Discussion
The cost of 10 pears, 8 guavas and 6 mangoes is ₹ 44. If the cost of each of the fruits, in rupees, is a natural number and cost of no two fruits is the same, find the cost of 4 mangoes and 3 guavas.
Answer: B
4 mangoes and 3 guavas cost ₹ 18.
Let a pear, a guava and a mango cost p, g and m rupees, all different natural numbers. Halving the given total:
\[ 10p + 8g + 6m = 44 \;\Rightarrow\; 5p + 4g + 3m = 22 \]
Try p = 1: 4g + 3m = 17 gives g = 2, m = 3. Try p = 2: 4g + 3m = 12 has no solution in natural numbers. Try p = 3: 4g + 3m = 7 gives g = m = 1, but no two prices may be equal. Larger p leaves too little. So p = 1, g = 2, m = 3 is the only solution.
\[ 4m + 3g = 12 + 6 = 18 \]
Because the prices are unique, 'Cannot be determined' is wrong; 17 and 14 would need different prices.
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