The GDP is sum total of the contributions from primary sector, secondary sector and the tertiary sector. If that be the case, then over 2004-05 to 2009-10, the share of tertiary sector at factor cost in GDP has increased from:

Value of the GDP from the tertiary sector in the year 2004-05 = 2971464 - 650454 - 744755 = 1576255

Hence, the share of tertiary sector at factor cost in GDP in the year 2004-05 = $$\dfrac{1576255}{2971464}\times 100$$ = 53.05 percent. 

Value of the GDP from the tertiary sector in the year 2009-10 = 6133230- 1243566 - 1499601 = 3390063

Hence, the share of tertiary sector at factor cost in GDP in the year 2009-10 = $$\dfrac{3390063}{6133230}\times 100$$ = 55.27 percent. 

We can see that the share of tertiary sector at factor cost in GDP increased from 53.05 percent to 55.27 percent. Therefore, option A is the correct answer.