Question

Everyday a fruit seller sells 50% of his stock. 10% of the stock
gets spoiled during the night. If a total of 1983 fruits got spoiled
in the three days period, how many fruits did he start with?
​

Answer 1

Solution :-

Let us assume that, the fruit seller starts with x fruits initially.

we have given that, Everyday a fruit seller sells 50% of his stock. 10% of the stock gets spoiled during the night.

So,

First day :-

→ Total fruits = x

→ Sold = 50% of x = (50x/100)

→ Remaining fruits = x - (50x/100) = (50x/100)

Now,

→ Spoiled in night = 10% of the remaining = (10 * 50x)/(100 * 100) = (x/20)

So,

→ Remaining fruits after first night = (50x/100) - (x/20) = (50x - 5x)/100 = (45x/100) = (9x/20)

Second Day :-

→ Fruits sold = 50% of (9x/20) = (1/2) of (9x/20) = (9x/40)

→ Remaining = (9x/40) { As 50% is equal to half.}

Now,

→ Spoiled in night = 10% of (9x/40) = (1/10) of (9x/40) = (9x/400)

So,

→ Remaining fruits after second night = (9x/40) - (9x/400) = (90x - 9x)/400 = (81x/400)

Third Day :-

→ Fruits sold= (1/2) of (81x/400) = (81x/800)

→ Remaining = (81x/800)

Now,

→ Spoiled in night = 10% of (81x/800) = (81x/8000)

Therefore,

→ Total Fruits spoiled in three nights = (x/20) + (9x/400) + (81x/8000) = 1983

→ (400x + 180x + 81x) / 8000 = 1983

→ 661x = 1983 * 8000

→ x = 24000. (Ans.)

Hence, The fruit seller start with 24,000 fruits.

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