A can do a work in 8 days and B in 12 days. They work together for 3 days. What part of the work is left?
\(\dfrac{3}{8}\)
Step 1 – Individual rates of work (per day):
\(\text{A's rate} = \dfrac{1}{8}, \quad \text{B's rate} = \dfrac{1}{12}\)
Step 2 – Combined rate per day:
\(\dfrac{1}{8} + \dfrac{1}{12} = \dfrac{3 + 2}{24} = \dfrac{5}{24}\)
Step 3 – Work completed in 3 days together:
\(3 \times \dfrac{5}{24} = \dfrac{15}{24} = \dfrac{5}{8}\)
Step 4 – Work remaining:
\(1 - \dfrac{5}{8} = \dfrac{3}{8}\)
Hence the part of work left is \(\dfrac{3}{8}\).
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