Question

a number consists of two digits the difference of whose digits is 5 if 8 times the number is equal to 3 times the number obtained by reversing the digits , find the number​

Answer 1

Let the digit in the ones place be y and tens place be x

Therefore the number = 10x + y

Number formed by reversing the digits = 10y + x

Given 8(10x + y) = 3(10y + x)

⇒ 80x + 8y = 30y + 3x

⇒ 77x – 22y = 0

∴ 7x – 2y = 0  → (1)

It is also given that the difference between the digits is 5.

Hence (y – x) = 5  

– x + y = 5 → (2)

Multiply equation(2) with 2 and add to equation (1), we get

7x – 2y = 0

–2x + 2y = 10

----------------

  5x = 10

∴ x = 2

Put x = 2 in – x + y = 5, we get

– 2 + y = 5

⇒ y = 7

Hence the number = (10x + y)

                              = (10×2 + 7)

                              = 27  

Answer 2

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