Multiple choice

A man spends $80$% of his income in expenditure, with the increase in the cost of living his expenditure increases by $\displaystyle 37\frac{1}{2}$ and his income increases by $\displaystyle 16\frac{2}{3}$, then the present percent saving is

  1. $\displaystyle 1\frac{2}{3}$
  2. $\displaystyle 7\frac{6}{5}$
  3. $\displaystyle 5\frac{5}{7}$
  4. $\displaystyle 9\frac{3}{11}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let Income = 100, Expenditure = 80, Saving = 20. New Expenditure = 80 * (1 + 3/8) = 80 * 11/8 = 110. New Income = 100 * (1 + 1/6) = 100 * 7/6 = 700/6 = 116.66. New Saving = 116.66 - 110 = 6.66. Percent saving = (6.66 / 116.66) * 100 = (40/6) / (700/6) * 100 = 40/700 * 100 = 40/7 = 5 5/7%.

AI explanation

Let the initial income be 100, so the expenditure is 80 and the saving is 20. The expenditure increases by 37 and a half percent, making the new expenditure 80 multiplied by 1.375, which is 110. The income increases by 16 and two-thirds percent, making the new income 100 multiplied by 7 divided by 6, which is 116 and two-thirds. The new saving is 116 and two-thirds minus 110, equaling 6 and two-thirds. The present percentage of saving is 6 and two-thirds divided by 116 and two-thirds multiplied by 100, resulting in 5 and five-sevenths percent.

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