### Student: Subroto Ganguly

#### Q. Can you explain me how to solve this ratio and proportion problems ? Rs.216 is divided among three persons A, B and C such that 8 times A’s share is equal to 12 times B’s share which is equal to 6 times C’s share. How much did A get?

Here is the solution with explanation.

Topic : Arithmetic, Ratio and Proportion
Concept : This kind of ratio and proportion problems where a certain quantity has to be divided can be solved using by first finding ratios as part of whole for each and then forming equation.  See the method below.
Method :

8 times A’s share = 12 times B’s share = 6 times C’s share.

Find out the L.C.M of 8, 12 and 6 and divide the L.C.M by each of the above numbers to get the ratio of their respective shares.

The L.C.M of 8, 12 and 6 is 24

Remember  8 times A’s share = 12 times B’s share = 6 times C’s share.

Therefore, the ratio A:B:C :: 24/8 : 24/12 : 24/6

On solving, we get   A : B : C :: 3 : 2 : 4

Now forming the equation from the ratios.

The sum of the total wages = 3x + 2x + 4x = 216

On solving we get  9x = 216

Hence   x = 24

Hence, A who gets 3x will get 3 * 48 = Rs. 72
We can discuss more such examples in upcoming blogs.
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