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John and his dad were calculating the ratios of their ages. Currently

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John and his dad were calculating the ratios of their ages. Currently  [#permalink]

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New post 25 Nov 2019, 00:12
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John and his dad were calculating the ratios of their ages. Currently, John's dad is four times as old as John. Eight years later, John's dad will be two and half times of John's age. What will be the ratio of John and John's dad 32 years later?

A. 5:8
B. 1:4
C. 8:5
D. 4:7
E. 7:4


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Re: John and his dad were calculating the ratios of their ages. Currently  [#permalink]

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New post 25 Nov 2019, 02:02
given
d=4j
d+8= 2.5(j+8)
4j+8=2.5j+20
j=8
d= 32
after 32 years ; 40/64 ; 5:8
IMO A


Bunuel wrote:
John and his dad were calculating the ratios of their ages. Currently, John's dad is four times as old as John. Eight years later, John's dad will be two and half times of John's age. What will be the ratio of John and John's dad 32 years later?

A. 5:8
B. 1:4
C. 8:5
D. 4:7
E. 7:4


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Re: John and his dad were calculating the ratios of their ages. Currently  [#permalink]

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New post 25 Nov 2019, 04:13
Bunuel wrote:
John and his dad were calculating the ratios of their ages. Currently, John's dad is four times as old as John. Eight years later, John's dad will be two and half times of John's age. What will be the ratio of John and John's dad 32 years later?

A. 5:8
B. 1:4
C. 8:5
D. 4:7
E. 7:4


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\(d=4j…d+8=2.5(j+8)…4j+8=2.5j+2.5(8)…1.5j=8(2.5-1)…(j,d)=(8,32)\)
\(d+32/j+32=40/64=10/24=5/8\)

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Re: John and his dad were calculating the ratios of their ages. Currently  [#permalink]

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New post 25 Nov 2019, 19:15

Solution



Given
• John's dad is four times as old as John
o So, if John is x years old then John’s dad is 4x years old.
• Eight years later, John's dad will be two and half times of John's age
o Eight year later, the age of John = x + 8
o Eight year later, the age of John’s father = 4x + 8
o 4x + 8= 5/2 (x+8)
To find
• The ratio of John and John's dad 32 years later
Approach and Working out
• 4x + 8= 5/2 (x+8)
• 8x + 16 = 5x + 40
• 3x = 24
• x = 8
• 4x = 32
32 years later, the age of john = 40 and his father’s age = 64
• Ratio = 40 : 64 = 5 : 8

Thus, option A is the correct answer.
Correct Answer: Option A
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Re: John and his dad were calculating the ratios of their ages. Currently   [#permalink] 25 Nov 2019, 19:15
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John and his dad were calculating the ratios of their ages. Currently

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