Question

Rajan is a fruit seller. On any day, he sells only one kind of fruit. On the first day, he buys $9\text{ kg}$ of blueberries. On the second day, he buys $22\text{ kg}$ of kiwis. On the third day, he buys $50\text{ kg}$ of peaches. The per kg purchase price of each fruit is an integer. Further, on each of these three days, he spends the same amount to purchase fruits. On the fourth day, he buys mangoes at $\text{Rs. } 35/\text{kg}$ and spends $\text{Rs. } 15$ less than any of the previous three days.

If he then sells all the mangoes at $\text{Rs. } 50/\text{kg}$ , what is his MINIMUM possible profit on the fourth day?

Accepted Answer

B. Let the per kg purchase prices be $b, k, p \in \mathbb{Z}^+$. Amount spent $M = 9b = 22k = 50p$. Thus $M$ must be a multiple of $	ext{LCM}(9, 22, 50) = 4950$. For minimum profit, choose minimum $M = 4950$. Spent on 4th day $= 4950 - 15 = 	ext{Rs. } 4935$. Weight of mangoes bought $= 4935 / 35 = 141	ext{ kg}$. Profit per kg $= 50 - 35 = 	ext{Rs. } 15$. Total profit on 4th day $= 141 	imes 15 = 	ext{Rs. } 2115$.

Rajan fruit seller minimum profit

Explanation

Practise this under exam conditions