Multiple choice

Two numbers are in the ratio $17:45$. One third of the smaller is less than $\displaystyle \frac{1}{5}$ of the bigger by 15. The smaller no is

  1. $\displaystyle 25\frac{12}{2}$
  2. $\displaystyle 67\frac{12}{2}$
  3. $\displaystyle 76\frac{1}{2}$
  4. $\displaystyle 86\frac{1}{2}$
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C Correct answer
Explanation

Let the numbers be 17k and 45k. The condition gives 45k/5 - 17k/3 = 15, so k = 4.5. The smaller number is therefore 17 × 4.5 = 76.5, or 76 1/2.

AI explanation

Let the smaller and bigger numbers be 17x and 45x. Based on the problem, one third of the smaller number is less than one fifth of the bigger number by 15, which gives the equation (45x / 5) - (17x / 3) = 15. Multiplying by 15 to clear the fractions results in 135x - 85x = 225, simplifying to 50x = 225, so x = 4.5. The smaller number is 17x, which is 17 * 4.5, equaling 76.5 or 76 and a half.

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