Question

A fruit seller sold big, medium, small sized apples for $Rs.15$, $Rs.10$ and $Rs.5$, respectively. The total number of apples sold were in the ratio $3:2:5$. Find the average cost of an apple?

Answer 1

Hint:
First find the cost of each type of apple assuming the apples of particular type were sold as $3x,2x\,and\,5x$. To find the average cost of the apple find the value of total cost of the apples (all types) to the total number of apples.

Complete step by step solution:
Given,
Cost of big size apples= $Rs.15$
Cost of medium sized apples=$Rs.10$
Cost of small sized apples= $Rs.5$
Ratio of apples of different size of apples=$3:2:5$
So, the total number of apples that were sold are=$3x + 2x + 5x = 10x........(1)$
Cost of total number of apples that were sold are,
$
   \Rightarrow 3x\left( {15} \right) + 2x\left( {10} \right) + 5x\left( 5 \right) \\
   \Rightarrow 45x + 20x + 25x \\
   \Rightarrow 90x........(2) \\
 $
So, to find the average cost of the apples, we need to find the value of $\dfrac{{Total\,\cos t\,of\,the\,apples}}{{Total\,number\,of\,apples}}$
From the values of (1) and (2),
Average cost of the apples,
$
   \Rightarrow \dfrac{{90x}}{{10x}} \\
   \Rightarrow Rs.9 \\
 $

So, the average cost of the apples that were sold are $Rs.9$

Note:
Always assume the given ratio $a:b:c$ in the form of $ax:bx:cx$, which becomes easy to solve the ratio problems, always remember to apply the condition to its respective variable.