Here’s and example of a SMART MATH problem for RATIO PROPORTION.
Problem
After the death of his grandfather, a man bequeathed 20% of the property, his father 25% of the remaining, his aunt 1/3rd of the remaining and 60% of the balance came to the man’s wife. If the man’s wife received $4000 more than her father-in-law, what was the total share of the man’s aunt?
- $35,000
- $25,000
- $30,000
- $40,000
- $20,000
The Usual Method
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Let $‘x’ be the total worth of grandfather’s property.
Hence share of the man = 0.2x
Balance =
Share of the man’s father =
Balance =
Share of the man’s aunt =
Balance =
Share of the man’s wife =
Difference in share of the man’s wife and his father = $4000
$100,000.
Hence share of the man’s aunt = Rs20,000
(Ans: 5)
Estimated Time to arrive at the answer = 45 seconds.
Using Technique
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Instead of taking the worth of property as ‘x’, take it as $100. Thus the shares now become:
Share of the man = $20
Share of the man’s father = (100 – 20) x 0.25 = $20
Share of the man’s aunt = (80 – 20) x 1/3 = $20
Share of the man’s wife = (60 – 20) x 0.6 = $24
Difference in share of the man’s wife and his father = 24 – 20 = $4.
But in reality it is $4000. Hence $20 (share of the man’s aunt) should correspond to $20,000 if $4 corresponds to $4000.
(Ans: 5)
Estimated Time to arrive at the answer = 30 seconds.
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