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

**Problem**

**Problem**

After the death of his grandfather, a man bequeathed 20% of the property, his father 25% of the remaining, his aunt 1/3^{rd} 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 = 0.2*x*

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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