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Father reduced the quantity of food bought for the family by 10% when he found…

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})