Suppose there are more than 2025 inhabitants. But these will violate the conditi

Question

Suppose there are more than 2025 inhabitants. But these will violate the condition that "There are more inhabitants than there are hairs on the head of any one inhabitants." As for any number more than 2025, there will be same number of inhabitants as the maximum number of hairs on the head of any inhabitant.

There are four groups of Mangoes, Apples and Bananas as follows:
Group I : 1 Mango, 1 Apples and 1 Banana
Group II : 1 Mango, 5 Apples and 7 Bananas
Group III : 1 Mango, 7 Apples and 10 Bananas
Group IV : 9 Mango, 23 Apples and 30 Bananas

Group II costs Rs 300 and Group III costs Rs 390.

Can you tell how much does Group I and Group IV cost?

Explanation / Answer

Group I costs Rs 120 and Group IV costs Rs 1710 Assume that the values of one mango, one apple and one banana are M, A and B respectively. From Group II : M + 5A + 7B = 300 From Group III : M + 7A + 10B = 390 Subtracting above to equations : 2A + 3B = 90 For Group I : = M + A + B = (M + 5A + 7B) - (4A + 6B) = (M + 5A + 7B) - 2(2A + 3B) = 300 - 2(90) = 300 - 180 = 120 Similarly, for Group IV : = 9M + 23A + 30B = 9(M + 5A + 7B) - (22A + 33B) = 9(M + 5A + 7B) - 11(2A + 3B) = 9(300) - 11(90) = 2700 - 990 = 1710 Thus, Group I costs Rs 120 and Group IV costs Rs 1710.

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