Question 59

The number of boys in a school was 30 more than the number of girls. Subsequently, a few more girls joined the same school. Consequently, the ratio of boys and girls became 3:5. Find the minimum number of girls, who joined subsequently.

Assume that there was at least one girl at the start.

Solution

Let the number of girls in the school be G. 
=> Number of boys = G+30.
Some girls joined the class and the number of boys and girls became 3:5. 
Let the number of girls who joined the class be 'X'.
It has been given that (G+30)/(G+X) = 3/5
5G + 150 = 3G + 3X
2G + 150 = 3X
=> X = (2G/3) + 50.
2G has to be divisible by 3. 
Therefore, the least value that G can take is 3. 
When G = 3, X = 2 + 50
X = 52. 
The least number of girls who could have joined is 52. 
Therefore, option E is the right answer.

Video Solution

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