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03 Dec 2020, 07:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
82% (01:58) correct
18%
(02:23)
wrong
based on 247
sessions
History
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Not Attempted Yet
The ratio of ages of a father and son is 17:7. 6 years ago the ratio of their ages was 3:1. What is the father's present age?
A. 64
B. 54
C. 51
D. 48
E. 34
A. 64
B. 54
C. 51
D. 48
E. 34
03 Dec 2020, 08:12
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Bunuel
I prefer to answer ratio questions using TWO variables.
Let F = the father's age NOW
Let S = the son's age NOW
So, F - 6 = the father's age SIX YEARS AGO
And S - 6 = the son's age SIX YEARS AGO
The ratio of ages of a father and son is (PRESENTLY) 17:7
We can write: F/S = 17/7
Cross multiply to get: 7F = 17S
Rewrite as: 7F - 17S = 0
6 YEARS AGO the ratio of their ages was 3:1
We can write: (F-6)/(S-6) = 3/1
Cross multiply to get: (1)(F-6) = (3)(S-6)
Expand to get: F - 6 = 3S - 18
Subtract 3S from both sides: F - 3S - 6 = -18
Add 6 to both sides: F - 3S = -12
What is the father's present age?
We have the following equations:
7F - 17S = 0
F - 3S = -12
Take the bottom equation and multiply both sides by 7 to get:
7F - 17S = 0
7F - 21S = -84
Subtract on the bottom equation from the top equation to get: 4S = 84
Solve: S = 21
So, the son's PRESENT age (S) is 21 years old
Since we already know that F/S = 17/7, we can substitute to get: F/21 = 17/7
Solve to get: F = 51
Answer: C
Cheers,
Brent
09 Mar 2021, 16:51
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Bunuel
1) We want to know the value of X, considering X the number by which each part of the fraction will be multiplied by.
So (17X-6)/(7X-6)=3/1
2) Cross multiply both fractions
(3)(7X-6)=(17x-6)
3) Solve for X
21X-18=17X-6
X=3
4) Multiply by 17
Father's age = 3*17 (C is the only option that ends with 1, so just go for it)
