Question

The sum of the digits of a 2-digit number is 11. The number obtained by
interchanging the digits exceeds the original number by 27. Find the number.​

Answer 1

$\large\bf\underline {To \: find:-}$

• We need to find the original number.

$\large\bf\underline{Given:-}$

• The sum of the digits of a 2-digit number is 11. The number obtained by interchanging the digits exceeds the original number by 27

$\huge\bf\underline{Solution:-}$

• Let the unit's place digit be y
• Let the ten's place digit be x
• So, Number = 10x + y

☣ According to question:-

Sum of digits of a two digit number is 11.

• x + y = 11
• x = 11 - y ....1)

The number obtained by interchanging the digits exceeds the original number by 27

Number obtained after reversing the digits is

• 10y + x

➛ (10y + x) -(10x + y) = 27

➛ 10y + x - 10x - y = 27

➛ 9 y - 9x = 27

• ✍︎ Divide both side by 9

➛ y - x = 3

• ◕ From equation 1)

➛ y -(11 - y) = 3

➛ y -11 + y = 3

➛ 2y = 3 + 11

➛ 2y = 14

➛ y = 14/2

• y = 7
• ✍︎ Putting value of y in 1)

➛ x = 11 - y

➛ x = 11 - 7

• x = 4

So,

❥ Original Number = 10 × 4 + 7 = 47

❥ Reversed number = 10 × 7 + 4 = 74

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Answer 2

$\huge\underline{\underline{\mathfrak{\color{plum} Given:}}}$

The sum of the digits of a 2-digit number is 11.The number obtained by interchanging the digits exceeds the original number by 27.

$\rule{300}{2}$

$\huge\underline{\underline{\mathfrak{\color{plum}ToFind}}}$

• The number.

$\rule{300}{2}$

$\huge\underline{\underline{\mathfrak{\color{plum}Solution}}}$

Let the unit's place digit be y.

And the ten's place digit be x.

Number= 10x + y

$\rule{300}{2}$

Now, by condition,

The sum of a 2- digit number is 11.

$\sf{x + y = 11}$

$\sf{x = 11 - y}$--------(1)

The number obtained by interchanging the digits exceeds the original number by 27.

Number obtained after interchanging the digits is

$\sf{10y + x}$

$\sf{\implies(10y + x) - (10x + y) = 27}$

$\sf{\implies 10y + x - 10x + y = 27}$

$\sf{\implies 9y - 9x = 27}$

$\sf{Now \: by \: dividing \: both \: sides \: by \: 9}$

$\sf{\implies y - x = 3}$

$\sf{\implies y(11 - y) = 3}[from \: eq(1)]$

$\sf{\implies y - 11 + y = 3}$

$\sf{\implies 2y = 3 + 11}$

$\sf{\implies 2y = 14}$

$\sf{\implies y = \cancel \frac{14}{2} }$

$\sf{\implies y = 7}$

$\sf{Putting \: the \: value \: of \: y \: in \: eq(1)}$

$\sf{x = 11 - y}$

$\sf{x = 11 - 7}$

$\sf{x = 4}$

$\rule{300}{2}$

Hence, the original number is =

$\sf{10 \times 4 + 7 = 47}$

And the interchanged number is=

$\sf{10 \times 7 + 4 = 74}$

$\rule{300}{2}$

$\huge\underline{\underline{\mathfrak{\color{plum} ThankYou}}}$