Latest CAT Aptitude Question SOLUTION: Q. A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?.

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Q. A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it?.

Asked In CAT Leelanand Kumar Yalla (10 years ago)

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Siba Kumar Sahu  (10 years ago)

ans:

let there are 18 works.
together they take 18 days so per day they complete 1 work.
so their efficiency per day is 1 work.

now,
let B completes the work in x days
so efficiency of B per day is 18/x works.

as per question B will complete half of the work in 3/4 times x
i.e; A will complete 0.5*(18) works in 3x/4 time
so A will complete 9 works in 3x/4 time
now the amount of work done by A in x time is (9)*(4/3) = 12 works

so efficiency of A per day is 12/x

together their efficiency per day is 1 work
so we can write 18/x + 12/x =1
30/x = 1
x=30
we get time taken by B to complete the work to be 30 days.

hope you like my solution. pls give feed back

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Preeti Choudhary  (10 years ago)

efficiency of A:B=2:3
time taken to complete the work =18 hrs
so if capability of both dng the wrk is 2+3=5,5 wrk in an hour...........total work will be=18*5 i.e 90
A time taken to do the work alone is (90/2=45 days)
abd B takes time to do the work alone is (90/3=30 days)

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Siba Kumar Sahu  (10 years ago)

mr ankit kedia your 2nd line is wrong according to question because A will complete the half of work in (3/4)x time k.

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Ankit Kedia  (10 years ago)

Let B take x days to complete the work
SO A will complete the work in (3/4)x days
now A's one day work = 1/x
B's one day work = 4/3 x
A + B 's one day work = 1/x + 4/3x
= 7/3x
therefore 7/3x = 1/18
using simple calculation x = 18 * 7 / 3
= 42
So B will complete the work in 42 days

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