Question

A shop sells bags in three sizes: small, medium and large. A large bag costs Rs.1000, a medium bag costs Rs.200, and a small bag costs Rs.50. Three buyers, Ashish, Banti and Chintu, independently buy some numbers of these types of bags. The respective amounts spent by Ashish, Banti and Chintu are equal. Put together, the shop sells 1 large bag, 15 small bags and some medium bags to these three buyers. What is the minimum number of medium bags that the shop sells to them?

Accepted Answer

E. Let $a, b, c$ be the amounts spent by Ashish, Banti, Chintu. $a = b = c = V$. One buyer bought the large bag (cost Rs 1000), so each buyer spent $V \ge 1000$. Total spend $3V \ge 3000$. Known spend on small bags = $15 	imes 50 = 750$. Known spend on large bag = $1000$. Total spend excluding medium bags = $1750$. Spend on medium bags = $200m$. Total revenue = $1750 + 200m = 3V \ge 3000$. $200m \ge 1250 \implies m \ge 6.25$. Check $m = 7$: Total revenue = $1750 + 1400 = 3150 = 3 	imes 1050$. Each person spends Rs 1050. Possible distribution: Person 1: 1 Large (1000) + 1 Small (50) = 1050. Person 2: 7 Small (350) + 3 Medium (600) = 1050. Person 3: 7 Small (350) + 4 Medium (800) = 1050. Total: 1 Large, 15 Small, 7 Medium. Each spends 1050. Minimum $m = 7$.

Minimum Medium Bags Sold

Explanation

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