A and B together can finish a piece of work in 10 days. B and C together can finish it in 15 days. A and C together can finish it in 18 days. In how many days will A, B and C finish it together?

Correct option is C

Given:

A and B together can finish the work in 10 days.

B and C together can finish the work in 15 days.

A and C together can finish the work in 18 days.

Solution:

Let the total work = 1 unit.

Let A’s 1-day work = A
Let B’s 1-day work = B
Let C’s 1-day work = C
From given conditions:
A + B = $$\frac{1}{10}$$​​

B + C = $$\frac{1}{15}$$​

A + C =$$\frac{1}{18}$$​​
Add all three equations:
(A + B) + (B + C) + (A + C)$$= \frac{1}{10} + \frac{1}{15} + \frac{1}{18}$$​​

​$$2A + 2B + 2C = \frac{9 + 6 + 5}{90} = \frac{20}{90} = \frac{2}{9}$$​​
A + B + C =$$\frac{1}{9}$$​​
Time taken by A, B, and C together:
​$$\text{Time} = \frac{1}{A + B + C} = \frac{1}{\frac{1}{9}} = 9 \text{ days}$$​​

Alternate Method:

Work done by (A + B + C) = $$2\times\frac {90}{20} =9$$

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