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Question

The ratio of number of boys to the number of girls in a school of 1430 student is 7 :6. If 26 new girls are admitted in the school, find how many new boys may be admitted so that the new ratio of number of boys to the number of girls may change to 8: 7.

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Solution

Number of students =1430
Ratio in number of boys and girls =7:6
Let number of boys =7x and of girls =6x
7x+6x=1430
13x=1430
x=110
Number of boys =7x=7×110=770
and number of girls =6x=6×110=660
Now adding 26 new girls, the number of girls will be =660+26=686
Let new boys be added =y
The number of boys =770+y
Now new ratio =8:7
770+y686=87
5390+7y=5488
7y=54885390=98
y=14
Number of new boys admitted =14

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