From the two conditions,
Mutton increase 30%, while Beef decrease 30%, a net increase of 0.3kg,
therefore
for every 10% increment of mutton, and 10% decrease of Beef,the net increment is 0.1kg

40% mutton and 60% beef, is actually a 20% increase for mutton and a 20% decrease for beef from the 1st condition, hence the net increase is 0.2kg.

4.2 + 0.2 = 4.4kg##

Let the mass of the mutton be x and the mass of the beef be y. 

0.2 x + 0.8 y = 4.2 => x + 4y = 21

0.5 x + 0.5 y = 4.5 => x + y = 9

Using simultaneous equation,

x = 5, y = 4

To find the mass of 40% mutton and 60% beef,

0.4x + 0.6y = 0.4(5) x 0.6(4) = 2 + 2.4 = 4.4kg.