The cost price of per mango is twice the cost price of per apple. And the selling price of per mango is thrice the selling price of per apple. If apples are sold at twice their cost price and the overall profit percentage on selling apples and mangoes is 150%, find the ratio of the number of mangoes and apples that are sold.
As stated, the utility of Alligation is far more than obvious. Even in scenarios like above, where applying the process of Alligation may not seem that obvious, one can solve the above using Alligation and save a lot of time. However, beware, applying Alligation without understanding the concepts behind it can be disastrous.
Short-Cut: Using Alligation
Overall profit percentage is given and thus this will be the average (weighted) of the individual profit percentages on apples and mangoes.
Apples earn a profit percentage of 100%. And mangoes earn a profit percentage of 200%. And the average profit percentage is 150%. Thus, the ratio of number of mangoes sold to apples sold, using Alligation turns out to be 1 : 1
Using Equation or Weighted Averages:
If CP of apple is taken as x, then SP of apple is 2x. And CP and SP of mangoes is 2x and 6x respectively. Let number of mangoes and oranges sold be m and a respectively. Thus, taking the ratio of total selling price and total cost price ……
, i.e. 250%.Cancelling out x and cross-multiplying results in 12m + 4a = 10m + 5a i.e.
.Which one is correct? And what is the error?
Needless to add, nothing is wrong with the equations and hence this answer has to be correct. The bigger learning is what is wrong with the Alligation process. And how can I use Alligation and yet arrive at the correct answer without having to waste time jotting down equations.
Send in your thoughts and we will continue the next couple of articles on unearthing the mysteries of the process of Alligation.
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