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

Question

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

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

Nik11 · Accepted Answer

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

SaquibHGMATWhiz · Answer

Solution: Let us break the question stem into statements present ages of a mother and her son are in the ratio 11 : 5: SFM.png 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 SFM2.png when the son becomes as old as his father is now i.e., 13x-5x=8x years from now SFM3.png 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 imes 5=65 Hence the right answer is Option C

swim2109 · Answer

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

finisher009 · Answer

Solution: 
1. Find the Key Relationship: The core of this problem is finding the relationship between the ages.
• Present Ages: Let the mother’s age be M = 11k and the son’s age be S = 5k.
• First Future Scenario: The son reaches the mother’s current age (11k) in `11k - 5k = 6k` years.
• In 6k years, the mother’s age will be `11k + 6k = 17k`. The father’s age will be `F + 6k`.
• The problem states the new ratio of the father’s age to the mother’s age is 19:17. So, (F + 6k) / 17k = 19 / 17.
• This simplifies to `F + 6k = 19k`, which means the father’s present age is F = 13k.

2. Eliminate Answer Choices: The father’s present age must be a multiple of 13.
• (A) 63 (Not a multiple of 13)
• (B) 64 (Not a multiple of 13)
• (C) 65 (This is 13 * 5)
• (D) 70 (Not a multiple of 13)
• (E) 72 (Not a multiple of 13)

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

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

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