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A whale goes on a feeding frenzy that lasts for 9 hours. For the first

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A whale goes on a feeding frenzy that lasts for 9 hours. For the first  [#permalink]

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New post Updated on: 23 Jun 2015, 12:00
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A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the sixth hour?

A. 38
B. 47
C. 50
D. 53
E. 62

Originally posted by reto on 23 Jun 2015, 11:36.
Last edited by Bunuel on 23 Jun 2015, 12:00, edited 2 times in total.
Added the OA.
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Re: A whale goes on a feeding frenzy that lasts for 9 hours. For the first  [#permalink]

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New post 23 Jun 2015, 11:55
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If you list the amount eaten each hour, you'll get an equally spaced list, increasing by 3 each hour. In any equally spaced list, the median equals the mean. Here, the mean is 450/9 = 50, so the median is also 50, and that is the amount eaten in the 5th hour. We need to add 3 to find the total eaten in the next hour, so the answer is 53.
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Re: A whale goes on a feeding frenzy that lasts for 9 hours. For the first  [#permalink]

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New post 23 Jun 2015, 12:01
reto wrote:
A whale goes on a feeding frenzy that lasts for 9 hours. For the first hour he catches and eats x kilos of plankton. In every hour after the first, it consumes 3 kilos of plankton more than it consumed in the previous hour. If by the end of the frenzy the whale will have consumed a whopping accumulated total 450 kilos of plankton, how many kilos did he consume on the sixth hour?

A. 38
B. 47
C. 50
D. 53
E. 62

The Answer is 53. This is an Arithmetic Progression Problem. in 9 hours the whale will eat
9(2x+24)/2=450

Solving, x=38
Therefor in 6th hour he consume x+3*5=38+15=53
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Re: A whale goes on a feeding frenzy that lasts for 9 hours. For the first  [#permalink]

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New post 23 Jun 2015, 12:47
Formula :
1. Sum of N terms of an AP = n/2[2a + (n-1)*d]
2. Nth term = a + (n-1)d


Suppose food eaten in first hour : x
The AP is : x, x+3, x+6, .... [Number of terms 'n' = 9]
Therefore,
9/2[2x + (9-1)*3] = 450.
Solving for x, x = 38.
Now, 6th term will be : x + (6-1)*d = 38 + 5*3 = 53.

Hence D !!
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Re: A whale goes on a feeding frenzy that lasts for 9 hours. For the first  [#permalink]

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New post 06 Apr 2019, 09:40
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Re: A whale goes on a feeding frenzy that lasts for 9 hours. For the first   [#permalink] 06 Apr 2019, 09:40
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