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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?

Explanation:

Let the number of medium bags sold = m

∴ Total amount spent by all three together = 1 × 1000 + 200 × m + 15 × 50 = 1750 + 200m.

Now since one of them buys a large bag (worth Rs. 1000) that person spends at least Rs. 1000.

∴ Each of them spends at least Rs. 1000 and hence total amount spent by them together is at least Rs. 3000.

⇒ 1750 + 200m ≥ 3000

⇒ m ≥ 6.25

∴ Minimum value of m can be 7.

If 7 medium bags are sold. Total amount spent = 1750 + 200 × 7 = 3150

⇒ Each of them spent 3150/3 = 1050

This is possible when
One of them buys a large bag and a small bag = 1000 + 50 = 1050
One other buys 5 medium bags and a small bag = 1000 + 50 = 1050
Third person buys 2 medium bags and 13 small bags = 400 + 650 = 1050

∴ Minimum number of medium size bags sold = 7.

Hence, option (a).