John gets $57 per hour of regular work and $114 per hour of overtime

Question

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

Are You Up For the Challenge: 700 Level Questions

GMATinsight · Answer

Video Solution of the problem is attached below

Answer: Option C

https://www.youtube.com/watch?v=QmFhie22JYQ

GMATWhizTeam · Answer

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.

eakabuah · Answer

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.

poojakhanduja3017 · Answer

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

PSKhore · Answer

(172 - r)*(114) = 0.15*(57r)
r = 160
Overtime = (172 - 160)
 =12

Gambrosio · Answer

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

John gets $57 per hour of regular work and $114 per hour of overtime

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GMAT Problem Solving (PS) Questions

John gets $57 per hour of regular work and $114 per hour of overtime

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