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In a room, there are n persons whose average height is 160 cm. If m more persons, whose average height is 172 cm, enter the room, then the average height of all persons in the room becomes 164 cm. Then m : n is
Initially, there are $$n$$ persons whose average height is 160 cm.
So, sum of all their heights =$$160n$$
Also, $$m$$ more persons enter the room with average height 172 cm.
Now, sum of their heights =$$172m$$
So, total height of all members =$$160n+172m$$
And total no. of persons are $$m+n$$
The final average height is given as 164
So, $$\dfrac{160n+172m}{m+n}=164$$
or, $$160n+172m=164\left(m+n\right)$$
or, $$160n+172m=164m+164n$$
or, $$8m=4n$$
or, $$m:n=1:2$$
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