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# [Smart Math] Ratio Proportion Problem 47

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? 1.$35,000
2. $25,000 3.$30,000
4. $40,000 5.$20,000

### The Usual Method

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 [contentblock id=google-adsense-post] 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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