Discussion of Question with ID = 089 under Time-and-Work

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Question

A, B and C can independently complete a work in 5, 15 and 16 days respectively. First C starts the work, then A joined after 7 days, and B after 6 days. In how many days was the work completed?

A

\$8{40/79}\$ days.

B

\$9{40/79}\$ days.

C

\$10{40/79}\$ days.

D

\$11{40/79}\$ days.

Soln.
Ans: a

Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A joins after n days, and B joins after m days, the work is completed in \${xyz}/{xy + yz + zx}\$ × \$(1 + n/x + m/y)\$ days. Putting the various values x = 5, y = 15, z = 16, n = 7, m = 6, and simplifying, we get \${672/79}\$, which is same as: \$8{40/79}\$.