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The sum of the digits of a two-digit number is 8. The difference between the number and the reversed number is 10 more than the reversed number. Find the number.

Respuesta :

Answer:

62

Step-by-step explanation:

Let the two digit number be XY

X+Y = 8

10X+Y - (10Y+X) = 10Y+X+10

10X+Y-10Y-X=10Y+X+10

8X-19Y=10

8(8-Y)-19Y=10

64-8Y-19Y=10

27Y=54

Y=2

The number is therefore 62.

ashishdwivedilVT

The required two-digit number with sum of digits as 8 is 62.

Let us say the number is xy

What is the place value of x and y in xy?

The place value of digits, x and y in the number xy are 10 and 1 respectively.

So the number xy can be written as 10x+y

When the digits are reversed

The new number or reversed number obtained will be yx

So the new number yx can be written as 10y+x

Since the difference between the original number and the reversed number is 10 more than the reversed number.

So, (10x+y) - (10y+x) = 10 + (10y+x)

8x-19y =10.......(1)

Since the sum of digits is 8

So, x+y = 8......(2)

By solving equations (1) and (2) we get

x=6, y=2

So, the required number is xy i.e. 62.

Therefore, The required two-digit number with sum of digits as 8 is 62.

To get more about linear equations visit:

https://brainly.com/question/14323743

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