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A man spends 20% of his income on house rent, 25% of the remaining

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A man spends 20% of his income on house rent, 25% of the remaining [#permalink]

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New post 14 Jul 2017, 22:11
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A man spends 20% of his income on house rent, 25% of the remaining income on food, and 30% of his total income on conveyance, and saves the rest. If he invested 40% of his savings in shares, how many shares did he purchase?

(1) He spends $80 on his food.
(2) He purchased shares of two different companies only and the price per share of these companies was in the ratio 5:7

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A man spends 20% of his income on house rent, 25% of the remaining [#permalink]

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New post Updated on: 12 Aug 2017, 11:18
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Gnpth wrote:
A man spends 20% of his income on house rent, 25% of the remaining income on food, and 30% of his total income on conveyance, and saves the rest. If he invested 40% of his savings in shares, how many shares did he purchase?

(1) He spends $80 on his food.
(2) He purchased shares of two different companies only and the price per share of these companies was in the ratio 5:7


Hi,
In order to determine the number of shares, we need the following information:
  • The amount spent on shares, and
  • The price of each share.

From(1) we can find the Total income of the man. => We can also find amount invested in shares. But we don't have any information about the price of each share. Hence, we can't find the number of shares. Insufficient.

From(2) we know only the ratio of the prices of two types of shares. No information about the amount invested in shares and price of each type of shares. Insufficient.

By combining (1) and (2): We know following:
  • the amount spent on shares, and
  • the ratio of the prices of each type of shares.

Still, we don't know the price of each share. Hence, Insufficient.

Answer(E)

Note: Please note that from statement(2) we know the ratio of the price of two types of shares is 5:7. This doesn't imply that price of the type1 share is 5, and price of type 2 share is 7.

Only we can conclude that price of the type1 share is some multiple of 5 and price of the type2 share is some multiple of 7.

Thanks.

Originally posted by ganand on 11 Aug 2017, 22:39.
Last edited by bb on 12 Aug 2017, 11:18, edited 1 time in total.
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Re: A man spends 20% of his income on house rent, 25% of the remaining [#permalink]

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New post 21 Apr 2018, 05:32
Gnpth wrote:
A man spends 20% of his income on house rent, 25% of the remaining income on food, and 30% of his total income on conveyance, and saves the rest. If he invested 40% of his savings in shares, how many shares did he purchase?

(1) He spends $80 on his food.
(2) He purchased shares of two different companies only and the price per share of these companies was in the ratio 5:7




1+2
Total income = $400 , He spends $80 on rent, $80 on food and $120 on Conveyance so he saves $120 , now 40% of $120 = $48 so he bought shares worth $48

If shares cost $5 and $7 then
5x+7y= 48 and we get x= 4 and y=4 so he bought 8 shares.

If shares cost $10 and $14 then:
10x+14y=48 , x=2 and y=2 so he bought 4 shares .

Hence answer is E.

( Initially had marked C )
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A man spends 20% of his income on house rent, 25% of the remaining [#permalink]

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New post 22 Apr 2018, 05:27
stne,

-------------------------------------------------------------------------------------
1+2
Total income = $400 , He spends $80 on rent, $80 on food and $120 on Conveyance so he saves $120 , now 40% of $120 = $48 so he bought shares worth $48

If shares cost $5 and $7 then
5x+7y= 48 and we get x= 4 and y=4 so he bought 8 shares.

If shares cost $10 and $14 then:
10x+14y=48 , x=2 and y=2 so he bought 4 shares .

Hence answer is E.

--------------------------------------------------------------------------------
Thanks .

However. I think, the savings will be $80(~25%), not $120 and amount spent on shares wil be $32 (40%of 80)

so the equation will be 5x+7y=32. We have two unkown variables that can yield mulitple solutions.

So, we can not come to a unique solution.
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A man spends 20% of his income on house rent, 25% of the remaining [#permalink]

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New post 22 Apr 2018, 11:20
valardohaeris wrote:
stne,

-------------------------------------------------------------------------------------
1+2
Total income = $400 , He spends $80 on rent, $80 on food and $120 on Conveyance so he saves $120 , now 40% of $120 = $48 so he bought shares worth $48

If shares cost $5 and $7 then
5x+7y= 48 and we get x= 4 and y=4 so he bought 8 shares.

If shares cost $10 and $14 then:
10x+14y=48 , x=2 and y=2 so he bought 4 shares .

Hence answer is E.

--------------------------------------------------------------------------------
Thanks .

However. I think, the savings will be $80(~25%), not $120 and amount spent on shares wil be $32 (40%of 80)

so the equation will be 5x+7y=32. We have two unkown variables that can yield mulitple solutions.

So, we can not come to a unique solution.


I think you are making a mistake some where. Please check again .
question says 25% of the REMAINING on food . So after spending 20% on rent he is left with 80% of his total income . Now of this he spends 25% on food .
so\(\frac{25}{100}\)* Remaining = 80 , hence remaining is $320
Now this $320 is 80%
so what is 100%?
100%= $400 , so his total income is $400

Now on Conveyance is spends 30% of 400 so that is $120
So how much is left now ?
( Rent ) 20% of 400 = $80
(Food ) 20% of 320 = $80
( Conveyance ) 30% of 400 = $120
400- (80+80+120) = 120 , this is what he saves
Now 40% of 120 ( saved amt) he buys shares ->\(\frac{40}{100}\)*120 = $48


also since number of shares have to be an integer hence if the price of shares are 5 and 7 respectively then x= 4 and y = 4 are the only solutions .
again if the price of shares are 10 and 14 then x= 2 and y= 2 are the only solutions .
and that is why the answer is E.

Hope its clear now !
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Re: A man spends 20% of his income on house rent, 25% of the remaining [#permalink]

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New post 22 Apr 2018, 11:24
valardohaeris wrote:
stne,

-------------------------------------------------------------------------------------
1+2
Total income = $400 , He spends $80 on rent, $80 on food and $120 on Conveyance so he saves $120 , now 40% of $120 = $48 so he bought shares worth $48

If shares cost $5 and $7 then
5x+7y= 48 and we get x= 4 and y=4 so he bought 8 shares.

If shares cost $10 and $14 then:
10x+14y=48 , x=2 and y=2 so he bought 4 shares .

Hence answer is E.

--------------------------------------------------------------------------------
Thanks .

However. I think, the savings will be $80(~25%), not $120 and amount spent on shares wil be $32 (40%of 80)

so the equation will be 5x+7y=32. We have two unkown variables that can yield mulitple solutions.

So, we can not come to a unique solution.


Hello

I think what Stne did was correct. Amount spent on food is 25% of 80%, which is basically 20% of total only, and is given as $80. So 1/5 of total = 80. Which means total income = 80*5 = $400. Thus rent = 20% of 400 = $80, food = 20% again = $80, conveyance = 30% of 400 = $120. Thus his savings = 400-80-80-120 = $120 only. Amount on shares = 40% of 120 = $48.
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Re: A man spends 20% of his income on house rent, 25% of the remaining [#permalink]

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New post 08 May 2018, 08:12
We need two things to calculate here
I) price of share
II) money spent on shares or total income

Both above info is not conveyed in statements above

So E is answer

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Re: A man spends 20% of his income on house rent, 25% of the remaining   [#permalink] 08 May 2018, 08:12
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