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MaxFabianKirchner
Joined: 02 Jun 2025
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Schools: ESSEC MiF '26 ESADE HEC Imperial LBS Oxford MFE '26 Sloan (MIT) NYU Stern NUS Bocconi IE'26
Posts: 65
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09 Jul 2025, 09:02
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Let the initial amount of money on Monday be A. An increase of m percent on Tuesday results in a balance of A(1 + m/100). A subsequent withdrawal of n percent from the Tuesday balance results in a final amount of A(1 + m/100)(1 - n/100). This final amount is given to be 50 percent of the initial amount, A, which establishes the governing equation A(1 + m/100)(1 - n/100) = 0.5A.
The variable A cancels from both sides of the equation. The remaining equation can be written as ( (100+m)/100 ) * ( (100-n)/100 ) = 1/2. Multiplying both sides by 10000 simplifies the expression to (100+m)(100-n) = 5000. To solve for n, the term containing it is isolated: 100 - n = 5000/(100+m). Rearranging the equation to solve for n gives n = 100 - 5000/(100+m). To express this as a single fraction, a common denominator is used, yielding n = (100(100+m) - 5000)/(100+m). Simplifying the numerator gives n = (10000 + 100m - 5000)/(100+m), which reduces to n = (5000 + 100m)/(100+m). Factoring 100 from the numerator produces the final required expression n = 100(50+m)/(m+100).
The correct answer is (A).
The variable A cancels from both sides of the equation. The remaining equation can be written as ( (100+m)/100 ) * ( (100-n)/100 ) = 1/2. Multiplying both sides by 10000 simplifies the expression to (100+m)(100-n) = 5000. To solve for n, the term containing it is isolated: 100 - n = 5000/(100+m). Rearranging the equation to solve for n gives n = 100 - 5000/(100+m). To express this as a single fraction, a common denominator is used, yielding n = (100(100+m) - 5000)/(100+m). Simplifying the numerator gives n = (10000 + 100m - 5000)/(100+m), which reduces to n = (5000 + 100m)/(100+m). Factoring 100 from the numerator produces the final required expression n = 100(50+m)/(m+100).
The correct answer is (A).
09 Jul 2025, 09:03
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Let M be the amount of money Elena had on Monday.
On Tuesday, she increased that amount by m percent.
Tuesday's balance = M * (1 + m/100)
On Wednesday, she withdrew n percent of her Tuesday's closing balance.
This means she was left with (100-n) percent of Tuesday's balance.
Wednesday's balance = [M * (1 + m/100)] * (1 - n/100)
We are told that her Wednesday's balance was exactly 50 percent of what she had on Monday.
So, Wednesday's balance = 0.50 * M
Now, let's set up the equation:
M * (1 + m/100) * (1 - n/100) = 0.50 * M
We can divide both sides by M (assuming M is not zero):
(1 + m/100) * (1 - n/100) = 0.50
Convert the decimals/percentages to fractions:
{(100+m)/100} * {(100−n)/100} = 50/100
Now, we need to solve for n in terms of m.
Multiply both sides by 100 * 100 = 10000:
(100 + m)(100 - n) = 5000
Divide both sides by (100 + m):
100 - n = 5000/(100+m)
Now, isolate n:
n = 100 - [5000/ (100+m)]
To combine the terms on the right side, find a common denominator:
n = [100(100+m)/(100+m)] - [5000/(100+m)]
n = {10000+100m−5000}/ {100+m}
n = {5000+100m} / {100+m}
Factor out 100 from the numerator:
n = 100(50+m)/ {100+m}
This matches option A.
The final answer is A
On Tuesday, she increased that amount by m percent.
Tuesday's balance = M * (1 + m/100)
On Wednesday, she withdrew n percent of her Tuesday's closing balance.
This means she was left with (100-n) percent of Tuesday's balance.
Wednesday's balance = [M * (1 + m/100)] * (1 - n/100)
We are told that her Wednesday's balance was exactly 50 percent of what she had on Monday.
So, Wednesday's balance = 0.50 * M
Now, let's set up the equation:
M * (1 + m/100) * (1 - n/100) = 0.50 * M
We can divide both sides by M (assuming M is not zero):
(1 + m/100) * (1 - n/100) = 0.50
Convert the decimals/percentages to fractions:
{(100+m)/100} * {(100−n)/100} = 50/100
Now, we need to solve for n in terms of m.
Multiply both sides by 100 * 100 = 10000:
(100 + m)(100 - n) = 5000
Divide both sides by (100 + m):
100 - n = 5000/(100+m)
Now, isolate n:
n = 100 - [5000/ (100+m)]
To combine the terms on the right side, find a common denominator:
n = [100(100+m)/(100+m)] - [5000/(100+m)]
n = {10000+100m−5000}/ {100+m}
n = {5000+100m} / {100+m}
Factor out 100 from the numerator:
n = 100(50+m)/ {100+m}
This matches option A.
The final answer is A
09 Jul 2025, 09:04
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Lets take the amount on Monday be 100, on Tuesday he added m percent which is 100+m/100, on wednesday he substracted n percent from tuesday closing which is (100+m/100)-n/100, which results in 50 percent of 100, i.e.100(m-50)/m+100, option B is the answer.
