A completes \(\displaystyle\frac{7}{20}\) of a work in 10 days. Then he completes the remaining work with the help of B in 5 days. The time required for A and B together to complete the entire work is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{100}{13}\) days
The question asks for the time A and B together take, so find the part of the work A and B do together in one day; the whole work then takes 1 divided by that part.
Work left after A’s 10 days \(=1-\displaystyle\frac{7}{20}=\frac{13}{20}\)
A and B together do \(\displaystyle\frac{13}{20}\) in 5 days, so in one day they do \(\displaystyle\frac{13}{20}\div5=\frac{13}{100}\)
Time for the whole work together \(=1\div\displaystyle\frac{13}{100}=\frac{100}{13}\) days