I approached this question by equating the weighted average of duration of assets & liabilites.
Since liability has a duration of 4 years. I took the current wt in the portfolio then determined the remaining funds in hand (69,640,000- current value of already invested govt. bonds) so 15,268,200 was the amount left to invested in bonds in question i.e. weight of 21.93%*.
I found the modified duration of bond A & B which was 1.94 & 7.06 (as calculated in guidelines answer) & as per their weight found out the Wt duration of govt bonds
= 1.94 x 35.26% (weight of A) + 7.06 x 42.81 (weight of B)
= 3.70 so only 0.30 was left to be immunized.
Only Bond X which has a Mod duration of 1.33 can give me weighted avg duration of = 0.29 (1.33 x 21.93%*)
Ok now the guidelines approached this question was equating the dollar duration. However the ans was same i.e choosing Bond X.
MY QUES: Was my approach right & shall i receive credits?