Question

A sweet shop sells laddus in boxes of different sizes. The laddus are priced at Rs. $10$ per laddu upto $400$ laddus, For every $10$ additional laddus the price of the entire lot goes down by $10$ paise per laddu. Find the size of the box that would have the maximum cost

• A. $600$
• B. $500$
• C. $700$
• D. $800$

Answer 1

Answer: (C)

$700$

$\text{For 400 laddus cost of laddus}=Rs10=1000paise$

For every 10 additional laddus price of entire lot goes down by 10 paise

Let number of additional laddus $=10n$

New price after deduction $=(1000-10n)paise$

$\therefore \text{Total cost}=(400+10n)(1000-10n)$

$100(40+n)(100-n)$

$=100(-n^2+60n+4000)$

$\text{Total cost is maximum at n}=\frac{-\left(60\right)}{2\times (-1)}=30$

$\therefore \text{Total size of box}=400+10n=700$