A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

### Concept & Fractional Work To find the remaining work, calculate the total work completed by adding the individuals' one-day work capacities, multiplying by the number of days worked, and subtracting from 1 (the whole work). $$ \text{Work Left} = 1 - (\text{Combined 1-day work} \times \text{Days worked}) $$ ### Step-by-Step Solution * **Given:** A's time = 15 days, B's time = 20 days. They work together for 4 days. * **Calculation:** Find the 1-day work for each. * A's 1-day work = $1/15$ * B's 1-day work = $1/20$ * (A + B)'s 1-day work = $1/15 + 1/20$ * Find a common denominator, which is 60: $(4 + 3)/60 = 7/60$ * So, A and B complete $7/60$ of the work in 1 day. * Work done by them in 4 days = $4 \times (7/60) = 28/60 = 7/15$. * The fraction of the work left = Total work - Work completed. * Work left = $1 - (7/15) = (15 - 7)/15 = 8/15$. ### Exam Strategy & Shortcut Use the LCM method (Total Work Method). LCM of 15 and 20 is 60. Let total work be 60 units. A's efficiency = $60/15 = 4$ units/day. B's efficiency = $60/20 = 3$ units/day. Total efficiency = 7 units/day. Work done in 4 days = $7 \times 4 = 28$ units. Remaining work = $60 - 28 = 32$ units. Fraction left = Remaining Work / Total Work = $32/60 = 8/15$. ### Common Pitfall Students often calculate the work completed ($7/15$) and mistakenly select it as the answer, forgetting the final step of subtracting it from 1 to find the work *left*. Always read the final requirement of the prompt carefully. ### Final Answer Therefore, the correct answer is **$\frac{8}{15}$**.