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Math Expert V
Joined: 02 Sep 2009
Posts: 59625
A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 74% (01:14) correct 26% (01:33) wrong based on 93 sessions

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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

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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1318
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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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
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Director  P
Joined: 18 May 2019
Posts: 530
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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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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VP  D
Joined: 20 Jul 2017
Posts: 1141
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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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
Senior Manager  G
Joined: 29 Jun 2019
Posts: 470
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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1
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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Senior Manager  P
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Concentration: Strategy, Social Entrepreneurship
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Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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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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VP  V
Joined: 19 Oct 2018
Posts: 1158
Location: India
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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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
SVP  D
Joined: 03 Jun 2019
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Location: India
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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1
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

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
Senior Manager  P
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Posts: 440
Location: India
GMAT 1: 580 Q43 V27 WE: Sales (Energy and Utilities)
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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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

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

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Manager  S
Joined: 05 Aug 2018
Posts: 72
Location: Thailand
Concentration: Finance, Entrepreneurship
GPA: 3.68
WE: Business Development (Energy and Utilities)
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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1
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 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
GMAT Club Legend  V
Joined: 18 Aug 2017
Posts: 5458
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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1
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
Senior Manager  P
Joined: 10 Apr 2018
Posts: 281
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34 GPA: 3.3
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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Quote:
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

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.
Director  P
Joined: 24 Nov 2016
Posts: 927
Location: United States
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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1
Quote:
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

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

Senior Manager  G
Joined: 25 Jul 2018
Posts: 392
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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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 = $$\frac{35}{29}$$

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Manager  G
Joined: 17 Jan 2019
Posts: 127
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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1
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?

(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
Intern  Joined: 05 Oct 2019
Posts: 3
Re: A type A machine can complete a job in 5 hours and a type B machine ca  [#permalink]

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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

Posted from my mobile device Re: A type A machine can complete a job in 5 hours and a type B machine ca   [#permalink] 18 Oct 2019, 22:15
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