Question

A+B can do a work in 10 days , B+C can can do it in 12 days , A+C can do it in 15 days. All 3 work for 6 days and A leaves. In how many days will be B+C finish it working together?Solve it step by step ​

Answer 1

A+B can do a work in 10 days

B+C can can do it in 12 days

A+C can do it in 15 days

Take the LCM of 10, 12 ,15 which is 60.

So , the total unit of work is 60 units

A+B can do 60 / 10 = 6 units per day ---- eq. 1

B+C can do 60 / 12 = 5 units per day ---- eq. 2

A+C can do 60 / 15 = 4 units per day ---- eq. 3

Add all the eq.s

A+B+B+C+A+C = 6 + 5 + 4

2A + 2B + 2C = 15

2 ( A + B + C ) = 15

A + B + C = 7.5 units

Now all 3 work for 6 days so , 7.5 × 6 = 45 units

Now remaining = 60 - 45 = 15 units

Now A leaves

B + C = 5 units per day

So , 15 / 5 = 3 days

So, B + C finishes work in 3 days

Total work completed in 6 days + 3 days.

So the correct answer is 3 days.

Hope it helps....