# Arun & Bijay can make paintings in 3 days, Bijay & Chandan can make those paintings in 5 days. If Arun, Bijay & Chandan together can finish the work i

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Arun & Bijay can make paintings in 3 days, Bijay & Chandan can make those paintings in 5 days. If Arun, Bijay & Chandan together can finish the work in 2 days, then Arun & Chandan together will do it in _____ days.
1. 4/3 days
2. 8.7 days
3. 15/7 days
4. 5 days

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Correct Answer - Option 3 : 15/7 days

Given:

Time to complete the whole work by Arun and Bijay together = 3 days

Time to complete the whole work by Bijay and Chandan together = 5 days

Time to complete the whole work by Arun, Bijay and Chandan together = 2 days

Formula used:

Efficiency = Work Done/Time taken

Calculations:

Let the total work be LCM of 3, 5, 2 i.e. 30 units.

Let efficiency of Arun, Bijay and Chandan be A, B and C respectively.

Efficiency of A and B together,

⇒ A + B = 30/3 = 10 units/day      ----(i)

Efficiency of Bijay and Chandan together,

⇒ B + C = 30/5 = 6 units/day      ----(ii)

Efficiency of Arun, Bijay and Chandan together,

⇒ A + B + C = 30/2 = 15 units/day      ----(iii)

⇒ 10 + C = 15

⇒ C = 5 units/day

B + C = 30/5 = 6 units/day

⇒ B = 6 - 5 = 1 unit/day

A + B = 30/3 = 10 units/day

⇒ A = 10 - 1 = 9 units/day

Efficiency of Arun and Chandan together,

⇒ A + C = 9 + 5

⇒ A + C = 14 units/day

Time taken by Arun and Chandan = 30/14

⇒ 15/7 days

Arun & Chandan together will do it in 15/7 days.