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18 Jul 2020, 11:14
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58% (01:59) correct
42%
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Q50. Each day, Allan eats 60% of the chocolates left with him. At the end of the end of the third day, 16 chocolates were left. How many chocolates were with him at the end of the first day?
A.50
B.100
C. 150
D. 200
E. 250
A.50
B.100
C. 150
D. 200
E. 250
yashikaaggarwal
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18 Jul 2020, 11:31
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Let Allan have X chocolates on first day
he ate 60% remaining 40% or 0.4x
on second day he ate 60% of 0.4x and 0.16 is remaining
on third day he ate 60% of 0.16x and 16 is remaining which is equal to 0.4*0.16x
0.064x = 16
x = 250
So he had 250 chocolates on first day starting out of which he ate 60%
so he is left with 0.4*250 = 100 chocolates at the end of first day.
Answer is B
he ate 60% remaining 40% or 0.4x
on second day he ate 60% of 0.4x and 0.16 is remaining
on third day he ate 60% of 0.16x and 16 is remaining which is equal to 0.4*0.16x
0.064x = 16
x = 250
So he had 250 chocolates on first day starting out of which he ate 60%
so he is left with 0.4*250 = 100 chocolates at the end of first day.
Answer is B
18 Jul 2020, 20:35
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Each day Allan eats 60% of the previous days chocolates. This means that each day Allan is left with 40% of the remaining chocolates of the previous day.
This is a successive percentage change and can be written as a straight line equation.
x * \(\frac{40}{100}\) * \(\frac{40}{100}\) * \(\frac{40}{100}\) = 16
Where x is the initial number of chocolates and 16 is the final number of chocolates after 3 days
Therefore x * \(\frac{64}{1000}\) = 16
x = 250
_____________________
When using the theory of successive discounts, if a % is decreasing then decrease that amount from 100% and if a % is increasing add it to 100%.
For eg a stock market price of $1000, fir decreased by 10% on the 1st day and then increased by 20% on the second day. What is it's price at the end of the second day?
Since the Percentages are successive, we simply write it as 1000 * \(\frac{90}{100}\) * \(\frac{120}{100}\) = $1080
We have decreased 10% from 100% to give 90% and added 20% to 100% to get 120%.
Note: When doing successive percentages based sums, do not add or subtract the percentages, for eg in the example above, doing -10 + 20, which gives an overall percentage of +10% is incorrect.
________________________
Arun Kumar
This is a successive percentage change and can be written as a straight line equation.
x * \(\frac{40}{100}\) * \(\frac{40}{100}\) * \(\frac{40}{100}\) = 16
Where x is the initial number of chocolates and 16 is the final number of chocolates after 3 days
Therefore x * \(\frac{64}{1000}\) = 16
x = 250
_____________________
When using the theory of successive discounts, if a % is decreasing then decrease that amount from 100% and if a % is increasing add it to 100%.
For eg a stock market price of $1000, fir decreased by 10% on the 1st day and then increased by 20% on the second day. What is it's price at the end of the second day?
Since the Percentages are successive, we simply write it as 1000 * \(\frac{90}{100}\) * \(\frac{120}{100}\) = $1080
We have decreased 10% from 100% to give 90% and added 20% to 100% to get 120%.
Note: When doing successive percentages based sums, do not add or subtract the percentages, for eg in the example above, doing -10 + 20, which gives an overall percentage of +10% is incorrect.
________________________
Arun Kumar
