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: 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 = \((1.035 - 1) \times 100% = 3.5%\) = \(\frac{35}{1000} = \frac{7}{200}\)
