B and C together can complete a work in 8 days, A and B together can complete the same work in 12 days, and A and C together can complete the same work in 16 days. In how many days can A, B and C together completes the work?Options3.6923076927.4166666673.4166666677.384615385
Question
B and C together can complete a work in 8 days, A and B together can complete the same work in 12 days, and A and C together can complete the same work in 16 days. In how many days can A, B and C together completes the work?Options3.6923076927.4166666673.4166666677.384615385
Solution
To solve this problem, we need to find the rates at which A, B, and C can complete the work individually, and then add them together to find the rate at which they can complete the work together.
Step 1: Find the rates of A, B, and C together
The rate of B and C together is 1 work/8 days = 0.125 work/day. The rate of A and B together is 1 work/12 days = 0.0833 work/day. The rate of A and C together is 1 work/16 days = 0.0625 work/day.
Step 2: Find the rates of A, B, and C individually
Let's denote the rates of A, B, and C as a, b, and c respectively. We have the following equations based on the rates we found in step 1:
b + c = 0.125 a + b = 0.0833 a + c = 0.0625
By adding all three equations together, we get 2a + 2b + 2c = 0.271. Dividing both sides by 2, we get a + b + c = 0.1355.
Step 3: Find the time it takes for A, B, and C to complete the work together
The time it takes for A, B, and C to complete the work together is 1 work / (a + b + c) = 1 work / 0.1355 = 7.3846 days.
So, the answer is 7.384615385 days.
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