A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone ?

### Concept & Equation Formulation for Work When individuals work for different durations to complete a single job, formulate a linear equation based on their daily work rates. $$ \text{Work Done} = \text{Rate} \times \text{Time} $$ ### Step-by-Step Solution * **Given:** (A + B) take 30 days. Let A's 1 day work be $a$, B's be $b$. * $a + b = 1/30$. * A works for 16 days, B for 44 days to finish the work: $16a + 44b = 1$. * Rewrite as: $16a + 16b + 28b = 1$. * $16(a + b) + 28b = 1$. * Substitute $(a + b) = 1/30$: $16(1/30) + 28b = 1$. * $8/15 + 28b = 1$. * $28b = 1 - 8/15 = 7/15$. * $b = \frac{7}{15 \times 28} = 1/60$. * B completes the whole work in 60 days. ### Exam Strategy & Shortcut Notice the pattern: A and B both worked together effectively for 16 days. Work done = $16/30 = 8/15$. Remaining work = $7/15$. B does this $7/15$ work in the remaining $(44 - 16) = 28$ days. B's total time = $28 \times (15/7) = 60$ days. ### Common Pitfall Trying to solve for $a$ and $b$ using complex substitution instead of grouping the terms to utilize the known $(a+b)$ value. ### Final Answer Therefore, the correct answer is **60 days**.