Latest self Aptitude Question SOLUTION: On planet Jupiterthe people use a certain number system to the base 'n' (n > 2), Jerk, a resident of the planet, one day received twice his daily wage because the digits of this w

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(#M40020934) SELF question Keep an EYE

On planet Jupiterthe people use a certain number system to the base 'n' (n > 2), Jerk, a resident of the planet, one day received twice his daily wage because the digits of this wage, which was a 2 digit number, were reversed. If the value of 'n' is the least possible value there the decimal representation of the difference between Jerk's correct wage for the day is

vikash singh (10 years ago)

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mohan lal garg  (10 years ago)

Let the base of the number system be n and the two digit number be ab
given 2(ab)n = (ba)n
⇒ nb + a = 2na + 2b
⇒ a(2n - 1) = b(n - 2)
⇒ab=n−22n−1

Now the maximum possible value of a or b is (n - 1) (base n) for n = 3 we get
ab=15 = which is not possible as in base 3, 5 won't exist.
Similarly, for n = 4
but for n = 5
We get ab=39i.e.13
a = 1, b = 3 is the only number possible when n is the least possible.

The correct wage = (13)5=(8)10
The actual wage paid = (31)5=(16)10
So difference = 8

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