Two women invest $125,000 and $85,000 respectively in a business. They

Question

Two women invest $125,000 and $85,000 respectively in a business. They agree that 60% of the profit will be divided equally between them. They also agree that the remaining amount of the profit will be considered as interest on the capital. If one of the women gets $300 more than the other, then what is the total profit made in the business?

(A) $1520.50

(B) $1849.00

(C) $3937.50

(D) $6582.00

(E) $9266.50

Show Answer

Official Answer

C

(A) $1520.50

(B) $1849.00

(C) $3937.50

(D) $6582.00

(E) $9266.50

stoned · Accepted Answer

Woman with $125,000 investment get 300 extra i.e. she get 300 interest for 40,000 (125000-85000).

40000 generate 300 interest
and 12500 will generate  \frac{3}{400} *12500 interest
and 85000 will generate  \frac{3}{400} *8500 interest

therefore total interest generated will be  \frac{3}{400} *12500 +  \frac{3}{400} *8500 = 1575 which is equal to 40% of the total profit (P)

40% of P= 1575
P=1575* \frac{5}{2} = 3937.50

pappal · Answer

let P be the profit
ratio of capital=25:17
since 0.6 of P is equally divided so will have no effect on the variation of the distribution of the profit
only 0.4P is divided in the ratio of the capital
difference in profits=(25/42 - 17/42)of 0.4P=$300
i.e. 8/42 *0.4P=300 
on solving p=3937.5
(C)

Nightzade · Answer

Let X = Amount of the profit that will be split unequally which is also...
X = Total profit - 60% of the profit split equally or 40% of the total profit

Total invested = $125,000 + $85,000 = $210,000

Woman 1 will receive 125,000/210,000 of X --> 25/42
Woman 2 will receive 85,000/210,000 of X --> 17/42

The difference in amount that each woman receives is therefore
25/42(X) - 17/42(X) = 8/42(X)

We are told that the difference between how much each is paid is $300 therefore
8/42*(X) = $300 ---> 4/21*(X) = $300 ---> 1/21*(X) = 75
X = 1575

Since we know X is 40% of the total profit, we can multiply X by .4 to get the total profit
1575/(.4) = 3937.5

The answer is   C

pappal · Answer

rest is correct just we need to divide X by 0.4 to get 3937.5

Nightzade · Answer

Whoops. Thanks for the catch

xiaxyl · Answer

Can someone please explain why interest is in the ratio of capital? The rates can be different also, then this may not be the case

pappal · Answer

Absolutely true if rates were specified.
But here, it's the same buisness and there is a mutual agreement that rest will be interest on capital, itself sufficient to support that it will be divided in capital's ratio.
IMO

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