Q) A can finish a work in 24 days, B in 9 days and C in 12 days. B and C start the work but are forced to leave after 3 days. The remaining work was done by A in:

a) 5 days                     b) 6 days             c) 10 days                     d) 11 days

Ans:

A’s 1 day work = 1/24

B’s 1 day work = 1/9

C’s 1 day work = 1/12

∴ (A + B + C)’s 1 day work = 1/24 + 1/9 + 1/12 = 17/72

∴ (B + C)’s 1 day work = 1/9 + 1/12 = 14/72

∴ (B + C)’s 3 day work = 3 x 14/72 = 7/12

∴ Balance work = 5/12

Time taken by A to complete 1/24 work = 1 day

∴ Time taken by A to complete 5/12 work = 1 x (5/12)/ (1/24) = 10 days

Hence, Answer is [C].

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