A and B together can do a work in 9 days. B and C can finish the same work in \(\frac{90}{7}\) days. A started the work and worked for 3 days. B and C continued for 9 days. Then the diffference of days in which C and A can complete the job is?

5 days

(B+ C)'s 9 days work = 9 × 7 = 63

Remaining work = 90 - 63 = 27

This was done by A in 3 days

Efficiency of A = \(\frac{27}{3}\) = 9 unit/day

A + B = 10 (eff)

B's efficiency = 10 - 9 = 1 unit/day

B + C = 7 unit/day

C's efficiency = 7 - 1 = 6 unit/day

C will take = \(\frac{90}{6}\) = 15 days to finish the work

A will take = \(\frac{90}{9}\) = 10 days to finish the work

Diff = C - A = 15 - 10 = 5 days