Lesson 1: Ratio

Hello,
see, with my point of view, ratio is the most important topic in Arithmentics. Now, you must be wondering why! so guys it makes your time and speed (TSD), Time & work and Mixtures questions quite easy. And if I say it will enhance your speed by atleast 2 times, then that will not be wrong. The start may be difficult, but beleive me, it helps.

Ratio can be treated as comparison by division:-

1. Lets take an example:-

No. of girls (G) = 30.

No. of boys (B)= 50.

so ratio of girls to boys = 30/50 = 3/5.

Now, we can see that the above statement typically means: no. of girls divided by no. of boys.

Now lets suppose, G= 18 and B= 30.

Therefore, G:B = 18/30 = 3/5 (by simplification). So we observe that no.of girls can be written as 3K

and no. of Boys = 5K

Quite simple! isnt't it?

2. Now let us take another concept:-

If the ratio is provided to you say, ratio of no. of girls to no. of boys = 3:5.

Can you find the no. of boys?

Some of you may come up with the correct ans but some of you may confuse this particular question with the above question.

We cannot find the no.of boys, why?

Because no. of boys may take any value. It can be 25 or 50 or 35, anything.

G:B= 3K/ 5K

So we can see the value depends upon the value of the variable(K). Unless and untill,we are having the value of k,we can't come on to the solution.

3.  Now, 

If the ratio is given as G : B= 3:5 and the number of girls is given to you, say G= 27 the what will be the number of boys?

Off course. It will be 45. Now, how can we do that without pen and paper (for beginners):-

Think!