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C takes twice as long as B to complete a work. A takes three times as long as C to complete the same work. A, B and C start working together. A leaves 6 days before the completion of work and B leaves 3 days before the completion of work and C works for x days. If B alone can complete the same work in 16 days, then in how many days the work will be completed?

C takes twice as long as B to complete a work. A takes three times as long as C to complete the same work. A, B and C start working together. A leaves 6 days before the completion of work and B leaves 3 days before the completion of work and C works for x days. If B alone can complete the same work in 16 days, then in how many days the work will be completed? Correct Answer 12 <span style="color: rgb(37, 37, 37);">days</span>

Given:

Let time taken by C alone to complete the work be a days.

⇒ B alone can complete the work in = a/2 = 16

⇒ C alone can complete the work in = 32 days

⇒ A alone can complete the work in = 3a = 3 × 32 = 96 days

Calculation:

LCM of their work time = LCM(96, 16 and 32) = 96

⇒ A, B and C works for = 1 units per day, 6 units per day and 3 unites per day.

⇒ A + B + C = 1 + 6 + 3 = 10 units per day

⇒ B + C = 6 + 3 = 9 units per day

⇒ Work done in last 3 days = 3 × 3 = 9 units

⇒ Work done in last six days = 9 + 9 × 3 = 36 units

⇒ Remaining work after 6 days = 96 - 36 = 60 units

⇒ 60 units completed in = 60/10 = 6 days

⇒ Total days = 6 + 6 = 12 days

∴ Time required to complete work is 12 days.

 

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