Multiple choice

If $177$ is divided into $3$ parts in the ratio $\dfrac {1}{2} : \dfrac {2}{3} : \dfrac {4}{5}$, then the second part is

  1. $75$
  2. $45$
  3. $72$
  4. $60$
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D Correct answer
Explanation

Convert ratios to a common denominator: 1/2 : 2/3 : 4/5 = 15/30 : 20/30 : 24/30. The ratio is 15:20:24. The sum of parts is 15+20+24 = 59. Each part is 177/59 = 3. The second part is 20 * 3 = 60.

AI explanation

Multiply the given fractional ratio by the least common multiple of the denominators 2, 3, and 5, which is 30, to get the simplified whole number ratio of 15 : 20 : 24. The sum of these parts is 59. To find the second part, calculate 20 divided by 59, multiplied by the total of 177. This equals 20 multiplied by 3, resulting in 60.

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