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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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

C

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

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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GMATinsight ; thanks a lot sir, understood where I went wrong... wording of question was little tricky especially end part ...

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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Hi pushpitkc

Could you explain how you went from the total 600$ increase to find the total profit?

This part: 600/ 2∗100=$30000

Thanks a lot

Question stem should be re-written as "Find the profit of B after the rise"?

Let the CP be x
At 5% profit, SP will be 1.05x and Profit 0.05x
At 7% profit, SP will be 1.07x and Profit 0.07x

Increase in actual profit when profit % rose from 5% to 7%: 0.07x - 0.05x = 0.02x
Now, increase in A's profit because of above change: 2/3 * 0.02x = 400
So, x = 30,000

For Profit 0.05x = 0.05 * 30,000 = 1500, Profit split is as follows
A= 2/3*1500 = 1000
B= 1/6*1500 = 250
C= 1/6*1500 = 250

For Profit 0.07x = 0.07* 30,000 = 2100, Profit split is as follows
A= 2/3*2100 = 1400
B= 1/6*2100 = 350
C= 1/6*2100 = 350

Hence, Profit share of B at 5% rate of profit is 250 and at 7% rate of Profit is 350
Ans C

A:B:C= 4:1:1

Let, total profits be $ x.

Then,

4/6 of(7% of x - 5% of x)=400

=> x = 30000

Now,

B's profit= 30000/6=5000

Posted from my mobile device

2/3rd is A's profit
Since B and C divide profit equally, so B's profit is 1/6th and same is C's.
Now as per the question 2/3 * (7%-5%)*x = 400
Thus, x = 30000
B's Profit = 1/6 * 7/100 * 30000 = 350

A's income is increased by $400 when the rate of profit rises from 5% to 7% : 2% rise = $400

So, 7% will be : 2 * 3.5 = 400 * 3.5

=> 7% = $1,400

A's profit: \(\frac{2}{3} * Total = $1,400\)

Total: \(1,400 * \frac{3}{ 2} = $2,100\)

Total - A: $2,100 - $1,400 = $700 [Remaining profit]

B + C = $700 [Since B and C dividing the remaining profit equally, therefore, B = C = $350 each]

Answer C
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