If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to

Question

If 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to complete a job, how many minutes will it take for 6 Machine A's and 15 Machine B's working together to complete the same job?

A. 66 minutes
B. 76 minutes
C. 96 minutes
D. 106 minutes
E. 120 minutes

gmatophobia · Answer

If 8 Machine A's take 3 hours to complete the work, 1 Machine A will take 8 times the time.

Time taken by 1 Machine A to complete the task = 3 * 8 = 24 hours

If 10 Machine B's take 4 hours to complete the work, 1 Machine B will take 10 times the time.

Time taken by 1 Machine B to complete the task = 10 * 4 = 40 hours

Let's assume that the task is LCM(24,40) = 120 units

Work done by 1 Machine A in 1 hour (rate of Machine A) = 120/24 = 5 units
 
 Work done by 1 Machine B in 1 hour (rate of Machine B) = 120/40 = 3 units

Work done by 6 Machine A's in 1 hour = 6 * 5 = 30 units
 
 Work done by 15 Machine B's in 1 hour = 15 * 5 = 45 units

Total work done by 6 Machine A's + 15 Machine B's in 1 hour = 30 +45 = 75 units

Time taken to complete the work =  \frac{120 }{ 75} = (1 + \frac{45}{75} ) hours

Time in minutes =  60(1 + \frac{45}{75}) = 60 + (9*4) = 60 + 36 = 96  minutes

Option C

JeffTargetTestPrep · Answer

8 Machines A:

Time = 3 hours
Work = 1 job
Rate = Work/Time = 1/3 job/hour

Rate of 1 Machine A = (1/8)(1/3) = 1/24 job/hour

10 Machines B:

Time = 4 hours
Work = 1 job
Rate = Work/Time = 1/4 job/hour

Rate of 1 Machine B = (1/10)(1/4) = 1/40 job/hour

6 Machines A and 15 Machines B together:

Rate = 6(1/24) + 15(1/40) = 25/40 = 5/8 job/hour
Work = 1 job
Time = Work/Rate = 1/(5/8) = 8/5 hours

8/5 hours = (8/5) × 60 = 96 minutes

Answer: C

SaquibHGMATWhiz · Answer

Solution: Let us assume the work be 12 8 Machine A's and 10 Machine B's take 3 and 4 hours respectively to complete a job wnrt.png 6 machine As will have rate 6 imes \frac{1}{2}=3 And 15 machine Bs will have rate =15 imes \frac{3}{10}= 4.5 Total rate =3+4.5=7.5 wnrt2.png Hence the right answer is Option C

Abhishek009 · Answer

8*a_e*3 = 10*4*b_e= 120  (120 = Total work)

SO,  a_e = 5  &  b_e = 3  { _e  represents efficiencies of respective machines}

\frac{120}{(6*5)+(15*3)}*60 = 96 , Answer must be (C)

bumpbot · Answer

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