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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 $$8:\ 7$$.


Solution

Number of students $$=1430$$
Ratio in number of boys and girls $$=7:6$$
Let number of boys $$=7x$$ and of girls $$=6x$$
$$7x+6x=1430$$
$$\Rightarrow 13x=1430$$
$$\Rightarrow x=110$$
Number of boys $$=7x=7 \times 110=770$$
and number of girls $$=6x=6 \times 110=660$$
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 $$=8:7$$
$$\dfrac{770+y}{686}=\dfrac{8}{7}$$
$$5390+7y=5488$$
$$7y=5488-5390=98$$
$$y=14$$
Number of new boys admitted $$=14$$

Mathematics

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