A and b together can do a work in 14 days, which b and c together can do in 16 days. After a has been working for 6 days and b for 8 days, c finishes it in 10 days. In how many days, c alone will do the work?
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Let’s solve this question arithmetically :
As A and B can finish the work in 12 days time, hence
(A + B)’s one day’s work = 1/12;
similarly
(B + C)’s one day’s work = 1/16
Now, A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1
A’s 5 days’ work + B’s 5 days’ work + B’s 2 days’ work + C’s 2 days’ work + C’s 11 days’ work = 1
Or {(A + B)’s 5 days’ work} + {(B + C)’s 2 days’ work} + C’s 11 days’ work = 1
i.e. 5/12 + 2/16 + C’s 11 days’ work = 1
or C’s 11 days’ work = 1 - (5/12 + 2/16)
or C’s 11 days’ work = 1 - 13/24
or C’s 11 days’ work = 11/24
or C’s 1 day’s work = 11/24 x 1/11 = 1/24
Therefore, C alone can finish the complete work in 24 days.
As A and B can finish the work in 12 days time, hence
(A + B)’s one day’s work = 1/12;
similarly
(B + C)’s one day’s work = 1/16
Now, A’s 5 days’ work + B’s 7 days’ work + C’s 13 days’ work = 1
A’s 5 days’ work + B’s 5 days’ work + B’s 2 days’ work + C’s 2 days’ work + C’s 11 days’ work = 1
Or {(A + B)’s 5 days’ work} + {(B + C)’s 2 days’ work} + C’s 11 days’ work = 1
i.e. 5/12 + 2/16 + C’s 11 days’ work = 1
or C’s 11 days’ work = 1 - (5/12 + 2/16)
or C’s 11 days’ work = 1 - 13/24
or C’s 11 days’ work = 11/24
or C’s 1 day’s work = 11/24 x 1/11 = 1/24
Therefore, C alone can finish the complete work in 24 days.
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