Question : When 5 children from class A join class B, the number of children in both classes is the same. If 25 children from B, join A, then the number of children in A becomes double the number of children in B. The ratio of the number of children in A to those in B is:
Option 1: 19 : 18
Option 2: 9 : 8
Option 3: 18 : 17
Option 4: 19 : 17
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Correct Answer: 19 : 17
Solution : Let the number of children in class A as $a$ and the number of children in class B as $b$. From the problem, When 5 children from A join B, the number of children in both classes is the same. $⇒a - 5 = b + 5$ ------------(1) When 25 children from B join A, the number of children in A becomes double the number of children in B. $⇒a + 25 = 2(b - 25)$ $⇒2b-a=75$ ----------------(2) Solving these equations, we get, $⇒a = 95$ $⇒b = 85$ Therefore, the ratio of the number of children in A to those in B is 95 : 85 = 19 : 17 Hence, the correct answer is 19 : 17.
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Question : A cuboid of sides 12 cm, 18 cm, and 27 cm is melted to form a cube. What is the ratio of the total surface area of the cuboid to that of the cube?
Option 1: $18 : 17$
Option 2: $17 : 19$
Option 3: $19 : 18$
Option 4: $17 : 23$
Question : Two numbers are, respectively, 10% and 25% more than the third number. The ratio of the two numbers is:
Option 1: 22 : 25
Option 2: 19 : 25
Option 3: 23 : 25
Option 4: 18 : 25
Question : In a factory, 48% of the number of male workers is equal to two-thirds of the number of female workers. What is the ratio of the number of males to that of the females in the factory?
Option 1: 25 : 12
Option 2: 12 : 25
Option 3: 18 : 25
Option 4: 25 : 18
Question : The area of two similar triangles is 324 cm2 and 289 cm2, respectively. What is the ratio of their corresponding altitudes?
Option 1: $\frac{17}{18}$
Option 2: $\frac{17}{19}$
Option 3: $\frac{19}{17}$
Option 4: $\frac{18}{17}$
Question : In a school, 391 boys and 323 girls have been divided into the largest possible equal classes, so that each class of boys numbers the same as each class of girls. What is the number of classes?
Option 1: 23
Option 2: 19
Option 3: 42
Option 4: 17
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