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The present ages of a mother and her son are in the ratio 11 : 5. When

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Bunuel
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The present ages of a mother and her son are in the ratio 11 : 5. When [#permalink] New post   10 Mar 2021, 03:30
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The present ages of a mother and her son are in the ratio 11 : 5. When the son becomes as old as his mother is now, then the ration of his father’s age to his mother’s are will be 19 : 17. And when the son becomes as old as his father is now, then the sum of his father’s age and his age will be 170 years. What is the father’s present age?

(A) 63 years
(B) 64 years
(C) 65 years
(D) 70 years
(E) 72 years
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Re: The present ages of a mother and her son are in the ratio 11 : 5. When [#permalink] New post   15 Mar 2021, 01:21
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Son ---> S
Mother ---> M
Father ---> F

M and S age relation -----> 11x ; 5x
F and M relation after 6x years from now (when S's age is 11x) ---> 19x ; 17x
Hence, the current F's age is 13x
170 years is equal to the sum of S's age when reached that of his father (13x, so after 8x years from now, since now S is 5x years old) and the F's age after these 8x years, so 13x+8x=21x -----> 13x + 21x = 170

Solve for x and you find x= 5

The F's present age is 5 * 13 = 65 years
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Re: The present ages of a mother and her son are in the ratio 11 : 5. When [#permalink] New post   12 Mar 2021, 15:17
C is the answer I guess. Final equation y=5*f/13

f: father's current age
y: son's current age

Since f needs to be a multiple of 13. therefore C
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Re: The present ages of a mother and her son are in the ratio 11 : 5. When [#permalink] New post   05 Nov 2022, 09:34
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Bunuel wrote:
The present ages of a mother and her son are in the ratio 11 : 5. When the son becomes as old as his mother is now, then the ration of his father’s age to his mother’s are will be 19 : 17. And when the son becomes as old as his father is now, then the sum of his father’s age and his age will be 170 years. What is the father’s present age?

(A) 63 years
(B) 64 years
(C) 65 years
(D) 70 years
(E) 72 years


Solution:

  • Let us break the question stem into statements
  • present ages of a mother and her son are in the ratio 11 : 5:
Attachment:
SFM.png
SFM.png [ 3.72 KiB | Viewed 4403 times ]

  • When the son becomes as old as his mother is now i.e., \(11x-5x=6x\) from now
  • the ratio of his father’s age to his mother’s are will be 19 : 17
Attachment:
SFM2.png
SFM2.png [ 8.05 KiB | Viewed 4301 times ]

  • when the son becomes as old as his father is now i.e., \(13x-5x=8x\) years from now
Attachment:
SFM3.png
SFM3.png [ 9.87 KiB | Viewed 4195 times ]

  • sum of his father’s age and his age will be 170 years i.e., \(13x+21x=170\)
    \(⇒34x=170\)
    \(⇒x=170/34\)
    \(⇒x=5\)
  • Therefore, father's present age \(=13x=13\times 5=65\)

Hence the right answer is Option C
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Re: The present ages of a mother and her son are in the ratio 11 : 5. When [#permalink] New post   17 Apr 2024, 04:16
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Re: The present ages of a mother and her son are in the ratio 11 : 5. When [#permalink]
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