Working alone Typewriters A B C can do a certain typing job consisting of a large number of pages in...........

Quant (SSC) Time and work

Working alone, Typewriters A, B, C can do a certain typing job, consisting of a large number of pages, in 12, 15 and 18 hours, respectively. What is the ratio of the time it takes Typewriter A to do the job, working alone at its rate, to the time it takes Type writer B and C to do the job, working together at their individual rate?

4/11

1/2

15/22

22/15

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Explanation:

Since Typewriter B can do the job in 15 hours,
it can do 1/15 of the job in 1 hour
Since Typewriter C can do the job in 18 hours
it can do 1/18 of the job in 1 hour.
Together Typerwriters B and C can do
(1/15 + 1/18) = (6/90 + 5/90) = 11/90 of the job in 1 hour
Which means that it takes them = 90/11 hours
to complete the job. Since Typewriter A completes the job in 12 hours, the ratio of the time required for A to do the job to the time required for B and C working together to do the job is
12 /90/11 = 12(11)/90 = 2(11)/15 = 22/15