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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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17 Oct 2019, 21:19
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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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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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17 Oct 2019, 21:30
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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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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17 Oct 2019, 21:31
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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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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17 Oct 2019, 21:42
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



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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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17 Oct 2019, 21:43
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 Posted from my mobile device
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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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17 Oct 2019, 21:53
Together time = x 2/A + 3/B = 1/x 2/5 + 3/7 = 1/x 29/35 =1/x x = 35/29 OA:D Posted from my mobile device
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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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17 Oct 2019, 21:54
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



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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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17 Oct 2019, 22:17
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
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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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17 Oct 2019, 22:55
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 IMO Answer D.
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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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18 Oct 2019, 01:04
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



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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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18 Oct 2019, 01:37
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



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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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18 Oct 2019, 02:03
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.



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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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18 Oct 2019, 06:36
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 Answer (D)



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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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18 Oct 2019, 13:14
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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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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18 Oct 2019, 22:04
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)=12/35rate 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



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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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18 Oct 2019, 22:15
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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Re: A type A machine can complete a job in 5 hours and a type B machine ca
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