Question

24) A takes twice as long as B and C together take to do a piece of work and B takes twice as
long as A and C together, however, the 3 men together can complete the work in 30 days.
How long will C alone take to do the work?
1) 45 days 2) 60 days
3) 75 days
4) 90 days​

Answer 1

Answer:

90 days

Step-by-step explanation:

let,

B+C TAKES x time to complete the work

hence

time taken by A to complete the work= 2x

also,

time taken by A+C to complete the work be y

hence,

time taken bye B to complete the work= 2y

we know that

efficiency ratio is inversely proportional to time ratio

hence

in first case

efficiency of A = 1 & B+C = 2

similarly

in second case

efficiency of B = 1 & A+C = 2

comparing these we get

efficiency of A+B+C+B+A+C= 1+2+1+2=6

Or

A+B+C = 6/2 = 3

But

given

they all can do the work in 30 days

as we know that

total work = efficiency × time taken

total work = 3 × 30 = 90 work

now we have efficiency of A+B+C = 3

& efficiency of A+B = 2

Hence

efficiency of C = 3-2 = 1

now

time taken by C to complete the work = 90/1 = 90 days (answer)