A and B can do a piece of work in 12 days B and C in 15 days C and A in 20 days then that numbers of days taken by A B and C together to finish the work are?
- 20 days
- 10 days
- 14 days
- None of these
Explanation
A and B can do the work in 12 days, so their combined rate of work is 1/12 of the work per day.
B and C can do the work in 15 days, so their combined rate of work is 1/15 of the work per day.
C and A can do the work in 20 days, so their combined rate of work is 1/20 of the work per day.
Now, let's add the three equations and simplify:
2(A + B + C) = 1/12 + 1/15 + 1/20
Combine like terms:
2(A + B + C) = (10 + 8 + 6) / 120
Simplify the fraction:
2(A + B + C) = 24 / 120
Divide both sides by 2:
A + B + C = 12 / 120
Simplify the fraction:
A + B + C = 1/10
So, A, B, and C together can complete 1/10 of the work in one day.
To find the number of days taken by A, B, and C together to finish the work, we take the reciprocal:
Number of days = 1 / (1/10) = 10 days
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