Optimizing Your Budget to Purchase 100 Items for 100 Rupees: A Mathematical Challenge

Ever faced a situation where the allocation of funds to buy specific items adds an interesting puzzle to your finance management? In this article, we will explore a fascinating problem that challenges your understanding of budget optimization and mathematics. You need to buy 100 items (coconuts, lemons, and chocolates) for 100 rupees. Let's dive in to find the perfect combination.

Optimal Combination: Coconuts, Lemons, and Chocolates

To buy 100 items of coconuts, lemons, and chocolates for 100 rupees, the optimal combination would be as follows:

10 coconuts at 5 rupees each 50 rupees 20 lemons at 1 rupee each 20 rupees 30 chocolates at 1 rupee for 4 7.5 rupees rounded up to 8 rupees

This totals to 50 20 8 78 rupees for 100 items, which is within the 100 rupee budget.

Another Approach: Coconuts, Mangoes, and Lemons

Another way to achieve this is by purchasing coconuts, mangoes, and lemons. The combination is as follows:

20 coconuts at 5 rupees each 100 rupees 80 mangoes at 1 rupee each 80 rupees 400 lemons at 1 rupee for 4 100 rupees

This combination gives you 20 coconuts, 80 mangoes, and 400 lemons, totaling 100 items and costing exactly 100 rupees.

Another Creative Solution: Bananas, Coconuts, and Lemons

Another creative solution involves purchasing bananas, coconuts, and lemons:

50 lemons at 12.5 rupees (since 4 lemons cost 1 rupee, you get 12.5 lemons for 1 rupee) 12.5 rupees 30 bananas at 1 rupee each 30 rupees 4 coconuts at 5 rupees each 20 rupees

This totals 12.5 30 20 62.5 rupees. To reach 100 items, you can adjust the quantities slightly:

19 coconuts at 5 rupees each 95 rupees 1 mango at 1 rupee 1 rupee 80 lemons at 1 rupee each 80 rupees

This totals to 95 1 80 - 4 (lemons), totaling exactly 100 items.

Mathematical Analysis

Let the number of Coconuts be C, Mangoes be M, and Lemons be L. The conditions are:

C M L 100 5C M 20L 100

From equation 2, we can rearrange to express M:

M 100 - 5C - 20L/100

Substituting M in equation 1:

C 100 - 5C - 20L/100 L 100 -4C - 0.95L 0 C 0.95L/4

By trial and error, if L 80, then C 19, and M 1, which satisfies the conditions.

Conclusion

Whether you decide to buy 10 coconuts, 20 lemons, and 30 chocolates or 20 coconuts, 80 mangoes, and 400 lemons, the key is to find the perfect combination that maximizes the number of items while keeping the cost within the budget. Understanding these puzzles not only tests your mathematical skills but also helps in better budget management in real-life scenarios.