Question

A two digit number became five sixth of itself when it's digits are reserved differ by what is the number

Answer 1

Hi there! I happened to come across the same question so here is how you can solve it! The answer is 54 but how to find it out you can look below..

let the units place digit be x and tens place digit be y

therefore the original number is 10y + x and new number is 10x + y

therefore:

50y+5x = 60x+6y

44y = 55x

4y - 5x = 0 ___ (i)

y-x = 1 ___ (ii)

(ii) × 4:

4y-4x = 4

(i) - (ii):

(4y-5x) - (4y-4x) = 0-4

-5x-4x = -4

-x = -4

x = 1

y = x + 1 = 5

therefore original number is 54

Answer 2

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Let the original number be ab.

According to the question, 

a - b = 1....(1)

ba=5/6 ab

=> 6(10b+a) = 5(10a+b)

=> 55b-44a=0......(2)

On solving equations (1) and (2), we get

a = 5

b = 4

Thus, the original number is 54.

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