Question

Sum of the digits of a two digit number is 6,When we interchange the digits,it is found that the resulting new number is greater than the original number by 18, what is the two digit number?

-Rendom questions 201-
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Answer 1

Given :-

Sum of the digits of a two digit number is 6,When we interchange the digits,it is found that the resulting new number is greater than the original number by 18,

To Find :-

Number

Solution :-

Let the number be xy

x + y = 6

Now

10x + y is the original number

10y + x is the interchanged number

10x + y + 18 = 10y + x

10x - x + y - 10y = -18

9x - 9y = -18

Divide both side by 9

9x - 9y/9 = -18/9

x - y = -2  ...2

Add both

x + y + x - y = 6 + (-2)

2x = 6 - 2

2x = 4

x = 4/2

x = 2

Using 1

x + y = 6

2 + y = 6

y = 6 - 2

y = 4

Hence the number is 24

Answer 2

Answer:

Let the unit place digit of a two-digit number be x.

Therefore, the tens place digit = 6-x

∵ 2-digit number = 10 x tens place digit + unit place digit

∴ Original number = 10(6-x)+x

According to the question, New number

= Original number + 18

10x+(6-x)=10(6−x)+x+18

⇒10+6−x=60−10x+x+18

⇒9x+6=78−9x

⇒9x+9x=78-6

18x=72

⇒x= 72/18

=4

Hence, the 2-digit number = 10(6-x)+x = 10(6-4)+4 = 10 x 2 + 4 = 20 +4 = 24

Step-by-step explanation:

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