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A, B and C are partners. A receives 2/3 of profit, B and C

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A, B and C are partners. A receives 2/3 of profit, B and C  [#permalink]

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New post 15 Apr 2019, 06:21
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Question Stats:

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A, B and C are partners. A receives 2/3 of profit, B and C dividing the remaining profit equally. A's income is increased by $400 when the rate of profit rises from 5% to 7%. Find the profit of B

a. $600
b. $850
c. $350
d. $1100
e. $2100

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A, B and C are partners. A receives 2/3 of profit, B and C  [#permalink]

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New post 15 Apr 2019, 06:31
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1
jackfr2 wrote:
A, B and C are partners. A receives 2/3 of profit, B and C dividing the remaining profit equally. A's income is increased by $400 when the rate of profit rises from 5% to 7%. Find the profit of B

a. $600
b. $850
c. $350
d. $1100
e. $2100

Posted from my mobile device


Let the cost = 100x
i.e. Profit = 5% of 100x = 5x

A's profit = (2/3)*5x
B's profit = (1/2)*(1/3)*5x = (1/6)*5x
C's profit = (1/2)*(1/3)*5x = (1/6)*5x

New Profit = 7% of 100x = 7x
i..e. Now A's profit = (2/3)*7x

Change in A's profit = (2/3)*7x - (2/3)*5x = (4/3)x

Given, (4/3)*x = $400

i.e. x = $300

B's profit = (1/6)*7x = 7*300/6 = $350

Answer: Option C
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A, B and C are partners. A receives 2/3 of profit, B and C  [#permalink]

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New post Updated on: 15 Apr 2019, 09:33
jackfr2 wrote:
A, B and C are partners. A receives 2/3 of profit, B and C dividing the remaining profit equally. A's income is increased by $400 when the rate of profit rises from 5% to 7%. Find the profit of B

a. $600
b. $850
c. $350
d. $1100
e. $2100

Posted from my mobile device


let profit be x
so for A given
profit is 2/3 it receives
so
1.07x*2/3-1.05x*2/3 = 400
or say
2x*.02 =1200
x= 30,000
now we need to determine profit of B @ 7%
so
0.07*30,000 * 1/3* 1/2 = 350$
IMO C

Originally posted by Archit3110 on 15 Apr 2019, 07:57.
Last edited by Archit3110 on 15 Apr 2019, 09:33, edited 1 time in total.
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Re: A, B and C are partners. A receives 2/3 of profit, B and C  [#permalink]

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New post 15 Apr 2019, 09:24
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Archit3110 wrote:
jackfr2 wrote:
A, B and C are partners. A receives 2/3 of profit, B and C dividing the remaining profit equally. A's income is increased by $400 when the rate of profit rises from 5% to 7%. Find the profit of B

a. $600
b. $850
c. $350
d. $1100
e. $2100

Posted from my mobile device


let profit be x
so for A given
profit is 2/3 it receives
so
1.07x*2/3-1.05x*2/3 = 400
or say
2x*.02 =1200
x= 30,000
so A share ; 30,000 * 2/3 = 20,000
left with 10,000 which is shared equally ; 5,000 each
GMATinsight ; sir where am I going wrong ? :( I did not assume value of interest like in your case , i solved using variables not sure where i got solution wrong please advise..



There are more than one mistake

if x is the profit in first case then 1.05x has no meaning as x itself must be 5% of cost that's why I started with assumption of cost as 100x and not profit.

second mistake is that the initial profit sharing of B is not what question is asking. Question is asking the later profit sharing of B

i.e. 0.07x is the profit in later case as per your calculation assuming that x is the cost

0.07x*(1/3)*(1/2) is teh profit sharing of B = (7/100)*(1/6)*30000 = $350

I hope you it helps!!! :)

Archit3110
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Re: A, B and C are partners. A receives 2/3 of profit, B and C  [#permalink]

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New post 15 Apr 2019, 09:30
GMATinsight ; thanks a lot sir, understood where I went wrong... wording of question was little tricky especially end part ... :|

GMATinsight wrote:
Archit3110 wrote:
jackfr2 wrote:
A, B and C are partners. A receives 2/3 of profit, B and C dividing the remaining profit equally. A's income is increased by $400 when the rate of profit rises from 5% to 7%. Find the profit of B

a. $600
b. $850
c. $350
d. $1100
e. $2100

Posted from my mobile device


let profit be x
so for A given
profit is 2/3 it receives
so
1.07x*2/3-1.05x*2/3 = 400
or say
2x*.02 =1200
x= 30,000
so A share ; 30,000 * 2/3 = 20,000
left with 10,000 which is shared equally ; 5,000 each
GMATinsight ; sir where am I going wrong ? :( I did not assume value of interest like in your case , i solved using variables not sure where i got solution wrong please advise..



There are more than one mistake

if x is the profit in first case then 1.05x has no meaning as x itself must be 5% of cost that's why I started with assumption of cost as 100x and not profit.

second mistake is that the initial profit sharing of B is not what question is asking. Question is asking the later profit sharing of B

i.e. 0.07x is the profit in later case as per your calculation assuming that x is the cost

0.07x*(1/3)*(1/2) is teh profit sharing of B = (7/100)*(1/6)*30000 = $350

I hope you it helps!!! :)

Archit3110
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A, B and C are partners. A receives 2/3 of profit, B and C  [#permalink]

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New post 15 Apr 2019, 15:48
4
I didn't use algebra because I couldn't create an equation.

Increasing from 5% to 7% = 400 usd, that means that the value of 2% is 400 usd.

So the total profit of A would be = 1,400 (7%) usd and this represent \(\frac{2}{3}\) of the total.

\(\frac{2}{3}\) = 1,400

So 2,100 usd (\(\frac{2}{3}=1400\) & \(\frac{1}{3}=700\))

So B & C will have to divide 700 between them.

350

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A, B and C are partners. A receives 2/3 of profit, B and C  [#permalink]

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New post 16 Apr 2019, 02:44
jackfr2 wrote:
A, B and C are partners. A receives 2/3 of profit, B and C dividing the remaining profit equally. A's income is increased by $400 when the rate of profit rises from 5% to 7%. Find the profit of B

a. $600
b. $850
c. $350
d. $1100
e. $2100

Posted from my mobile device


In order to determine the ratio in which the profit is split, we can assume a simple
number to be the total profit. Let that be $300 - A will receive \(\frac{2}{3}*300 = $200\)
B and C get an equal share of the remaining $100. Ratio of profits is 4:1:1

We are told that for a 2% increase in profit, the income of A increases by $400.
Tthe total income of the partners increases by $600(ratio is 4:1:1). The total
amount on which the profit is generated is \(\frac{$600}{2}*100 = $30000\).

Therefore, the total profit that B takes home is \(\frac{1}{6}*\frac{7}{100}*30000\) = $350(Option C)
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A, B and C are partners. A receives 2/3 of profit, B and C   [#permalink] 16 Apr 2019, 02:44
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