Father reduced the quantity of food bought for the family by 10% when he found that the cost of living had increased 15%. Thus the fractional increase in the family food bill is now

A.
(frac{1}{12}) 
B.
(frac{6}{35}) 
C.
(frac{19}{300}) 
D.
(frac{7}{200}) 
E.
(frac{5}{100})
Correct Answer: Option D
Explanation
Let the cost of living = y.
The new cost of living = (y + frac{15y}{100} = 1.15y)
The food bill now = ((1 – frac{90}{100})(1.15y))
= (1.035y)
The fractional increase in food bill = ((1.035 – 1) times 100% = 3.5%)
= (frac{35}{1000} = frac{7}{200})