The borrower and the lender problem
Q. Once two friends say ‘h’ & ‘j’ went to a restaurant named 'Springdale' in Colorado, USA to have their dinner. After they had their dinner, the bill was placed on their table. Say the total bill was $x, but ‘j’ took a credit of $y from ‘h’ before and ‘j’ decided to repay it on the total bill. So ‘j’ deducted $y from $x (total bill amount) and divided the remaining amount say $z into two halves ($z/2 each). So ‘h’ paid $z/2 and ‘j’ paid a total of ($z/2+$y). When ‘h’ reached his house and was in his bathtub with a glass of wine in his hand, he found that he had lost a half of his credit instead. Is the last statement true or false? (Explanation along with the answer will be appreciated.)
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1 solution
In normal circumstances the bill of $x would have been divided equally between h and j This means amount meant to be paid by h would have been $x/2 In the given scenario h is paying $(x-y)/2 So, we can see that h is paying $y/2 less. But his initial credit to j was $y. Hence, he lost half of his credit.