A can do a certain work in 15 days. B is 25% more efficient than A. Both worked together for 4 days. C alone completed the remaining work in 8 days. A, B and C together will complete the same work in ?

5 days

A = 15 days,

B is 25% more efficient than A i.e;

                  A   :   B

Efficiency    100 :  125

                  4   :   5

⇒ Total work = Efficiency of A x Days to complete the work = 4 x 15 = 60 units.

⇒ A + B worked for 4 days = (5 + 4) x 4 = 36 units.

⇒ Remaining work = 60 -36 = 24, is completed by C in 8 days. 

⇒ Therefore Efficiency of C = \(\frac{24}{8}\) = 3.

⇒ Time taken by complete the total work together = \(\frac{60}{4 + 5+ 3}\) = \(\frac{60}{12}\) = 5 days.