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# During a certain week, a seal ate 50% of the first 80 smelt

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During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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24 May 2013, 15:44
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During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80
[Reveal] Spoiler: OA

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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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24 May 2013, 15:50
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80

Total smelt = x.

Then, 0.5*80+0.3(x-80)=0.4*x --> x=160 --> 0.4*x=64.

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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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25 May 2013, 03:34
Bunuel wrote:
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80

Total smelt = x.

Then, 0.5*80+0.3(x-80)=0.4*x --> x=160 --> 0.4*x=64.

Bunuel why I am getting a different answer?

Let say Total number of Smelt be - 100

Seal ate - 50% of 80 I.e 40
Than.....- 30% of remaining 20(100-80) I.e 6
Which comes to total of 46(40+6)

Now its given seal ate total of 40%....

In that case 46/40*100 comes to 115 total no of spate......

Where I am going wrong ...can you explain please???
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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25 May 2013, 03:37
nikhilsehgal wrote:
Bunuel wrote:
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80

Total smelt = x.

Then, 0.5*80+0.3(x-80)=0.4*x --> x=160 --> 0.4*x=64.

Bunuel why I am getting a different answer?

Let say Total number of Smelt be - 100

Seal ate - 50% of 80 I.e 40
Than.....- 30% of remaining 20(100-80) I.e 6
Which comes to total of 46(40+6)

Now its given seal ate total of 40%....

In that case 46/40*100 comes to 115 total no of spate......

Where I am going wrong ...can you explain please???

The number of smelt is some particular number you cannot assume that it's 100.
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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23 May 2014, 02:45
Hi,

I am getting a different answer. My approach:
1. First Part - 80 smelts - 50% eaten = 40 ....... Statement 1
2. 2nd Part - x smelts - 30% eaten = 0.3x ....... Statement 2

Total Smelts = 1st part + 2nd part = 80+x
Seal ate 40% of total smelts => 0.4 (80+x) ....... Statement 3

Therefore , combining Statement 1,2,3
40 + 0.3x = 0.4(80+x) . This is giving x = 80 and 32 as the answer.

Kindly assist where I have gone wrong. Thanks
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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23 May 2014, 03:04
mayankgc wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80

Hi,

I am getting a different answer. My approach:
1. First Part - 80 smelts - 50% eaten = 40 ....... Statement 1
2. 2nd Part - x smelts - 30% eaten = 0.3x ....... Statement 2

Total Smelts = 1st part + 2nd part = 80+x
Seal ate 40% of total smelts => 0.4 (80+x) ....... Statement 3

Therefore , combining Statement 1,2,3
40 + 0.3x = 0.4(80+x) . This is giving x = 80 and 32 as the answer.

Kindly assist where I have gone wrong. Thanks

We are told that the seal ate 30% of the remaining smelt it came across. Thus x in your solution must be the number of the remaining smelt. Which makes the total number of smelt equal to 80 + x = 160. 40% of 160 is 64.

Does this make sense?
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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24 May 2014, 07:51
Yes it clears out my confusion
Thanks Bunuel...
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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25 May 2014, 23:25
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80

Responding to a pm:

The seal ate 50% of first portion and 30% of second portion. Overall (average), it ate 40% of the entire portion.

Using scale method, Second portion/First portion = (50 - 40)/(40 - 30) = 1/1

So both portions need to be equal i.e. of 80 smelts each. So both portions together had 160 smelts and the seal ate 40% of it i.e. (40/100)*160 = 64 smelts
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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19 Sep 2015, 14:24
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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22 May 2016, 00:09
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80

Let total no of smelts be X.
eaten smalts:- 50% of first 80==40 && 30 % of remaining (X-80)==30(X-80)/100
total 40% of X
40+ 30(X-80)/100=40X/100
X=160.
so eaten smelts= 40*160/100==64
Ans D.
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Re: During a certain week, a seal ate 50% of the first 80 smelt [#permalink]

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22 May 2016, 11:15
pikachu wrote:
During a certain week, a seal ate 50% of the first 80 smelt it came across, and 30% of the remaining smelt it came across. If the seal ate 40% of the smelt it came across during the entire week, how many smelt did it eat?

A. 32
B. 40
B. 55
D. 64
E. 80

First the seal ate 50% of 80 i.e 40 smelt.

Suppose the number of remaining smelts is x. Seal then ate .30x of these remaining smelts.

Total smelts are 80+ x and seal ate 40% of 80+x

.4(80+x)= 40+.3x
x= 80

Total smelts eaten are .4(80+80)= 64

D is the answer
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Re: During a certain week, a seal ate 50% of the first 80 smelt   [#permalink] 22 May 2016, 11:15
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# During a certain week, a seal ate 50% of the first 80 smelt

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