A force produces an acceleration of 4 in a body of mass m1 and the same force produces an acceleration of 6 in another body of mass m2 if the same force is applied to m1+m2 then the acceleration will be

We know that the force applied separately on both the masses is equal. The force on first body of mass m1, F= ma = 4m1. And on the second body, F= ma= 6m2. Now, 4m1=6m2 so, m2= 2/3m1. Now, force on second body was 6m2 so, 6m2= 6* (2/3m1) = 4m1. Now, when the same force is applied on the two bodies together, Mass= m1+m2= m1 + 2/3m1 = 5/3m1 and Force= 4m1 Using a= F/m, a= 4m1/(5/3m1) = 2.4 m/s^2.