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Ratio Proportion Smart Math

[Smart Math] Ratio Proportion Problem 47

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

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?

  1. $35,000
  2. $25,000
  3. $30,000
  4. $40,000
  5. $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 = x-0.2x=0.8x

Share of the man’s father = 0.25\times 08x=0.2x

Balance = 0.8x-0.2x=0.6x

Share of the man’s aunt = \frac{1}{3}\times 0.6x=0.2x

Balance = 0.6x-0.2x=0.4x

Share of the man’s wife = 0.6\times 0.4x=0.24x

Difference in share of the man’s wife and his father = 0.24x-0.2x=0.04x= $4000

\therefore x=\frac{4000}{0.04}= $100,000.

Hence share of the man’s aunt = 0.2x=0.2\times 100000= 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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