Aptitude - Ratio and Proportion - Discussion

@Stark Vin.

We are taking X because ratio means dividing the total quantity into some parts and the number of parts we divide them into is represented in the form of the ratio.

For example, if I have 30 chocolates and if I want to divide them in the ratio 1:2 then first I will see into how many equal parts I need to divide the chocolates into that is 3 in this case why? Because ratio is 1:2 that is to parts I want is 3. That means I need to divide 30 into 3 equal parts and then take 1 part on one side and other part on the other side. This simply means if I divide 30 by 3 I get 10. This means I divided 30 into 3 equal parts where each part contains 10 chocolates. Now I need to divide them in the ratio 1:2 so I take 10 chocolate on one side which is one part of 30 in this example and remaining 2 parts which add up to 20 in other parts. Now 10 by 20 equals 1 by 2 or 1:2 that is what we call as ratio. That is ratio is the representation of total quantity in its simplest form. We could have written it as 10:20 by we need to simplify as much as possible so we take it as 1:2. Now coming to this question we have the boys to girls ratio as 7:8 that simply means the total strength was divide into 7+8 parts but since we do not know what is the total strength we take it as some variable say t now, t by 15 we assume as x. This means now I have divided total strength into 15 equal parts were each part contains x. In that 7x we take as number of boys and 8x as number of girls.

Boys 7 = 20%.
Girls 8 = 10%.
120/ 100 = 1.2x7 = 84
110/ 100 = 1.1x8 = 88.

Here (boys& girls) so divided by 2.
84/2 = 42
88/2 = 44.

Again divided by 2.
42/2=21
44/2=22
So, new ratio = 21:22.

Simply find 20% of 7 and 10% of 8.

It will be 1.4 and 0.8 respectively.
Till this ok then,how 8.4:8.8.
And how to convert it into fraction.
So the ratio is 8.4:8.8.

Then convert the fraction into whole numbers.

If I multiply by 10 I will get 84:88 now we can easily simplify it.

So we get 21:22.

7:8 can also be written as 70:80
120/100*70 = 84
110/100*80 = 88
so,new ratio= 84 : 88
or 42 : 44
or 21 : 22

(7x+0.2*7x)/(8x+0.1*8x)=21:22

@Kiran Kumar

note that something we included to get 20%

For example the ratio of the ratio of to boys ages was 5:2
we can write it as 5x : 2x we get exact ratio we will not consider it alone

For that way 7x 8x will appear

then

to covert 20% into no. it will be 20/100

note that the unknown was x

then 20/100x*x

so we take common one x(20/100+1)

so x(20/100+100)

x(120/100)

that was we get 120/100
forget x because that x which is in 7x both are same so we get 120/100*7x

I like ramesh's methods ! thanks a lot :).

Ramesh your to good.

Why do we multiply 120% by 7x and 100% by 8x
Why not we simply multiply 20% by 7x and 10% by 8x ?

Please someone explain me.

RAMESH very well said. ! keep posting your SHORTCUT method. Its very useful for us. !i search at every discussion. Because of you. !