Question

A,B and C can do a work in 16 days, 12 4/5 days and 32 days respectively. they started the work together but after 4 days A left .B left the work 3 days before the completion of the work. in how many days was the work completed​

Answer 1

Solution :-

→ LCM of 16 , (64/5) & 32 = 64 units = Let Total work.

So,

→ Efficiency of A = (Total work) / (Total No. of Days.) = (64/16) = 4 units/day.

Similarly,

→ Efficiency of B = (Total work) / (Total No. of Days.) = 64/(64/5) = 5 units/day.

Similarly,

→ Efficiency of C = (Total work) / (Total No. of Days.) = (64/32) = 2 units/day.

then,

→ Efficiency of (A + B + C) = 4 + 5 + 2 = 11 units / day.

so,

→ in first 4 days (A + B + C) completed = 4 * 11 = 44 units of work .

then,

→ Left work to be done = Total work - completed in 4 days = 64 - 44 = 20 units.

Now, Statement :-

• After 4 days A left the work.
• 3 days before the completion of the work B left .

Conclusion :-

• we can conclude that, for last 3 days only C works alone .

so,

→ in last 3 days C done = 3 * 2 = 6 units of work.

therefore,

→ Left work now = 20 - 6 = 14 units.

we can say that, this left work was done by (B + C) .

so,

→ Time taken by (B + C) = 14/(5 + 2) = 14/7 = 2 days.

hence,

→ Total time taken to complete whole work = 4(A + B + C) + 2(B + C) + 3(C) = 4 + 2 + 3 = 9 days. (Ans.)

∴ The work was completed in 9 days.

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