A teacher corrected the first half of a stack of exams at a rate of 9

Question

A teacher corrected the first half of a stack of exams at a rate of 9 exams per hour and the second half of the stack at a rate of 18 exams per hour. If it took her 4 hours to correct all of the exams, how many exams were in the stack?

A. 48
B. 50
C. 52
D. 54
E. 56

A. 48 
B. 50
C. 52
D. 54
E. 56

culpatenetur · Answer

So first half is marked at 9 eph (exams per hour) second half at 18 eph.

Since the rate doubles from 9 -> 18, the time taken to complete the same of work is halved. (we know the work is the same amount as they each perform 1/2).

So when working at 18 eph is takes 1T of time to complete half, and when working at 9 eph it takes 2T to complete a half. So total time takes 3T

work done = rate x time

This means the total work done (D) = 18T + 9(2T)

4 hours total divided by 3T means T=4/3 hours

18(4/3) + 9 x 2 x(4/3) = 48

GmatTest2026 · Answer

By applying the matrix approach, we can get an answer

Rate 
 Time 
 Exam 
 
  First half 
 9 
 E/9 
 E 
 
  Second half 
 18 
 E/18 
 E

As we know

\frac{E}{9}  +  \frac{E}{18}  = 4(total time mentioned in the question)

E= 24

Total Exams = 24 +24 = 48

Answer: A

A teacher corrected the first half of a stack of exams at a rate of 9

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