Question

A can do a piece of work in 10 days and B can do a work in 20 days. After 4 days B left and C joins. Then A and C work together in 2 days. In how many days C alone can do the work?

• A. 12 days
• B. 15 days
• C. 10 days
• D. 20 days

Hint:

When multiple people are working together, use their individual work rates and the total work completed to find the time taken for the remaining work.

Answer 1

The Correct Option is C

Let the total work be represented by 1 unit. - A can do the work in 10 days, so A's work rate is \( \frac{1}{10} \) per day. - B can do the work in 20 days, so B's work rate is \( \frac{1}{20} \) per day. In the first 4 days, A and B work together: \[ \text{Work done by A and B in 4 days} = 4 \left( \frac{1}{10} + \frac{1}{20} \right) = 4 \times \frac{3}{20} = \frac{12}{20} = \frac{3}{5} \] So, after 4 days, \( \frac{3}{5} \) of the work is completed, and \( \frac{2}{5} \) of the work remains. Now, A and C work together for the remaining \( \frac{2}{5} \) of the work. Let C's work rate be \( \frac{1}{x} \), where \( x \) is the number of days C alone can complete the work. In 2 days, A and C together complete the remaining \( \frac{2}{5} \) of the work: \[ 2 \left( \frac{1}{10} + \frac{1}{x} \right) = \frac{2}{5} \] Simplifying: \[ \frac{2}{10} + \frac{2}{x} = \frac{2}{5} \] \[ \frac{1}{5} + \frac{2}{x} = \frac{2}{5} \] \[ \frac{2}{x} = \frac{1}{5} \] \[ x = 10 \] Thus, C alone can do the work in \( \boxed{10} \) days.