Multiple choice

The average age of a class of 35 students is 15 years. If the teacher's age is also included, the average age increases by one year. The average age of the teacher's family, having a wife and a son, is 40 years and the son's age is 80% less than his mother's age. Find the age of the teacher's wife.

  1. 57.5 years

  2. 50 years

  3. 47.5 years

  4. 55.5 years
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A Correct answer
Explanation

The total age of 35 students is 35 * 15 = 525. Including the teacher, the average becomes 16 for 36 people, so the teacher's age is (36 * 16) - 525 = 576 - 525 = 51. The family average is 40 for 3 people (teacher, wife, son), so their total age is 120. If the son is 80% less than the mother (M), son = 0.2M. Teacher + M + 0.2M = 120, so 51 + 1.2M = 120, 1.2M = 69, M = 57.5.

AI explanation

The total age of the 35 students is 35 multiplied by 15, which equals 525 years. When the teacher is added, the average becomes 16, making the combined age 36 multiplied by 16, or 576. The teacher's age is 576 minus 525, which is 51. The average age of the teacher's family of three is 40, so their total age is 120; subtracting the teacher's 51 years leaves 69 years for the wife and son. The son's age is 80 percent less than the mother's, meaning the son is 20 percent of the wife's age (W), so W plus 0.2W equals 69. This gives 1.2W equals 69, meaning the wife's age is 57.5 years.

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