Two digits in hunter's age are the same as the digit in the titan's ag

hunters age = 10a+b
titans age = 10b+a
∆ in age = 9(a-b)
5 years later
10a+b+5=2*(10b+a+5)
10a+b+5 = 20b+2a+10
8a=19b+5

∆ in age = 9(a-b)
answer will be one with ∆ of 5
(A) 9 = not possible
(B) 18 ; 18-5 ; 13 and 31 ; correct
(C) 27; 22 ; not possible
(D) 36; 31 and 13 not possible
(E) 45 ; 41 and 14 not possible
IMO B

Let the hunter's age = xy = 10x + y
--> Age of titan = yx = 10y + x

After 5 years, age of hunter = 10x + y + 5
and age of titan = 10y + x + 5

In five years hunter will be twice as old as titan will be then
--> 10x + y + 5 = 2(10y + x + 5)
--> 8x - 19y = 5
--> 8x = 19y + 5
So, y has to be odd,
If y = 1, 8x = 24 --> x = 3 --> Possible
If y = 3, 8x = 62 --> Not Possible
If y = 5, 8x = 100 --> Not Possible (x will have 2 digits)

--> Only Possible value of xy = 31
--> Age of hunter = 31 & age of titan = 13
--> Difference = 31 - 13 = 18

IMO Option B

Let Hunter's Age be MN and Titan's age be NM.
In 5 yrs
MN+5 = 2(NM+5)- eq 1
MN+5 = 2NM + 10
MN-2NM = 5
MN-NM-NM = 5
MN-NM = 5 + NM ---> (MN-NM is the difference in their current ages)

Substituting option B
18 = 5+ NM
NM = 13
So MN would be 31
Now substitute in eq1 to check if the values are correct
31+5 = 2(13+5)
36 = 36

IMO B

Hi chetan2u
Can you please help me understand how b is odd?

Thank you!

Posted from my mobile device

In 8a=19b+5, the left hand side 8a is EVEN, so the right hand side 19b+5=Even.....19b=E-5=odd, so b is odd

We know H+5=2(T+5)
2T-H=-5
Reverse plug in answer choices for second equation
(C) H-T=27
T=22, H=49 (Does not satisfy first condition i.e. H & T have reversed one's and ten's)
(B) H-T=18
T=13, H=31 (That's our answer)

We will attack on answer.
H = Hunters age = is greater
T = Titans age = starts with 1 series
(A) 9 :means H=21, T=12
After 5 years H=26, T=17
Not true
(B) 18 :means H=31, T=13
After 5 years H=36, T=18
true =Answer
(C) 27
(D) 36
(E) 45

Answer is B

Posted from my mobile device

This will probably be the simplest way to solve this question:

Consider Hunter's age to be AB (since we know it is a two digit number)
Also, let Titan's ahe be BA (again, two digit with the digits reversed)

According to the question:
AB + 5 = 2 (BA + 5)
AB + 5 = 2BA + 10
AB - 2BA = 5
AB - BA = BA + 5 ...... (1)

Now, simply plug in the values from the answer choices to determine the correct option.

(A) 9
AB - BA cannot be 9 because according to (1), BA will have to be 4. And BA is a two digit number, so (A) is incorrect.

(B) 18
AB - BA = BA + 5 = 18
Therefore, BA = 13 and AB = 31 (only the digits are reversed, as given in the question)
Let's add five to both ages to find out whether they satisfy the condition given in the question:
BA + 5 = 13 + 5 = 18
AB + 5 = 31 + 5 = 36

Voila!! AB + 5 = 2 (BA + 5)

Since our condition is satisfied....the answer has to be (B)!

Had trouble at 1st, but Number Properties become so important in Higher-Level Questions

NOW
_______________
Hunter = 10a + b

Titan = 10b + a



+5 years
_________________
Hunter Age + 5 = 2 * (Titan Age + 5)
10a + b + 5 = 2 * (10b + a + 5)
10a + b + 5 = 20b + 2a + 10

8a = 19b + 5



No matter which Digit a is: (Even * a) = EVEN

thus, the b-Digit must be ODD:

19b + 5 = Odd * (Odd) + Odd = EVEN


try a Random Odd b-Digit: b = 5 : and plug-into the Above Equation to see if 8 Divides Evenly

8a = 19(5) + 5
8a = 100

NO


b= 3

8a = 19(3) + 5
8a = 62

NO

b = 1

8a = 19(1) + 5
8a = 24
a = 3

YES----WORKS


a = 3 ; b = 1

Hunter Age NOW = 10a + b = 31

Hunter Age + 5 Years = 36


Titan Age NO = 13

Hunter Age + 5 Years = 18


in +5 years -----> 36 = 2*(18)



Difference in Age's NOW:

31 - 13 = 18


ANSWER -B-

Hunter= xy, Titan= yx, given xy>yx

and, xy+5 = 2* (yx+5) or, xy- yx = yx + 5

A) 9, not possible, Hunter and Titan are 2 digit aged.
B) 18, yx= 13 = Titan, Hunter= 31, possible.
C) 27, yx= 22 = Titan, not possible, as given xy>yx
D) 36, yx= 31 = Titan, Hunter =13= xy, not possible, as given xy>yx
E) 45, yx= 40= Titan, Hunder= 4= xy, not possible, as given xy>yx

So, I think B.

1. Let the digits in Titan's age be \(xy\) and in Hunter's age be \(yx\) (Two digits in hunter's age are the same as the digit in the titan's age, but in reverse order)

2. We are asked for the difference in their current age \(= (10x + y) - (10y + x) = 9x - 9y = 9(x - y)\). This tells us that the age will be a multiple of \(9\)

3. \(10x + y + 5 = 2 (10y + x + 5)\) (In five years hunter will be twice as old as titan will be then)

4. Solving 3. further we get, \(10x + y + 5 = 20y + 2x + 10\) -> \(8x = 19y + 5\)

5. When we take \(y = 1\) we get \(x = 3\)

6. Substituting in 2. we get \(9(3 - 1) = 9(2) = 18\)

Ans. B

Current age : ab & ba
5 Years later : ab+5 & ba+5,
where ab+5=2(ba+5)
ab+5=2ba+10
ab-2ba=5
(ab-ba)-ba=5
Substitute given values of difference ab-ba from the answer choices,
Let's late 27 first which is C option
(ab-ba)-ba=5 becomes 27-ba=5, so ba = 22, ba = 22 is not a possible answer,
Now let's take 18,
(ab-ba)-ba=5 becomes 18-ba=5, so ba=13 gives ab=31, now you can double check by adding 5 to each and it follows the equation
13+5=18
31+5=36
36=2*18
So 18 is right answer

it took me over 3 min to get to the bottom till 8x=19y +5 it's fine from there on we have to figure out the possiblity with 1 and 3 nice one bunuel............

hunter's (H) age > 10a+b
Titan's (T) age > 10b+a
were are given H+5=2T+5
substituting, we end up with
8a=5+19b
now a<=9, so max value of 8a is 72. Then 8a has to be even, which mean that 19b has to be odd so b has to be odd.
so 5+19b<=72, 19b<=67, b can only be 1 or 3. at b=1, a=3 and at b=3, a= 7 point something
remember that a,b are positive integers.
so ab = 31, ba=13. the difference is 18

Through simplification we reach 9*(x-y) and
8*(x-y) = 11y +5
When we substitue just y=1 we get 9*(x-y) = 18

THerefore IMO B

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