Question

A number consists of two digits whose sum is 8.If 18 is added to the number its digits are reversed.Find the number
OR
The numerator of a fraction is 4 less than the denominator.If 1 is added to both its numerator and denominator,it becomes 1/2.Find the fraction.
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Answer 1

Question 1

Let,

One digit of the number be $x$,

Then its ten digits digits will be $(8-x).$  

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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,

$(80 -9x) + 18 = 9x + 8$

$(80 - 9x) + 18 = 9x + 8$

$90 = 18x$

$x = 5$

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Given number :-

$= 80- 9x$

$= 80 - 9$ × $5$

$= 80 - 45$

$= 35$

∴ The number is $35$.

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