Question

In a camp there are 420 boys and 180 girls. Find the ratio of boys to girls.

Answer 1

Hint: In general a ratio indicates how many times one number contains another. ‘ : ’ is used to represent a ratio. For example, if there are eight oranges and six lemons then the ratio of oranges to lemons is 8:6, similarly the ratio of lemons to oranges is 6:8.

Complete step by step answer:
A ratio remains the same if both the antecedent and consequent are multiplied or divided by the same non zero number
a:b = ap : bp = \[\dfrac{a}{p}:\dfrac{b}{p}\]
From our question we have 180 girls and 420 boys
Let the number of girls be represented by G and the number of boys be represented by B.
G = 180, B= 420
Now let us find the ratio of number of boys to girls which is B : G
Substituting the values of B and G we have
B : G = 420 : 180
The above ratio can be simplified by using the properties of ratios.
Let us divide the above ratio with 60 on both sides, we will have
B : G =\[\dfrac{420}{60}:\dfrac{180}{60}=7:3\]

Therefore, the ratio of 420 boys to 180 girls is 420 : 180 also can be written as 7 : 3 in its simplified form.

Note: While solving this problem one should always take care of what is being asked in the question the ratio of what to what, like here in this question we have been asked the ratio of boys to girls and not the ratio of girls to boys which would be the other way around.