The ratio of two numbers is 3:4. If their sum is 70, what is the larger number?
Solution: Let the numbers be 3x and 4x. Their sum is 7x, which is equal to 70. Therefore, x = 10. The larger number is 4x = 4 * 10 = 40. Hence, the answer is (d) 40.
If a:b = 5:7 and b:c = 4:9, then what is the value of a:c?
Solution: To find the value of a:c, we need to find the product of the given ratios. Multiply a:b by b:c to get a:c. Therefore, (a:b) * (b:c) = (5:7) * (4:9) = 20:63. Hence, the answer is (a) 20:63.
The ratio of boys to girls in a class is 2:3. If there are 30 girls, how many boys are there?
Solution: The ratio of boys to girls is 2:3. Let the number of boys be 2x. Then, the number of girls is 3x. We are given that there are 30 girls, so 3x = 30. Therefore, x = 10. The number of boys is 2x = 2 * 10 = 20. Hence, the answer is (b) 20.
The ratio of the present ages of A and B is 4:7. If the sum of their ages is 66, what is the age of B?
Solution: Let the present ages of A and B be 4x and 7x, respectively. Their sum is 4x + 7x = 11x, which is equal to 66. Therefore, x = 6. The age of B is 7x = 7 * 6 = 42. Hence, the answer is (d) 42.
The ratio of the prices of two similar products is 3:5. If the price of the first product is Rs.45, what is the price of the second product?
Solution: Let the price of the second product be 5x. The price of the first product is given as Rs.45, which is equal to 3x. Therefore, x = 15. The price of the second product is 5x = 5 * 15 = Rs.75. Hence, the answer is (c) Rs.75.
The ratio of the ages of a father and his son is 7:1. After 8 years, the sum of their ages will be 56. What is the present age of the father?
Solution: Let the present ages of the father and son be 7x and x, respectively. After 8 years, their ages will be 7x + 8 and x + 8. The sum of their ages is given as 7x + 8 + x + 8 = 56. Simplifying, we get 8x = 40, which gives x = 5. The present age of the father is 7x = 7 * 5 = 35. Hence, the answer is (a) 40.
The ratio of the number of boys to the number of girls in a school is 3:4. If there are 240 students in the school, how many girls are there?
Solution: The ratio of boys to girls is 3:4. Let the number of boys be 3x and the number of girls be 4x. We are given that the total number of students is 240, so 3x + 4x = 240. Simplifying, we get 7x = 240, which gives x = 34. The number of girls is 4x = 4 * 34 = 136. Hence, the answer is (d) 180.
The ratio of the ages of two friends is 5:8. If the sum of their ages is 65, what is the age of the younger friend?
Solution: Let the ages of the two friends be 5x and 8x, respectively. Their sum is 5x + 8x = 13x, which is equal to 65. Therefore, x = 5. The age of the younger friend is 5x = 5 * 5 = 25. Hence, the answer is (a) 25.
The ratio of the areas of two similar triangles is 4:9. If the area of the first triangle is 36 square units, what is the area of the second triangle?
Solution: Let the area of the second triangle be 9x square units. The area of the first triangle is given as 36 square units, which is equal to 4x. Therefore, x = 9. The area of the second triangle is 9x = 9 * 9 = 81 square units. Hence, the answer is (d) 81 square units.
The ratio of the lengths of two sides of a rectangle is 5:3. If the perimeter of the rectangle is 64 units, what is the length of the longer side?
Solution: Let the lengths of the sides of the rectangle be 5x and 3x, respectively. The perimeter is given as 2(5x + 3x) = 64. Simplifying, we get 16x = 64, which gives x = 4. The length of the longer side is 5x = 5 * 4 = 20 units. Hence, the answer is (b) 30 units.
The ratio of the volumes of two similar cubes is 8:27. If the volume of the first cube is 64 cubic units, what is the volume of the second cube?
Solution: Let the volume of the second cube be 27x cubic units. The volume of the first cube is given as 64 cubic units, which is equal to 8x. Therefore, x = 8. The volume of the second cube is 27x = 27 * 8 = 216 cubic units. Hence, the answer is (d) 216 cubic units.
The ratio of the ages of a father and his son is 5:2. After 5 years, the father’s age will be 40. What is the present age of the son?
Solution: Let the present ages of the father and son be 5x and 2x, respectively. After 5 years, the father’s age will be 5x + 5 = 40. Solving for x, we get x = 7. The present age of the son is 2x = 2 * 7 = 14. Hence, the answer is (d) 20.
The ratio of the base radii of two cylinders is 2:3. If the volume of the first cylinder is 64π cubic units, what is the volume of the second cylinder?
Solution: Let the base radii of the second cylinder be 3x. The volume of the first cylinder is given as 64π cubic units, which is equal to 2x^2h, where h is the height. Canceling out π, we get 2x^2h = 64. Therefore, x^2h = 32. The volume of the second cylinder is 3^2x^2h = 9x^2h = 9 * 32 = 288 cubic units. Hence, the answer is (d) 216π cubic units.
The ratio of the lengths of two diagonals of a rhombus is 3:4. If the length of one diagonal is 12 units, what is the length of the other diagonal?
Solution: Let the length of the other diagonal be 4x units. The length of one diagonal is given as 12 units, which is equal to 3x. Therefore, x = 4. The length of the other diagonal is 4x = 4 * 4 = 16 units. Hence, the answer is (b) 16 units.
The ratio of the prices of two books is 7:10. If the price of the second book is Rs.70, what is the price of the first book?
Solution: Let the price of the first book be 7x dollars. The price of the second book is given as Rs.70, which is equal to 10x. Therefore, x = 7. The price of the first book is 7x = 7 * 7 = Rs.49. Hence, the answer is (a) Rs.49.
The ratio of the weights of two objects is 5:9. If the weight of the first object is 20 kg, what is the weight of the second object?
Solution: Let the weight of the second object be 9x kg. The weight of the first object is given as 20 kg, which is equal to 5x. Therefore, x = 4. The weight of the second object is 9x = 9 * 4 = 36 kg. Hence, the answer is (b) 36 kg.
The ratio of the sides of two similar triangles is 2:5. If the perimeter of the first triangle is 18 cm, what is the perimeter of the second triangle?
Solution: Let the perimeter of the second triangle be 5x cm. The perimeter of the first triangle is given as 18 cm, which is equal to 2x. Therefore, x = 9. The perimeter of the second triangle is 5x = 5 * 9 = 45 cm. Hence, the answer is (c) 45 cm.
The ratio of the areas of two similar rectangles is 2:9. If the area of the first rectangle is 36 square units, what is the area of the second rectangle?
Solution: Let the area of the second rectangle be 9x square units. The area of the first rectangle is given as 36 square units, which is equal to 2x. Therefore, x = 18. The area of the second rectangle is 9x = 9 * 18 = 162 square units. Hence, the answer is (d) 162 square units.
The ratio of the number of red balls to the number of blue balls in a bag is 4:7. If there are 44 blue balls, how many red balls are there?
Solution: The ratio of red balls to blue balls is 4:7. Let the number of red balls be 4x. We are given that there are 44 blue balls, so 7x = 44. Therefore, x = 6. The number of red balls is 4x = 4 * 6 = 24. Hence, the answer is (b) 28.
The ratio of the perimeters of two similar triangles is 3:5. If the perimeter of the first triangle is 24 cm, what is the perimeter of the second triangle?
Solution: Let the perimeter of the second triangle be 5x cm. The perimeter of the first triangle is given as 24 cm, which is equal to 3x. Therefore, x = 8. The perimeter of the second triangle is 5x = 5 * 8 = 40 cm. Hence, the answer is (c) 40 cm.
The ratio of the ages of two brothers is 4:9. If the difference between their ages is 10 years, what is the age of the older brother?
Solution: Let the ages of the brothers be 4x and 9x, respectively. The difference between their ages is given as 9x – 4x = 10. Simplifying, we get 5x = 10, which gives x = 2. The age of the older brother is 9x = 9 * 2 = 18. Hence, the answer is (b) 25.
The ratio of the radii of two spheres is 3:5. If the volume of the first sphere is 36π cubic units, what is the volume of the second sphere?
Solution: Let the radius of the second sphere be 5x units. The volume of the first sphere is given as 36π cubic units, which is equal to (4/3)π(3x)^3. Simplifying, we get 27x^3 = 36. Therefore, x^3 = 4/3. The volume of the second sphere is (4/3)π(5x)^3 = (4/3)π(125x^3) = 4/3 * 125 * 4/3 * π = 64π cubic units. Hence, the answer is (c) 64π cubic units.
The ratio of the heights of two persons is 5:8. If the height of the shorter person is 160 cm, what is the height of the taller person?
Solution: Let the height of the taller person be 8x cm. The height of the shorter person is given as 160 cm, which is equal to 5x. Therefore, x = 32. The height of the taller person is 8x = 8 * 32 = 256 cm. Hence, the answer is (b) 256 cm.
The ratio of the areas of two similar circles is 1:4. If the area of the first circle is 16π square units, what is the area of the second circle?
Solution: Let the area of the second circle be 4xπ square units. The area of the first circle is given as 16π square units, which is equal to xπ. Therefore, x = 16. The area of the second circle is 4xπ = 4 * 16π = 64π square units. Hence, the answer is (c) 64π square units.
The ratio of the lengths of the diagonals of a rectangle is 3:4. If the length of one diagonal is 10 cm, what is the length of the other diagonal?
Solution: Let the length of the other diagonal be 4x cm. The length of one diagonal is given as 10 cm, which is equal to 3x. Therefore, x = 10/3. The length of the other diagonal is 4x = 4 * 10/3 = 40/3 cm. Hence, the answer is (b) 12 cm.
The ratio of the areas of two similar squares is 9:25. If the area of the first square is 36 square units, what is the area of the second square?
Solution: Let the area of the second square be 25x square units. The area of the first square is given as 36 square units, which is equal to 9x. Therefore, x = 4. The area of the second square is 25x = 25 * 4 = 100 square units. Hence, the answer is (c) 100 square units.
The ratio of the number of marbles to the number of candies in a jar is 3:7. If there are 84 candies, how many marbles are there?
Solution: The ratio of marbles to candies is 3:7. Let the number of marbles be 3x. We are given that there are 84 candies, so 7x = 84. Therefore, x = 12. The number of marbles is 3x = 3 * 12 = 36. Hence, the answer is (b) 36.
The ratio of the perimeters of two similar rectangles is 4:9. If the perimeter of the first rectangle is 48 cm, what is the perimeter of the second rectangle?
Solution: Let the perimeter of the second rectangle be 9x cm. The perimeter of the first rectangle is given as 48 cm, which is equal to 4x. Therefore, x = 12. The perimeter of the second rectangle is 9x = 9 * 12 = 108 cm. Hence, the answer is (b) 54 cm.
The ratio of the areas of two similar triangles is 1:9. If the area of the first triangle is 16 square units, what is the area of the second triangle?
Solution: Let the area of the second triangle be 9x square units. The area of the first triangle is given as 16 square units, which is equal to x. Therefore, x = 16. The area of the second triangle is 9x = 9 * 16 = 144 square units. Hence, the answer is (d) 144 square units.
The ratio of the lengths of the bases of two similar triangles is 2:5. If the length of the base of the first triangle is 10 cm, what is the length of the base of the second triangle?
Solution: Let the length of the base of the second triangle be 5x cm. The length of the base of the first triangle is given as 10 cm, which is equal to 2x. Therefore, x = 5. The length of the base of the second triangle is 5x = 5 * 5 = 25 cm. Hence, the answer is (d) 25 cm.