A and B can finish a work in 12 days, B and C can finish the same work in 18 days and A and C can finish the same work in 15 days, then find the time taken by A, B and C to complete the whole work together.?

Question

A and B can finish a work in 12 days, B and C can finish the same work in 18 days and A and C can finish the same work in 15 days, then find the time taken by A, B and C to complete the whole work together.?

360 days
360/37 days
120 days
240/37 days

LohaHridoy

6 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : 360/37 days

Given:

Time to complete the whole work by A and B together = 12 days

Time to complete the whole work by B and C together = 18 days

Time to complete the whole work by A and C together = 15 days

Formula used:

Efficiency = Work Done/Time taken

Calculations:

Let the total work be LCM of 12,18, 15 i.e. 180 units.

Let efficiency of A, B and C be A, B and C respectively.

Efficiency of A and B together,

⇒ A + B = 180/12 = 15 units/day ----(i)

Efficiency of B and C together,

⇒ B + C = 180/18 = 10 units/day ----(ii)

Efficiency of A and C together,

⇒ A + C = 180/15 = 12 units/day ----(iii)

Adding equation (i), (ii) and (iii), we get,

(A + B) + (B + C) + (A + C) = 15 + 10 + 12

⇒ 2A + 2B + 2C = 37

⇒ A + B + C = 37/2 units/day

Time taken by A, B and C to complete the whole work together = 180/(37/2)

⇒ 360/37 days

∴ The time taken by A, B and C to complete the whole work together = 360/37 days