Question

A and B together can complete a piece of work in 18 days, B and C in 24 days and A and C in 36 days. In how many days, will all of them together complete the work?
A. 10 days
B. 12 days
C. 15 days
D. 16 days

Answer 1

Answer:

Step-by-step explanation:

Let X be the total amount of work ,

given ,

X = 18(A+B) = 18A +18B ,

X = 24(B+C) = 24B + 24C ,

X=36(A+C) = 36A+36C ,

therefore 18A+18B = 24B+24C = 36A + 36C ,

So 18A = 6B +24C or A = B/3 + 4C/3 from the first 2 equations ,

substituting for A in the second and third equations ,

24B +24C = 36(B/3 +4C/3) +36C ,

24B +24C = 12 B +48C + 36C ,

24B +24C = 12 B+ 84C which simplifies to ,

12B = 60C or B = 5C ,

and thus from the first equation ,

A = B/3 + 4C/3 = 5C/3 +4C/3 = 9C/3 = 3 C ,

so substituting back into X = 18(A + B) ,

X = 18(3C +5 C) = 18(8C) = 144C ,

C needs 144 days to complete the task alone.

Hope it helps you.

Answer 2

Answer:

The answer is option (D) 16 days