A two-digit number is obt in d by either multiplying the sum of the di

1.	A two-digit number is obt in d by either multiplying the sum of the digits by 8 and thensubtracting 5 or by multiplyng the difference of the digits by 16 and then adding 3. Find thenumber
Answer» 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) - 510x + y = 8x + 8y - 510x - 8x + y - 8y = - 52x - 7y = - 5 .................(1) And,10x + y = 16(x - y) + 310x + y = 16x - 16y + 310x - 16x + y + 16y = 3- 6x + 17y = 3 ................(2) Now, multiplying the equation (1) by 17 and (2) by 7, we get34x - 119y = - 85 ...............(3)- 42x + 119y = 21 ..............(4) Now, adding (3) and (4), we get 34x - 119y = - 85- 42x + 119y = 21_________________- 8x = - 64_________________ ⇒ 8x = 64x = 64/8x = 8So, tens digit is 8. Substituting the value of x = 8 in (1), we get2x - 7y = - 52*8 - 7y = - 516 - 7y = - 5- 7y = - 5 - 16- 7y = - 217y = 21y = 21/7y = 3 Ones digit is 3.So, the required number is 83.

A two-digit number is obt in d by either multiplying the sum of the digits by 8 and thensubtracting 5 or by multiplyng the difference of the digits by 16 and then adding 3. Find thenumber

Answer»

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) - 510x + y = 8x + 8y - 510x - 8x + y - 8y = - 52x - 7y = - 5 .................(1)

And,10x + y = 16(x - y) + 310x + y = 16x - 16y + 310x - 16x + y + 16y = 3- 6x + 17y = 3 ................(2)

Now, multiplying the equation (1) by 17 and (2) by 7, we get34x - 119y = - 85 ...............(3)- 42x + 119y = 21 ..............(4)

Now, adding (3) and (4), we get

34x - 119y = - 85- 42x + 119y = 21_________________- 8x = - 64_________________

⇒ 8x = 64x = 64/8x = 8So, tens digit is 8.

Substituting the value of x = 8 in (1), we get2x - 7y = - 52*8 - 7y = - 516 - 7y = - 5- 7y = - 5 - 16- 7y = - 217y = 21y = 21/7y = 3

Ones digit is 3.So, the required number is 83.