Question

In a school, the ratio of the number of boys to the number of teachers 2 : 3; and the ratio of the number of teachers to the number of girls is 4 : 5. What is the ratio of the number boys to girls.

Answer 1

Answer:

Here we consider the number of teachers, boys and girls as variables initially to compute and find them out.

Step-by-step explanation:

Let X be no of girls.

Y be no of boys.

Z be no of teachers.

Then given ratio of Boys and teachers is given as,

> 2 : 3 = Y : Z.

> By cross multiplication we get,

2Z = 3Y

Y = (2/3)*Z........1

Given ratio of Teachers and girls as,

> 4 : 5 = X : Z.

> 4Z = 5X

X = (4/5)*Z.........2

We are asked to find ratio of boys to girls,

So > X : Y

From 1 and 2 equations we can write

X : Y = (2/3)*Z : (4/5)*Z

for proportion common term z can be cancelled out

X : Y = (2 /3) : (4/5)

denominators are 3,5 so their LCM would be 15 and multiply 15 on both sides of proportion we get

X : Y = 5 * 2 : 3 * 4

X : Y = 10 : 12

X : Y = 5 : 6

That would be the required one.