A fruit seller sells half of his fruits plus half an orange, again he sells…
2016
A fruit seller sells half of his fruits plus half an orange, again he sells half of what remains plus half an orange, and so again a third time. His store is now exhausted; how many did he start from?
- A.
5 / ५
- B.
7 / ७
- C.
9 / ९
- D.
11 / ११
Attempted by 50 students.
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Correct answer: B
Let the initial number of fruits be x.
After the first sale (he sells half of x plus 1/2): remaining = x − (x/2 + 1/2) = x/2 − 1/2.
After the second sale (he sells half of the remaining plus 1/2): remaining = (x/2 − 1/2) − (1/2*(x/2 − 1/2) + 1/2) = x/4 − 3/4.
After the third sale (he again sells half of the remaining plus 1/2): remaining = (x/4 − 3/4) − (1/2*(x/4 − 3/4) + 1/2) = x/8 − 7/8.
The store is exhausted, so final remaining = 0. Solve x/8 − 7/8 = 0 ⇒ x = 7.
Check with x = 7: first sale sells 3.5 + 0.5 = 4, remaining 3.
Second sale sells 1.5 + 0.5 = 2, remaining 1.
Third sale sells 0.5 + 0.5 = 1, remaining 0 (store exhausted).