P and Q completed a work together and were paid ₹1,080 and ₹1,440, respectively. If P can do the entire work in 20 days, how many days did they take to complete the work together?

$8\frac{4}{7}$

Calculations,

                    P     :    Q

                  1080 : 1440

Efficiency      9     :    12

                   3      :    4

⇒ As given, Q can complete the total work in 20 days,

Therefore, 3 x 20 = 60 units        ..(Efficiency × Days = Total work) 

⇒ Time taken to complete the work together = \(\frac{60}{3 + 4}\) = \(\frac{60}{7}\) = \( { 8}_{ 7}^{4 } \) days.