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 = 2^{3} × 10^{3} = 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

**[Similar Problem]** Every day a mango seller sells half of his stock, 60% of the stock overnight gets spoiled, if 87336 mango rotted over three nights then how many did he starts with on the first day? – (a) 1000000 (b) 400000 (c) 582240 (d) 340000

## Join Us

Join the discussion and ask any question of maths and reasoning directly to us and other like-minded user just like you!

Erik OlsonFantastic beat ! I would like to apprentice while you amend your web site, how could i subscribe for a blog site? The account helped me a acceptable deal. I had been a little bit acquainted of this your broadcast offered bright clear concept

drover sointeruWay cool, some valid points! I appreciate you making this article available, the rest of the site is also high quality. Have a fun.