Work done by rajan in 1 day = x = 1/24
Work done by amit in 1 day = y = 1/30
So, work done by both of them in 1 day = x+y = 54/120 = 3/40
Total work done in x days by both of them = 1.
Thus, (x)(3/40)=1 i.e. x=40/3 =13.3333
So, if both of them work together it will take 13.3333 days for them to complete work.