Question 288305: I noticed that when I interchanged the digits of my father’s age, I got my own age. When I was born, his age was between twenty and thirty years. What was my father’s age when I was born?
(A) 20 (B) 26 (C) 27 (D) 30 (E) None of these
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! f=10a+b,
s=10b+a,
20<=f-s<=30
20 and 30 are not between 20 and 30
so it must be 26 or 27
It is 27.
a = 9-n, b = 6-n, f = 96-11 n, s = 69-11 n, n element Z, n>=0
let n=1
a=8; b=5
possible ages for father and son
85-58=27
96-69=27
74-47=27
63-36=27
52-25=27
41-14=27
30-3=27
b=a-3
f=11a-3
s=11a-30
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! I noticed that when I interchanged the digits of my father’s age, I got my own age. When I was born, his age was between twenty and thirty years. What was my father’s age when I was born?
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Let father's age be 10t+u where t is the ten's digit and u is the unit's digit.
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My age 10a+b now
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Equations etc.
10u+t = 10a+b.
20 < (10t+u)-(10a+b) < 30
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Working with the inequality you get:
Substitute for 10a+b to get:
20 < (10t+u)-(10u+t) < 30
20 < 9t-9u < 30
20/9 < t-u < 30/9
2.22< t-u < 3.33
But t and u are positive whole numbers
So t-u = 3
t = u+3
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Ans: D
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Cheers,
Stan H.
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(A) 20 (B) 26 (C) 27 (D) 30 (E) None of these
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