A completes $\frac{7}{10}$ of a work in 15 days. Then he completes the remaining work with the help of B in 4 days. The time required for A and B together to complete the entire work is (S.S.C., 2005)

### Concept & Fractional Work Scaling If you know the time taken by a group of workers to complete a specific fraction of a job, you can find the time it takes them to complete the entire job by setting up a simple proportion or multiplying the time by the reciprocal of the work fraction. ### Step-by-Step Solution * **Given:** A completes $7/10$ of a work in 15 days. A and B together complete the remaining work in 4 days. * **Calculation:** First, determine what fraction of the work remains after A's solo portion. * Remaining work = $1 - 7/10 = 3/10$. * We are given that A and B working together can complete this $3/10$ fraction of the work in exactly 4 days. * To find the time required for A and B together to complete 1 entire work (the whole job), we scale the time up. * Let $T$ be the total time for A and B to do the whole work. * $(3/10) \times \text{Total Work} = 4 \text{ days}$ * $\text{Total Time } T = 4 \times (10 / 3) = 40 / 3$ days. * Converting the improper fraction to a mixed number: $40 / 3 = 13\frac{1}{3}$ days. ### Exam Strategy & Shortcut Recognize that the information about A taking 15 days is a distractor and not needed to solve the problem. Focus only on the final phase: A and B do $3/10$ of the work in 4 days. The time for the full work is simply $4 \times (10/3) = 40/3 = 13\frac{1}{3}$ days. ### Common Pitfall A common pitfall is getting bogged down trying to calculate A's individual efficiency from the first sentence, leading to unnecessary complex calculations with B's efficiency. ### Final Answer Therefore, the correct answer is **$13\frac{1}{3}$ days**.