P completes 80% of a certain work in 20 days. Then with the help of Q, he is able to finish it in 3 more days. How many days will Q take to finish the work, if he works alone?

let the total work be 100

$$ work done = efficiency \times time $$

P completes 80% of a certain work in 20 days

80% of work done = $$ 100 \times \frac{80}{100} = 80 $$

so work done by P = 80

efficiency of P = $$ \frac{80}{20} = 4 $$

remaining work = 100 - 80 = 20

with the help of Q, P finish the remaining works in 3 days

$$ 20 = (4 + efficiency of Q ) \times 3 $$

$$ efficiency of Q = \frac{20}{3} - 4 = \frac{8}{3} $$

time taken by Q to complete the work

$$ t = \frac{300}{8} = 37.5 $$