:b = 7:9 and b:c = 4:5, what is the ratio of a:b:c?**

a) 7:9:5

b) 28:36:45

c) 4:5:7

d) 14:18:20

**Answer: b) 28:36:45**

**7. The length, width, and height of a rectangular box are in the ratio 3:2:5. If the volume is 300 cubic units, what is the height of the box?**

a) 5 units

b) 10 units

c) 15 units

d) 20 units

**Answer: a) 5 units**

**8. If the sum of two numbers is 35 and their ratio is 3:5, what are the two numbers?**

a) 12, 23

b) 15, 20

c) 18, 17

d) 21, 14

**Answer: b) 15, 20**

**9. The income of A and B are in the ratio 4:7. If the total income is $33,000, what is B’s income?**

a) $12,000

b) $21,000

c) $15,000

d) $18,000

**Answer: b) $21,000**

**10. If the cost of 5 pens is $25, what is the cost of 8 pens?**

a) $32

b) $40

c) $45

d) $50

**Answer: c) $45**

Certainly! Here are the next 10 moderately challenging multiple-choice questions on ratios and proportions along with their answers:

**11. The ratio of the ages of John and Mary is 5:3. If the sum of their ages is 64, how old is John?**

a) 30

b) 35

c) 40

d) 45

**Answer: a) 30**

**12. If the ratio of the angles in a triangle is 2:3:4, what is the measure of the smallest angle?**

a) 20 degrees

b) 30 degrees

c) 40 degrees

d) 50 degrees

**Answer: b) 30 degrees**

**13. The ratio of the lengths of two rectangles is 3:4, and the ratio of their widths is 5:2. What is the ratio of their areas?**

a) 3:4

b) 5:8

c) 15:8

d) 20:7

**Answer: c) 15:8**

**14. If the ratio of the number of boys to girls in a class is 2:5 and the total number of students is 105, how many boys are there?**

a) 21

b) 30

c) 35

d) 42

**Answer: d) 42**

**15. The length of a rectangle is twice its width. If the perimeter is 30 meters, what is the area of the rectangle?**

a) 25 square meters

b) 30 square meters

c) 35 square meters

d) 40 square meters

**Answer: a) 25 square meters**

**16. The present ages of A, B, and C are in the ratio 3:4:5. If the sum of their ages is 72, what will be the sum of their ages 3 years from now?**

a) 81

b) 84

c) 87

d) 90

**Answer: b) 84**

**17. The ratio of the incomes of two persons is 5:8. If the second person’s income is $480 more than the first person’s income, what is the income of the first person?**

a) $320

b) $400

c) $560

d) $640

**Answer: b) $400**

**18. The ratio of the ages of a father and his son is 9:2. If the father is 45 years older than the son, what are their ages?**

a) Father: 54 years, Son: 12 years

b) Father: 63 years, Son: 14 years

c) Father: 72 years, Son: 16 years

d) Father: 81 years, Son: 18 years

**Answer: c) Father: 72 years, Son: 16 years**

**19. If the ratio of the prices of two similar products is 3:4 and the first product costs $24, what is the cost of the second product?**

a) $18

b) $32

c) $36

d) $48

**Answer: c) $36**

**20. The ratio of the speeds of two trains is 5:7. If the first train covers 300 km in 4 hours, how long will it take for the second train to cover the same distance?**

a) 3 hours

b) 3.5 hours

c) 4 hours

d) 4.5 hours

**Answer: d) 4.5 hours**