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John gets $57 per hour of regular work and $114 per hour of overtime 13 Apr 2020, 04:38
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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55% (hard)

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71% (02:57) correct 29% (03:05) wrong based on 307 sessions

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John gets $57 per hour of regular work and $114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?

A. 10
B. 11
C. 12
D. 14
E. 160


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C
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John gets $57 per hour of regular work and $114 per hour of overtime 13 Apr 2020, 04:53
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Bunuel
John gets $57 per hour of regular work and $114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?

A. 10
B. 11
C. 12
D. 14
E. 160

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Video Solution of the problem is attached below

Answer: Option C

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John gets $57 per hour of regular work and $114 per hour of overtime 13 Apr 2020, 05:17
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Bunuel
John gets $57 per hour of regular work and $114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?

A. 10
B. 11
C. 12
D. 14
E. 160


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Solution:

    • Let x and y be the number of regular work hour and overtime hours respectively,
      o \(x + y = 172\)…(i)
    • Now, \(\frac{15}{100}*57*x = 114*y\)
      o \(\frac{3}{20}*x = 2*y\)
      o \(3x = 40y\)
      o \(x = \frac{40*y}{3}\)
    • On substituting the above value in equation (i), we get
      o \(\frac{40*y}{3} + y = 172\)
      o \(43*y = 172*3\)
      o \(y = \frac{172*3}{43} = 4*3 = 12\)
Hence, the correct answer is Option C.­
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John gets $57 per hour of regular work and $114 per hour of overtime 13 Apr 2020, 05:41
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Alternatively

Let the number of regular hours worked be \(r\), and the number of hours worked overtime be \(v\)
Then \(r+v=172\), hence \(r=172-v\) ------\((1)\)
From the question, we are given that portion of the income earned overtime is 15% of the total income earned during regular hours.
Hence, \(\frac{15}{100}*57*(172-v)=114*v\)
\(15*57*172=(57*2)*100v+15*57v\)
\(15*172=215v\)
\((5*3)*(4*43)=(5*43)v\)
\(v=12\)

The answer is therefore C.
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John gets $57 per hour of regular work and $114 per hour of overtime 10 May 2020, 11:26
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IMO C
Question Understanding: Let x and y be the number of regular work hour and overtime hours.
Step 1: x+y=172x+y=172
Step 2: $57 per hour, and $114 for overtime. Relation between these two:
Step 3: (15/100)*57*x=114*y
Step 4: (x*3/20)=2*y
Step 5: 3*x=40*y
Step 6: (x=40∗y)/3
Step 7: Substitution: ((40∗y)/3)+y=172
Step 8: Solving for y: y=12
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John gets $57 per hour of regular work and $114 per hour of overtime 16 Sep 2025, 07:35
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Bunuel
John gets $57 per hour of regular work and $114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?

A. 10
B. 11
C. 12
D. 14
E. 160


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(172 - r)*(114) = 0.15*(57r)
r = 160
Overtime = (172 - 160)
=12
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John gets $57 per hour of regular work and $114 per hour of overtime 17 Sep 2025, 03:33
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Bunuel
John gets $57 per hour of regular work and $114 per hour of overtime work. He works altogether 172 hours and his income from overtime hours is 15% of his income from regular hours. Then, for how many hours did he work overtime?

A. 10
B. 11
C. 12
D. 14
E. 160


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Notice that 114 = 2*57. We can therefore simplify to $1 for regular and $2 for overtime hours. Let's call them x. We know that 15% of his salary is from overtime hours. Leads to the equation:

0.15x = 2* (172-x). Only one variable left. Solve the equation to x = 160, which is the regular hours worked. Since 160 = 172 - 12, the hours worked overtime are 12.

Ans C
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