A can do a work in 80 days He works at it for 10 days and then B alone - Maths - Direct and Inverse Proportions

Question

A can do a work in 80 days He works at it for 10 days and then B
alone finishes the remaining work in 42 days In how many days will
the work be completed if both work together?

Shridhar Kaushik · Accepted Answer

Given that:â€“ A can do a work in 80 days $S o, w ork of A in 1 day = \frac{1}{80} ∴ Work of A in 10 days = \frac{10}{80} = \frac{1}{8}$ i e , $\frac{1}{8}$ th part of a work has been finished by A in 10 days Now, remaining $(1 - \frac{1}{8})^{th} i e {(\frac{7}{2})}^{th}$ part of a work is done by B in 42 days $∴ B can complete the work in \frac{42}{(\frac{7}{8})} days = \frac{42}{7} \times 8 days = 48 days ∴ Work of B in 1 day = \frac{1}{48}$ If both A and B work together, then total work of A and B in 1 day = ( work of A in 1 day) + (work of B in 1 day) $= \frac{1}{80} + \frac{1}{48} = \frac{48 + 80}{80 \times 48} = \frac{128}{80 \times 48} = \frac{1}{30}$ Hence, A and B can complete the work in 30 days if they work together

A can do a work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days will the work be completed if both work together?