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Averages Smart Math

[Smart Math] Averages Problem 14

Here’s and example of a SMART MATH problem for AVERAGES.

Averages

Problem

The average age of a couple married four years ago was 25 years then. The average age of the family consisting of husband, wife and a child now is 20 years. What is the child’s present age?

  1. less than 1 year old
  2. 1 year
  3. 2 years
  4. 3 years
  5. 4 years

The Usual Method

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Total age of couple 4 years ago = 25 x 2 = 50 years.

Present total age = 50 + 4 + 4 = 58 years.

Present total age of family = 20 x 3 = 60 years.

Hence age of child = 60 – 58 = 2 years.

(Ans: 3)

Estimated Time to arrive at the answer = 30 seconds.

Using Technique

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The average age of the couple 4 years ago = 25 years, then present average age = 25 + 4 = 29 years. Present average age of family = 20 years. Reduction of (29 – 20) 9 years is attributable to the child. Total reduction = 9 x 3 = 27 years (Since there are 3 members). Hence age of child = 29 – 27 = 2 years.

(Ans: 3)

Estimated Time to arrive at the answer = 15 seconds.
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