Here’s and example of a SMART MATH problem for 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?
- less than 1 year old
- 1 year
- 2 years
- 3 years
- 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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