Multiple choice

There are 14 members in a yoga training centre. Four members of it leave and 6 new members join the centre. As a result, the average age of the members of the centre decreases by 5 years and the sum of all members also decreases by 20 years. What is the new average age of the members?

  1. 28 years

  2. 27 years

  3. 25 years

  4. 29 years

  5. 24 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let S be the initial sum of ages. Initial average = S/14. New sum = S - 20. New number of members = 14 - 4 + 6 = 16. New average = (S-20)/16. Given S/14 - (S-20)/16 = 5. 16S - 14(S-20) = 5 * 14 * 16 = 1120. 2S + 280 = 1120 => 2S = 840 => S = 420. New average = (420-20)/16 = 400/16 = 25.

AI explanation

Let the initial average age be A, so the original sum of the ages of the 14 members is 14 multiplied by A. The new sum of the ages after 4 members leave and 6 join is 16 multiplied by (A - 5), which expands to 16A minus 80; the problem also states this new sum equals the original sum minus 20, giving us the equation 14A minus 20 equals 16A minus 80. Solving for A gives an original average age of 30 years, so the new average age is 30 minus 5, resulting in 25 years.

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