A type A machine can complete a job in 5 hours and a type B machine ca

Question

Competition Mode Question

A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

GMATBusters · Answer

let the total work would be 35 units (LCM of 5 & 7)
Since type A machine takes 5 hours to complete the work, A machine does 7 units of work per hour.
Similarly, type B machine does 5 units of work per hour.
Now, work done per hour by 2 type A machines and 3 type B machines working together 
= 2*7+3*5 = 14+15= 29 units
time taken = total work required/work done per hour = 35/29 = D

eakabuah · Answer

Ta=5hrs, Tb=7hrs
We are to find how long 2 machine As and 3 machine Bs can finish the work working together.

I/Tc = 1/5 + 1/5 + 1/7 + 1/7 + 1/7 = 2/5 + 3/7 = 29/35
Hence Tc = 35/29.

The answer is therefore option D in my view.

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CareerGeek · Answer

Formula: Work = Rate*time

Let the total work = LCM (5, 7) = 35 units

Rate of A,  R_A = \frac{35}{5} = 7 u nits/hr &
Rate of B,  R_B = \frac{35}{7} = 5  units/hr

Rate of 2 type A & 3 type B =  2*R_A + 3*R_B   = 2*7 + 3*5 = 29

--> Time taken = Work/Rate =  \frac{35}{29}

IMO Option D

Mohammadmo · Answer

2A machines can do 2/5 of a job in one hour.
3B machines can do 3/7 of a job in one hour.
So, (2/5 + 3/7)X=1
X=35/29
Option D

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madgmat2019 · Answer

Together time = x
2/A + 3/B = 1/x
2/5 + 3/7 = 1/x
29/35 =1/x
x = 35/29

OA:D

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nick1816 · Answer

Assume total work= LCM(5,7)=35 units

Type A machine can do 7 units/hour
Type B machine can do 5 units/hour

Total time taken by 2 type A machines and 3 type B machines working together=  \frac{35}{(2*7+3*5)} =  \frac{35}{29}  hours

D

Kinshook · Answer

A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

Work done by type A machine in 1 hour = 1/5
Work done by type B machine in 1 hour = 1/7

Work done by 2 type A machines and 3 type B machines in 1 hour = 2/5 + 3/7 = (14+15)/35 = 29/35

Hours taken by 2 type A machines and 3 type B machines to complete the job = 35/29 hours

IMO D

unraveled · Answer

A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

Work done in 1 hour by a Type A machines =  \frac{1}{5}  units
Work done in 1 hour by 2 Type A machines =  \frac{2}{5}  units

Work done in 1 hour by a Type B machines =  \frac{1}{7}  units
Work done in 1 hour by 3 Type B machines =  \frac{3}{7}  units

Work done in 1 hour by 2 Type A and 3 Type B machines =  \frac{2}{5} + \frac{3}{7}  =  \frac{29}{35}  units
Thus time taken to complete the job by the five machines =  \frac{1}{29/35}  =  \frac{35}{29}  hours

IMO Answer D.

LalitaSiri · Answer

A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

A machine complete a job in 5 hours, so in 1 hour A machine can complete 1/5 of jobs.
B machine complete a job in 7 hours, so in 1 hour B machine can complete 1/7 of jobs.

2 A machines, can complete 2/5 jobs per hour
and 3 B machines, can complete 3/7 jobs per hour

working together, they can complete 2/5 + 3/7 = 29/35

Thus, it requires 1/ (29/35) = 35/29 hours to complete the job.

Therefore D is the correct answer

Archit3110 · Answer

rate of A; 1/5 and rate of B ; 1/7
rate of 2 A and 3 B ; 2/5 and 3/7
together rate ; 2/5+3/7 =29/35 ; time ; 35/29
IMO D

A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

siddharthkapoor · Answer

Rate= \frac{Work}{Time taken}

Let the required work to do be 1 unit.

So, rate of doing work of machine A= \frac{1}{5} 
Thus, rate of doing work of 2 machine A= \frac{2}{5}  
Similarly, rate of doing work of machine B= \frac{1}{7}  
Thus, rate of doing work of 3 machine B= \frac{3}{7}

Total rate=  \frac{2}{5}+\frac{3}{7} = \frac{29}{35} 
So, Total time=1/29/35= \frac{35}{29}

Thus, the correct answer is option D.

exc4libur · Answer

rate=job*time, rA=1/5, rB=1/7

job/rate=time, 1/(2a+3b)=t, 1/(2/5+3/7)=t, t=35/29

Answer (D)

lacktutor · Answer

a type A machine — \frac{1}{5} 
a type B machine— \frac{1}{7} 
———————
 2( \frac{1}{5})+ 3( \frac{1}{7}) =  \frac{1}{x}  ???

—>  \frac{2}{5}+ \frac{3}{7} =  \frac{(14+ 15)}{35} = \frac{1}{x} 
—> x =  \frac{35}{29}

The answer is D.

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joohwangie · Answer

A type A machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type A machines and 3 type B machines working together and independently to complete the job?

A. 1/5
B. 29/35
C. 5/6
D. 35/29
E. 35/12

(1/5)+(1/7)=12/35--rate
time is reciprocal of rate, therefore, 35/12 hours for 1A and 1B

2A and 3B
2/5+3/7=14/35+15/35=29/35
reciprocal = 35/29
Therefore, D

sheikhtraders · Answer

A complete the 1/5 of work in one hour and B 1/7 in one hour.

so 2A+ 3B in one hour is (2/5+3/7) of work
==> 29/35 work in one hour
==> total work in 1/(29/35) = 35/29

Ans:: D

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A type A machine can complete a job in 5 hours and a type B machine ca

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A type A machine can complete a job in 5 hours and a type B machine ca

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