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 is D

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 = \((1.035 - 1) \times 100% = 3.5%\)

= \(\frac{35}{1000} = \frac{7}{200}\)