Question

sum of the digits of a two digit number is 8. when we interchange the new number obtained is smaller than the original number by 18. find the number




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Answer 1

Answer:

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Correct option is

A

35

Let the number be in the form of 10x+y,  where x and y are the tens digit and the units digit respectively.  

Applying the first condition:, we get 

x+y=8 ....(1)

Applying the second condition, given in the problem 

10x+y+18=10y+x

⇒9x−9y=−18

⇒x−y=−2 ....(2)

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

x=3 and y=5 

Therefore, the number is 35.

Answer 2

Step-by-step explanation:

suppose,

units digit = x

Tens digit = 8 - x

Original number = 10 (8 - x) + x

= 80 - 10x + x = 80 - 9x

When interchanging its digits the number obtained = 10x + (8 - x)

= 10x - x + 8 = 9x + 8

ATQ,

>> 80 - 9x - 18 = 9x + 8

80 - 18 - 9x = 9x + 8

62 - 8 = 9x + 9x

54 = 18x

x = 54/18

x = 3

units digit = 3

Tens digit = 8 - x

= 8 - 3 = 5

Tens digit = 5

Number = 53

The number is 53