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18 Jun 2019, 09:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
75% (02:23) correct
25%
(02:25)
wrong
based on 355
sessions
History
Date
Time
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Not Attempted Yet
The manufacturing cost of a certain product consists of two parts – production cost and testing cost. In a year, the manufacturing cost increased by 23%, whereas the production and testing costs increased by 25% and 20% respectively. Before the increase, the testing cost was what percentage of the production cost?
A. 25%
B. 33.33%
C. 50%
D. 66.67%
E. 125%
A. 25%
B. 33.33%
C. 50%
D. 66.67%
E. 125%
ramlala
Joined: 22 Aug 2020
Last visit: 13 Dec 2022
Posts: 468
Given Kudos: 30
Location: India
Concentration: International Business, Finance
Schools: IIMA PGPX'23 INSEAD Jan'23 intake Sloan (MIT) ISB HEC Said
GPA: 4
WE:Project Management (Energy)
16 Oct 2020, 09:57
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Manufacturing cost (M) = Production cost (P) + Testing cost (T)
M = P + T
1.23 M = 1.25 P + 1.2 T
As the mean of 25% & 20% is 23%, weightage of the Production is more than Testing cost i.e. P>T
in other way P>50% of M & T<50% of M
A. 25% < 50%
B. 33.33% < 50%
C. 50% = 50%
D. 66.67% as required
E. 125% > 100% N.A.
Ans D
M = P + T
1.23 M = 1.25 P + 1.2 T
As the mean of 25% & 20% is 23%, weightage of the Production is more than Testing cost i.e. P>T
in other way P>50% of M & T<50% of M
A. 25% < 50%
B. 33.33% < 50%
C. 50% = 50%
D. 66.67% as required
E. 125% > 100% N.A.
Ans D
General Discussion
19 Jun 2019, 01:09
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This is a question where assuming some variables smartly may help speed up the solution.
Since the production cost increased by 25%, let’s assume the production cost as 4x. Therefore, new production cost after the increase = 4x (1+\(\frac{1}{4}\)) = 5x.
Similarly, since the testing cost increased by 20%, let’s assume the testing cost as 5y. Therefore, new testing cost after the increase = 5y (1+\(\frac{1}{5}\)) = 6y.
The old manufacturing cost will be 4x + 5y and the new manufacturing cost will be 5x + 6y.
We know that the new manufacturing cost is 23% more than the old. Therefore,
5x + 6y = 123% (4x + 5y). Simplifying the above, we get,
\(\frac{x}{y}\) = \(\frac{15}{8}\).
So, old production cost = 4x = 60; old testing cost = 5y = 40. So, before the increase,
Testing cost, 40 is \(\frac{2}{3}\)rd of the production cost, 60. \(\frac{2}{3}\) is equivalent to 66.67%.
So, the correct answer option is D.
Note that, we could have solved the same question by assuming x and y as the old production and testing costs; but this would have introduced unnecessary calculations. So, we chose to leverage the data given to assume values for our calculations.
Hope this helps!
Since the production cost increased by 25%, let’s assume the production cost as 4x. Therefore, new production cost after the increase = 4x (1+\(\frac{1}{4}\)) = 5x.
Similarly, since the testing cost increased by 20%, let’s assume the testing cost as 5y. Therefore, new testing cost after the increase = 5y (1+\(\frac{1}{5}\)) = 6y.
The old manufacturing cost will be 4x + 5y and the new manufacturing cost will be 5x + 6y.
We know that the new manufacturing cost is 23% more than the old. Therefore,
5x + 6y = 123% (4x + 5y). Simplifying the above, we get,
\(\frac{x}{y}\) = \(\frac{15}{8}\).
So, old production cost = 4x = 60; old testing cost = 5y = 40. So, before the increase,
Testing cost, 40 is \(\frac{2}{3}\)rd of the production cost, 60. \(\frac{2}{3}\) is equivalent to 66.67%.
So, the correct answer option is D.
Note that, we could have solved the same question by assuming x and y as the old production and testing costs; but this would have introduced unnecessary calculations. So, we chose to leverage the data given to assume values for our calculations.
Hope this helps!
