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16 Jun 2021, 05:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
48% (02:53) correct
52%
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wrong
based on 164
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An apple vendor sells 50% of his stock everyday. 10% of his stock gets spoiled overnight. After three nights he calculates that a total of 3,305 apples have spoiled. How many apples did he start out with on the first day? (Assume that he has purchased apples only on the first day.)
(A) 25,000
(B) 30,000
(C) 35,000
(D) 40,000
(E) 45,000
(A) 25,000
(B) 30,000
(C) 35,000
(D) 40,000
(E) 45,000
25 Jun 2021, 07:28
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Bunuel
Beginning of first day let him have \(x\)
End of first day he has \(\frac{x}{2} \)
First night \(\frac{10}{100}* \frac{x}{2}\) = gets spoiled
So second day he will start with \(\frac{90}{100} * \frac{x}{2}\)
Second day :
As calculated he starts with \(\frac{90}{100}* \frac{x}{2}\)
After selling \(50\% \) he has remaining \(\frac{1}{2}*\frac{90}{100}* \frac{x}{2}\)
\(2\)nd night \(\frac{10}{100} *\frac{1}{2}*\frac{90}{100}* \frac{x}{2}\)= get spoiled
So \(3\)rd day he will start with = \(\frac{90}{100}* \frac{1}{2}*\frac{90}{100}* \frac{x}{2} \)
Third day :
As calculated he starts with \(\frac{90}{100} *\frac{1}{2}*\frac{90}{100}* \frac{x}{2}\)
After selling \(50\% \) he has left \(\frac{1}{2}*\frac{90}{100} *\frac{1}{2}*\frac{90}{100}* \frac{x}{2}\)
\(3\)rd night \( \frac{10}{100} *\frac{1}{2}*\frac{90}{100} *\frac{1}{2}*\frac{90}{100}* \frac{x}{2} \) gets spoiled
After \(3\) nights total apples spoiled \(= 3305\)
\(\frac{10}{100}* \frac{x}{2}+ \frac{10}{100} *\frac{1}{2}*\frac{90}{100}* \frac{x}{2}+ \frac{10}{100} *\frac{1}{2}*\frac{90}{100} *\frac{1}{2}*\frac{90}{100}* \frac{x}{2}= 3305 \)
Solving for \(x\) we get \(x= 40,000 \)
Ans -D
Hope it's clear.
27 Sep 2025, 12:34
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No need to use single variable here. We just need to pick smart number and let them as total apples on first day.
To do this, we first need to understand fractions that we need to tackle in this question
1/2 got sold, 1/2 remains from which 1/10 got spoiled
It means that 1/20 of apples got spoiled overnight and there are 3 nights that we are talking about
Therefore, Let the total apples be 20*20*20 = 8000x on the first day
and remaining not sold as well as non-spoiled will be (1/2)*(9/10)=9/20
(It'll all happen in your mind once you start taking numbers instead of variables)
Now, Day1: spoiled = 8000x/20 = 400x
remaining (not sold, non-spoiled and carried to next day) = 3600
Day2: spoiled = 3600x/20 = 180x
remaining (not sold, non-spoiled and carried to next day) = 1620
Day3: spoiled = 1620x/20 = 81x
Total spoiled apples will be = 400x+180x+81x = 661x
661x = 3305
x = 5
Total apples = 8000*5 = 40,000
To do this, we first need to understand fractions that we need to tackle in this question
1/2 got sold, 1/2 remains from which 1/10 got spoiled
It means that 1/20 of apples got spoiled overnight and there are 3 nights that we are talking about
Therefore, Let the total apples be 20*20*20 = 8000x on the first day
and remaining not sold as well as non-spoiled will be (1/2)*(9/10)=9/20
(It'll all happen in your mind once you start taking numbers instead of variables)
Now, Day1: spoiled = 8000x/20 = 400x
remaining (not sold, non-spoiled and carried to next day) = 3600
Day2: spoiled = 3600x/20 = 180x
remaining (not sold, non-spoiled and carried to next day) = 1620
Day3: spoiled = 1620x/20 = 81x
Total spoiled apples will be = 400x+180x+81x = 661x
661x = 3305
x = 5
Total apples = 8000*5 = 40,000
