Question

A and B together can complete a task in 7 days. B alone can do it in 20 days. What part of the work was carried out by A? 
Statement I - A completed the job alone after A and B worked together for 5 days.
Statement II - Part of the work done by A could have been done by B and C together in 6 days.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both, statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

In work problems, calculate rates of work and use them to find the total work completed in various stages.

Answer 1

The Correct Option is A

From Statement I:
A and B together can complete the task in 7 days, so their combined rate of work is: \[ \frac{1}{7} { of the work per day}. \] B alone can do it in 20 days, so B’s rate of work is: \[ \frac{1}{20} { of the work per day}. \] Since A and B work together for 5 days, the amount of work completed by both A and B is: \[ 5 \times \left( \frac{1}{7} \right) = \frac{5}{7} \] The remaining work is: \[ 1 - \frac{5}{7} = \frac{2}{7}. \] A then completes the remaining work alone. The rate of work of A is: \[ \frac{1}{7} - \frac{1}{20} = \frac{20 - 7}{140} = \frac{13}{140}. \] The time A takes to complete the remaining work is: \[ \frac{2}{7} \div \frac{13}{140} = \frac{2}{7} \times \frac{140}{13} = \frac{280}{91} = \frac{20}{13} { days}. \] Thus, Statement I alone is sufficient to answer the question.