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 6:1We can write: M/S = 6/1
Cross multiply to get: M = 6S
Rearrange to get:
M - 6S = 0Five years from now, the ratio of the ages will be 7:2M + 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 = 25We now have two equations
2M - 7S = 25M - 6S = 0What 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 = 25Answer: C
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