Question

4. A number consists of two digits whose sum is 8. If 18 is added to the number its digits are
reversed. Find the number.
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Answer 1

Answer:

35

Step-by-step explanation:

let the two digit number be xy

so x+y=8

y=8-x

TENS =10x.... and ones =1(8-x)....original number

Tens =10(8-x) and ones =1(x)...... reversed number

A/Q... we have

10x+8-x+18=10(8-x)+1(x)

9x+26=80-9x

Then x=3

y=8-x...... 8-3=5

Then the expression is xy... so

the original number is 35

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Answer 2

Let one digit of the number be x , then its ten digits digits will be (8−x) .

So , given number =10(8−x)+x

=80−10x+x

=80−9x

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Now if digits are reversed , then Number obtained

=10x+(8−x)

=10x+8−x

=9x+8

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According to question

(80−9x)+18=9x+8

98−9x=9x+8

90=18x

x=5

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⇒ given number =80−9x=80−9×5

=80−45

=35 ______________________

HENCE∴ the number is 35

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