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
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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