SOLUTION: 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 wa

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?
---
Let father's age be 10t+u where t is the ten's digit and u is the unit's digit.
--------------------
My age 10a+b now
------
Equations etc.
10u+t = 10a+b.
20 < (10t+u)-(10a+b) < 30
----
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
-------------------
Ans: D
--------------
Cheers,
Stan H.
====================

(A) 20 (B) 26 (C) 27 (D) 30 (E) None of these

RELATED QUESTIONS
Q.5 When I was born, my mother was 23 years of age. After 6 years, when my sister was... (answered by Cromlix)
My brother is 3 years elder to me. My father was 28 years of age when my sister was born... (answered by ikleyn)
My son my father and I were all born on fathers day. When my son was born I was 3/7 the... (answered by ankor@dixie-net.com,josmiceli)
My great grandmother,grandmother,mother & myself. If u reverse the digits of my age u... (answered by richwmiller)
When my daughter was born I was 30 years old. At what age of mine, my age will be 3 times (answered by Edwin McCravy)
My father was 30 years old when I was born. Last year, he was twice my age. What is my... (answered by Alan3354)
When you were born, Claire, I was 24 years old. Today I'm twice the age you were when I... (answered by ankor@dixie-net.com,ikleyn)
My father was born on 18 february 1966 ,I was born on 22 april 1990 ,when will I be... (answered by richwmiller)
I was 17 when my little nephew was born. At some point my age will be three times his... (answered by josmiceli)