## Two digit number thistime by multiplying the sum of digits by eight and then subtracting five or so it is obtained by multiplying the differ

Question

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## Answers ( )

Answer:Step-by-step explanation: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.

Solution :Let the ten’s place digit be

r& unit’s place digit bem.A/qFrom equation (2),we get;

∴ Putting the value of

rin equation (1),we get;∴ Putting the value of

min equation (3),we get;Thus;