Every day a mango seller sells half of his stock, 10% of the stock overnight gets spoiled, if 1983 mango rotted over three nights then how many did he starts with on the first day?
(a) 25000
(b) 30000
(c) 24000
(d) 32000

Ans: (c) 24000

Explanation:

The seller sells half of his mangoes in the day and he wish to sell sell the remaining half on next day but 10% spoils, so he actually sells 90% of the stock on next day.

In the question total rotten mangoes over three night is given. So, we would find out rotten mangoes for each night.

Let, starting number of mangoes = x

Rotten mangoes in 1^st night

= x\times \displaystyle\frac{1}{2}\times \frac{10}{100}

= \displaystyle \frac{x}{20}

Rotten mangoes in 2^nd night

= x\times \displaystyle\frac{1}{2}\times \frac{90}{100}\times \frac{1}{2} \times \frac{10}{100}

= \displaystyle \frac{9x}{400}

Rotten mangoes in 3^rd night

= x\times \displaystyle\frac{1}{2}\times \frac{90}{100}\times \frac{1}{2} \times \frac{90}{100}\times \frac{1}{2}\times \frac{10}{100}

= \displaystyle \frac{81x}{8000}

Hence, \displaystyle \frac{x}{20} + \displaystyle \frac{9x}{400} + \displaystyle \frac{81x}{8000} = 1983

\qquad \Rightarrow 400x + 180x + 81x = 1983 × 8000

\qquad \Rightarrow 661x = 1983 × 8000

\qquad\Rightarrow x = 3 × 8000 = 24000

Aliter

The seller sells in three day as \displaystyle\frac{1}{2}, \displaystyle\frac{1}{2} and \displaystyle\frac{1}{2}

Rotten mangoes are \displaystyle\frac{1}{10}, \displaystyle\frac{1}{10} and \displaystyle\frac{1}{10}

Product of denominators = 2³ × 10³ = 8000

Let, number of mangoes on the first day = 8000

Mango stock = \displaystyle\frac{8000}{2} = 4000

Mango rotten = 4000 × \displaystyle\frac{10}{100} = 400

Remaining = 4000 – 400 = 3600
This 3600 mangoes will be sold next day

For second day,
Stock = 1800
Rotten = 180
Remaining = 1800 – 180 = 1620

For third day,
stock = 810
Rotten = 81

Total rotten over three nights = 400 + 180 + 81 = 661

Now, Rotten mango to Total mango
661 ⟶ 8000
1983 ⟶ 3 × 8000 = 24000

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