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Two spinning machines A and B can together produce 3,00,000 m of cloth

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Bunuel
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Two spinning machines A and B can together produce 3,00,000 m of cloth [#permalink] New post   03 Dec 2020, 07:00
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Two spinning machines A and B can together produce 3,00,000 m of cloth in 10 hour, if machine B alone can produce the same amount of cloth in 15 hour, then how much cloth can machine A produce alone in 10 hour?

A. 2,00,000 m

B. 1,00,000 m

C. 1,50,000 m

D. 50,000 m

E. 40,000 m
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B
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Re: Two spinning machines A and B can together produce 3,00,000 m of cloth [#permalink] New post   03 Dec 2020, 23:17
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Bunuel wrote:
Two spinning machines A and B can together produce 3,00,000 m of cloth in 10 hour, if machine B alone can produce the same amount of cloth in 15 hour, then how much cloth can machine A produce alone in 10 hour?

A. 2,00,000 m

B. 1,00,000 m

C. 1,50,000 m

D. 50,000 m

E. 40,000 m


A and B can produce 3,00,000 m in 10 hour.
B can produce 3,00,000 m in 15hr, or B can produce \(10*\frac{300000}{15}=200000\) in 10 hrs.
So, remaining \(300000-200000\) or \(100000\)m is produced in 10 hrs by A

B
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Re: Two spinning machines A and B can together produce 3,00,000 m of cloth [#permalink] New post   04 Dec 2020, 01:35
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Bunuel wrote:
Two spinning machines A and B can together produce 3,00,000 m of cloth in 10 hour, if machine B alone can produce the same amount of cloth in 15 hour, then how much cloth can machine A produce alone in 10 hour?

A. 2,00,000 m

B. 1,00,000 m

C. 1,50,000 m

D. 50,000 m

E. 40,000 m



Efficiency(A+B) = 3,00,000/10 = 30,000

Efficiency(B) = 3,00,000/15 = 20,000

Efficiency(A) = 30000 - 20000 = 10,000

A in 10 hrs = 10000*10 = 1,00,000

B
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Re: Two spinning machines A and B can together produce 3,00,000 m of cloth [#permalink] New post   14 Jul 2021, 07:17
My method of solving work rate problem is going by unitary method (this is somewhat parallel to efficiency calculation method)

A+B produce in 10hrs
B produce in 15hrs
Total units of work = LCM(B,A+B) = 30
Rate of work done by A+B = 30/10 = 3
Rate of work done by B alone = 30/15 = 2

Rate of A + Rate of B = Rate of A+B
x + 2 = 3
Therefore rate of A is 1. This implies efficiency of A is 1/3rd the efficiency of A+B.

So if A+B produces 3,00,000 in 10hrs, A alone will produce 1/3 of it, which is 1,00,000.

Hence the answer is Option B
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Re: Two spinning machines A and B can together produce 3,00,000 m of cloth [#permalink] New post   14 Jul 2021, 07:28
A and B together take 10hrs
(1/A) + (1/B) = (1/10)
(1/B) = (1/15)
(1/A) = (1/10) - (1/15)
(1/A) = (15-10)/150 = 5/150 = 1/30
A alone can do the work in 30 hours
So in 10 hrs i.e 1/3(30), it will be able to do 1/3rd of work
1/3(300000) = 100000

The ans IMO: B

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Re: Two spinning machines A and B can together produce 3,00,000 m of cloth [#permalink]
14 Jul 2021, 07:28
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