Rajan fruit seller minimum profit

XAT 2026 · Quantitative Ability & Data Interpretation · Hard · Arithmetic

Rajan is a fruit seller. On any day, he sells only one kind of fruit. On the first day, he buys 9 kg9\text{ kg} of blueberries. On the second day, he buys 22 kg22\text{ kg} of kiwis. On the third day, he buys 50 kg50\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 Rs. 35/kg\text{Rs. } 35/\text{kg} and spends Rs. 15\text{Rs. } 15 less than any of the previous three days.

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

  1. A.

    Rs. 2130

  2. B.

    Rs. 2115

  3. C.

    Rs. 2085

  4. D.

    Rs. 2265

  5. E.

    None of the other options is correct

Answer

B

Explanation

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

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