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

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Math Expert
Joined: 02 Sep 2009
Posts: 61510
John and his dad were calculating the ratios of their ages. Currently  [#permalink]

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25 Nov 2019, 00:12
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Difficulty:

45% (medium)

Question Stats:

71% (02:13) correct 29% (02:14) wrong based on 41 sessions

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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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Joined: 18 Aug 2017
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Location: India
Concentration: Sustainability, Marketing
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Re: John and his dad were calculating the ratios of their ages. Currently  [#permalink]

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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

Are You Up For the Challenge: 700 Level Questions
VP
Joined: 24 Nov 2016
Posts: 1242
Location: United States
Re: John and his dad were calculating the ratios of their ages. Currently  [#permalink]

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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

Are You Up For the Challenge: 700 Level Questions

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

Ans (A)
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3256
Re: John and his dad were calculating the ratios of their ages. Currently  [#permalink]

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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.
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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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