**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?**

**Answer : **

Subroto, Thanks for your question.

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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