book Maths Puzzle Numerical Ability

Let T be a linear operator in V. Prove that T^2 = 0 if and only if the range T is a subset of null T.

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book Other Question

Triangle ABC has area 240. Points X,Y,Z lie on sides AB,BC, and CA, respectively. Given that segment AX/BX=3, BY/CY=4, CZ/AZ=5, find the area of triangle XYZ. How many pounds of chocolates costing $4.60 per pound may be mixed with 6 lb of chocolates costing $5 per pound to produce a mixture that can be sold for $4.90 per pound?