Question

Q26.The Sum of digits of a two number is 15. the number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the Given Number.

25

78

32

none of these

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Answer 1

The number is 78

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Answer 2

$\boxed{\fcolorbox{pink}{green}{Given}}$

• The sum of digits of two number is 15.

• The number obtained by reversing the order of digits of the given number exceeds the given number by 9.

$\boxed{\fcolorbox{pink}{green}{To \: Find}}$

• The number.

$\boxed{\fcolorbox{pink}{green}{Solution}}$

Let the unit's place digit be y and the ten's place digit be x.

Number = 10x + y

✷The sum of digits of two number is 15.

Now,

By first condition,

$\tt{x + y = 15}$

$\tt{\implies x = 15 - y}......(1)$

✷The number obtained by reversing the order of digits of the given number exceeds the given number by 9.

Reversed Number = 10y +x

$\tt\underline{</strong><strong>A</strong><strong>ccording \: to \: question}$

$\tt{10y + x = 10x + y + 9}$

$\tt{\implies 0 = - (10y + x) + 10x + y + 9}$

$\tt{\implies 0 = - 10y - x + 10x + y + 9}$

$\tt{\implies - 9 = 9x - 9y}$

Divided by 9 from both side.

$\tt{\implies - 1 = x - y }......(2)$

Now, putting the value of x in eq(2)

$\tt{\implies - 1 = 15 - y - y}$

$\tt{\implies - 1 - 15 = - 2y}$

$\tt{\implies - 14 = - 2y}$

$\tt{\implies \cancel\frac{ - 14}{ - 2} = y }$

$\tt{\implies y = 7}$

Now, again putting the value of y in eq(1)

$\tt{\implies x = 15 - 7}$

$\tt{\implies x = 8}$

• Number = 10y+x
• Number = 10(7)+8
• Number = 70+8
• Number = 78

Hence, the given number is 78.

❥ Option (B) is correct.