Question

The sum of a two digit number and the number obtained by reversing the digits is 66. If the digits differ by two. Find the number?
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Answer 1

$\huge\fbox\purple{Answer}$

Two digit numbers are 42 and 24

Answer 2

Given:–

• The sum of a two digit number and the number obtained by reversing the digits is 66.
• The difference of the digits of a two digit number is 2.

To Find:–

• What is the original number ?

Solution:–

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

• NUMBER = 10x + y

❍ Reversed Number = 10y + x

Case:– ❶

❖ The sum of a two digit number and the number obtained by reversing the digits is 66

${\underline{\bf{According \: To \: Question:-}}}$

$\rm{\longrightarrow 10x + y + 10y + x = 66 }$

$\rm{\longrightarrow 11x + 11y = 66 }$

Dividing by "11" on both sides

$\rm{\longrightarrow x + y = 6...1)}$

Case:–❷

❖ The difference of the digits of a two digit number is 2.

${\underline{\bf{According \: To \: Question:-}}}$

$\rm{\longrightarrow x - y = 2}$

$\rm{\longrightarrow x = 2 + y...2) }$

On putting the value of 'x' in equation 1), we get

$\rm{\longrightarrow 2 +y + y = 6 }$

$\rm{\longrightarrow 2y = 6-2 }$

$\rm{\longrightarrow 2y = 4}$

$\rm{\longrightarrow y = \cancel\dfrac{4}{2}}$

$\bf{\large{\longmapsto{\red{\underline{\underline {\: \star \: y = 2 \: \star}}}}}}$

Put the value of 'y' in equation 2)

$\rm{\longrightarrow x = 2 + 2 }$

$\bf{\large{\longmapsto{\red{\underline{\underline {\: \star \: x = 4 \: \star}}}}}}$

◆ NUMBER = 10x + y

◆ NUMBER = 10(4) + 2

◆ NUMBER = 42

❝ Hence, the number formed is 42 ❞

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