Question

Sum of the digits of a two digit number is 10. When we interchange the digits, it is found that the resulting number is greater than the original number by 36. Find the number.

Answer 1

Let the two digits of the number be:

• x and y

Let the number be:

• 10x+y

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It's given that

• Sum of two digits = 10

Thus, $\bold{\purple{\boxed{x+ y =10--- i}}}$

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Also given,

when we interchange the digits, the resulting number is greater than the original number by 36.

The original number = 10x+ y

The number after interchanging the digits= 10y+ x

10y+ x = 10x+ y + 36

→ 10y- y + x -10x =36

→ 9y -9x = 36

→ 9(y-x)= 36

→ $\bold{\purple{\boxed{ y -x =4--- ii}}}$

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Adding i and ii we get,

x+y + y -x = 10+ 4

→ 2y = 14

→ y =7

Substitute y=7 in equation ii,

y- x=4

→7- x =4

→ x = 7-4

→ x =3

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Thus the number is:

10x + y

→ 10×3 + 7

→ $\large{\red{\bold{\boxed{37}}}}$

∴ The number is 37

Answer 2

Given

• Sum of the digits of a two digit number is 10.
• When we interchange the digits, it is found that the resulting number is greater than the original number by 36.

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To find

• The required number.

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Solution

• Let the tenth digit number be x.
• Let the ones digit number be y.

Therefore,

• Required Number = 10x + y

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★ It is given in the question that sum of the two digits is 10.

$\boxed{\sf{\orange{x + y = 10}}}$⠀⠀....[1]

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★ When we interchange the digits, it is found that the resulting number is greater than the original number by 36.

⠀

• After interchanging = 10y + x

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According to the question

$\large{\tt{\longmapsto{(10y + x) - (10x + y) = 36}}}$

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$\large{\tt{\longmapsto{10y + x - 10x - y = 36}}}$

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$\large{\tt{\longmapsto{9y - 9x = 36}}}$

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$\large{\tt{\longmapsto{9(y - x) = 36 }}}$

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$\large{\tt{\longmapsto{y - x = \dfrac{36}{9} }}}$

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$\boxed{\sf{\orange{y - x = 4}}}$⠀⠀.....[2]

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★ Adding equation [1] and [2]

$\tt:\implies{(x + y) + (y - x) = 10 + 4}$

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$\tt:\implies{\cancel{x} + y + y - \cancel{ x} = 14}$

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

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$\tt:\implies{y = \dfrac{14}{2}}$

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$\tt:\implies{y = 7}$

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★ Putting the value of y in equation [1]

$\tt:\implies{x + (7) = 10}$

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$\tt:\implies{x = 10 - 7}$

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$\tt:\implies{x = 3}$

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Hence, the required number is

$\tt\longrightarrow{10(3) + (7)}$

$\tt\longrightarrow{30 + 7}$

$\tt\longrightarrow{\boxed{\orange{37}}}$

⠀

Therefore,

• Required Number = 37

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