Two machines A and B work at constant rates which are in the ratio of 1:2 respectively. If the two machines work together, they can complete 1/3rd of a job in 3 hours. If machine A starts working on the job and works alone for 18 hours, how many hours would machine B working alone take to complete the remaining work?a)3.5b)4c)4.5d)5e)5.5Correct answer is option 'C'. Can you explain this answer?

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Two machines A and B work at constant rates which are in the ratio of 1:2 respectively. If the two machines work together, they can complete 1/3rd of a job in 3 hours. If machine A starts working on the job and works alone for 18 hours, how many hours would machine B working alone take to complete the remaining work?

a)
3.5
b)
4
c)
4.5
d)
5
e)
5.5

Correct answer is option 'C'. Can you explain this answer?

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Test: Time And Work- 2

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Two machines A and B work at constant rates which are in the ratio of ...

Given:

Let the rate of machine A be x units of work per hour
- Therefore the rate of machine B = 2x units of ork per hour
Let the total amount of work to be done be W units
- Time taken by machines A and B working together to complete
Machine A works alone for 18 hours

To Find: Time taken by machine B to complete the remaining work

Approach:

We know that Work = Rate * Time

c. So, to find the time taken, we either need to find the amount of remaining work and the rate of machine B or the ratio of

2. For finding the remaining work, we need to find the amount of work done by machine A in 18 hours

Remaining work = W – work done by machine A in 18 hours
Work done by machine A in 18 hours = Rate of machine A * 18
- As, rate of machine A is in terms of x, work done by machine A in 18 hours can be expressed in terms of x
Remaining work = W – work done by machine A in 18 hours
- This will be an expression in terms of W and x. As the rate of machine B is in terms of x, we need to express W also in

3. We are given that machines A and B working together take 3 hours to complete W/3 units of work.

We will use the above relation to express W in terms of x

Working out:

Machines A and B working together take 3 hours to complete W/3 units of work

2. Amount of work done by machine A working alone for 18 hours = x * 18 = 18x

3. Remaining work = W – 18x = 27x – 18x = 9x
4. Amount of time taken by machine B to complete the remaining work =

Answer : C

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