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Question

# A two digit number is obtained by either multiplying the sum of the digits by 8 then subtracting5 or by multiplyimg the difference by 16 and then adding 3 find the number

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Solution

## Solution :- Let the two digit number be 10x + y where x is the tens digit and y is the ones digit. Now, according to the question. 10x + y = 8(x + y) - 5 10x + y = 8x + 8y - 5 10x - 8x + y - 8y = - 5 2x - 7y = - 5 .................(1) And, 10x + y = 16(x - y) + 3 10x + y = 16x - 16y + 3 10x - 16x + y + 16y = 3 - 6x + 17y = 3 ................(2) Now, multiplying the equation (1) by 17 and (2) by 7, we get 34x - 119y = - 85 ...............(3) - 42x + 119y = 21 ..............(4) Now, adding (3) and (4), we get 34x - 119y = - 85 - 42x + 119y = 21 _________________ - 8x = - 64 _________________ ⇒ 8x = 64 x = 64/8 x = 8 So, tens digit is 8. Substituting the value of x = 8 in (1), we get 2x - 7y = - 5 2*8 - 7y = - 5 16 - 7y = - 5 - 7y = - 5 - 16 - 7y = - 21 7y = 21 y = 21/7 y = 3 Ones digit is 3. So, the required number is 83.

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