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A man distributed his wealth among his wife and three sons such that

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Bunuel
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A man distributed his wealth among his wife and three sons such that [#permalink] New post   02 Jun 2020, 05:25
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A man distributed his wealth among his wife and three sons such that his second son got twice the amount the eldest son received, his youngest son received twice the amount the second son got and his wife got twice the amount the youngest son received. If the man were to represent his wealth in a circle diagram, how many degrees of the circle must be allocated to represent the portion that the second son receives?

A. 24
B. 36
C. 48
D. 72
E. 96
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Re: A man distributed his wealth among his wife and three sons such that [#permalink] New post   02 Jun 2020, 05:34
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Bunuel wrote:
A man distributed his wealth among his wife and three sons such that his second son got twice the amount the eldest son received, his youngest son received twice the amount the second son got and his wife got twice the amount the youngest son received. If the man were to represent his wealth in a circle diagram, how many degrees of the circle must be allocated to represent the portion that the second son receives?

A. 24
B. 36
C. 48
D. 72
E. 96



IMO C.48.
Sol.
Son1=1
Son2=2
Son3=4
Wife=8

total wealth=1+2+4+8=15 units.

share of second son by total wealth=2/15
converted to 360 degree=2/15*360=48.
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A man distributed his wealth among his wife and three sons such that [#permalink] New post   02 Jun 2020, 06:35
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Bunuel wrote:
A man distributed his wealth among his wife and three sons such that his second son got twice the amount the eldest son received, his youngest son received twice the amount the second son got and his wife got twice the amount the youngest son received. If the man were to represent his wealth in a circle diagram, how many degrees of the circle must be allocated to represent the portion that the second son receives?

A. 24
B. 36
C. 48
D. 72
E. 96


Solution


    • Let us assume that his eldest son received x amount.
      o Amount received by 2nd son \(= 2x\)
      o Amount received by the youngest son \(= 2*2x = 4x\)
      o Amount received by his wife \(= 2*4x = 8x\)
    • Therefore the degrees of the circle allocated to represent the portion received by 2nd son \(= \frac{2x}{(x +2x+ 4x + 8x)}*360 =\frac{2}{15}*360= 48\)
Thus, the correct answer is Option C.
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Re: A man distributed his wealth among his wife and three sons such that [#permalink] New post   02 Jun 2020, 06:53
The answer is c. Since if we take w as wife, 1st son as a, 2nd son as b and 3rd son as c we get the total inheritance as w+a+b+c ....... (1)
We are given that
b=2a, c=2b, w=2c
If we convert these expressions in terms of b we get w=4b, c=2b and a= b/2
So substituting these values in equation (1) we get (8b+b+2b+4b)/2= 15b/2 =360° so b= 360*2/15= 48°

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A man distributed his wealth among his wife and three sons such that [#permalink] New post   02 Jun 2020, 08:29
imo c

Let eldest son got x

Second son = 2x
Youngest Son = 2(Second Son) = 4x
Wife = 2 (Youngest Son) = 8x

Total wealth of man = Wealth given to Wife + Wealth given to eldest son + Wealth given to Second son + Wealth given to Youngest Son
= 15x

Circle total angle = 360
==> Using unitary method::

15x ------------ 360

1 ------------ 360/(15x)

Second son welath = 2x, hence:
2x ------------- (360 * 2x) / 15x = 48
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A man distributed his wealth among his wife and three sons such that [#permalink]
02 Jun 2020, 08:29
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