P can finish a work in 19 days. He start doing the work and after 7 days Q joined him. If both of them together completed the remaining work in \(\frac{20}{19}\) days, then in how many days can Q alone finish \(\frac{13}{19}\) of the same work?
Answer & explanation
Correct answer: option 1
Let total work = 19
P can do it in 19 days, therefore,
Efficiency of P = 1 w/d
Work done by P in 7 days = 7
Remaining work = 19 - 7 = 12
Remaining work done by P + Q in \(\frac{20}{19}\) days
Efficiency of P + Q = \(\frac{12}{\frac{20}{19}}\) = \(\frac{57}{5}\)
Efficiency of Q = \(\frac{57}{5}\) - 1 = \(\frac{52}{5}\)
Q will do \(\frac{13}{19}\) work in = 19 × \(\frac{13}{19}\) × \(\frac{5}{52}\) = \(\frac{5}{4}\) days