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The ratio of current ages of a mother and son

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The ratio of current ages of a mother and son [#permalink] New post 11 Sep 2018, 05:28
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The ratio of current ages of a mother and her son is 6:1. Five years from now, the ratio of the ages will be 7:2. what was the age of the mother, when her son was born?


A)21

B)23

c)25

D)27

E)30
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Re: The ratio of current ages of a mother and son [#permalink] New post 11 Sep 2018, 10:18
Expert's post
6x is the mother and x is the son, considering their ration is in order of \(\frac{6}{1}\).

Add 5 years and we do have \(\frac{6x+5}{x+5}=\frac{7}{2}\)

Cross multiply and perform calculations you will end up that x = 5

The mother 6*5 = 30 and the son is x=5. The difference is when the child was born is 25.

Hope this helps.
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Re: The ratio of current ages of a mother and son [#permalink] New post 11 Sep 2018, 10:55
Expert's post
AchyuthReddy wrote:
The ratio of current ages of a mother and her son is 6:1. Five years from now, the ratio of the ages will be 7:2. what was the age of the mother, when her son was born?


A)21

B)23

C)25

D)27

E)30


We can also solve the question using 2 variables.

Let M = the Mom's CURRENT age
Let S = the Son's CURRENT age

The ratio of CURRENT ages of a mother and her son is 6:1
We can write: M/S = 6/1
Cross multiply to get: M = 6S
Rearrange to get: M - 6S = 0

Five years from now, the ratio of the ages will be 7:2
M + 5 = the Mom's age FIVE YEARS FROM NOW
S + 5 = the Son's age FIVE YEARS FROM NOW
We can write: (M + 5)/(S + 5) = 7/2
Cross multiply to get: 2(M + 5) = 7(S + 5)
Expand: 2M + 10 = 7S + 35
Rearrange: 2M - 7S = 25

We now have two equations
2M - 7S = 25
M - 6S = 0

What was the age of the mother, when her son was born?
This is the same as asking "The mother is how many years older than her son?"
Or we can just ask, "What is the value of M - S?

Just take our two equations above, and subtract the bottom equation from the top equation to get: M - S = 25

Answer: C
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Re: The ratio of current ages of a mother and son   [#permalink] 11 Sep 2018, 10:55
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