Question

By buying a certain number of apples at 3 apples for Rs. 5 and 5/6th of the number at 4 apples for Rs. 5 and selling them at 11 apples for Rs. 20, I gain Rs. 15. What is the number of apples ?

Answer 1

Let total number of apples be x.
$\frac{5}{6}$ of x apples bought at 4 apples for Rs. 5

$\therefore$CP of one apple = $\frac{(5\times 4)}{(6\times 5)}x=Rs.\frac{2}{3}x$

Rest apples=$x-\frac{5}{6}x=\frac{x}{6}$

$\frac{x}{6}$, bought at 3 apples for 5

$CP=\frac{\left(3x\right)}{(6\times 5)}=\frac{x}{10}$

So Average CP $=\frac{\left(\frac{2x}{3}\right)+\left(\frac{x}{10}\right)}{2}=\frac{23x}{30}=0.76x$ per apple.

Now, average selling price $=\frac{20x}{11}=1.81x$
Gain = Rs 15
$\Rightarrow 1.81x-0.76x=15$
$\Rightarrow 1.05x=15$
$\Rightarrow x=14.28$
Thus, no. of apples = 14