Question

The sum of two digit number is 17. If the number formed by reversing the digits is less than the original number by 9,find the original number.​

Answer 1

Answer:

★FIND:

the original number = ?

★GIVEN,

The sum of two digit number is 17.

If the number formed by reversing the digits is less than the original number by 9.

★SOLUTION:

The sum of two digit number is 17

➡️8+9=17

➡️9+8=17

So the 8+9=17 is correct.

if we reverse 89 then we get 98.

Subtract 9 from the reversed number 98

=>98-9

=>89

The original number is 98.

Answer 2

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find the original number

$\huge\bf\underline \red{ \mathcal{S}olution...}$

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

• Sum of digits of a two digit number = 17
• number formed by reversing the digits is less than the original number by 9.

${ \blue{ \mathscr{ \underline{Let : - }}}}$

• Let units place digit be x
• Let ten's place digit be y

↠ Number formed = 10x + y

$\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

Sum of digits of a two digit number = 17.

• x + y = 17
• x = 17 - y .....1)

Number formed by reversing the digits is less than the original number by 9.

• Original number = 10x + y
• Number formed on revercing the digits is 10y + x.

⇢ 10x + y -(10y + x) = 9

⇢ 10x + y - 10y - x = 9

⇢ 9x - 9y = 9

• Dividing both sides by 9

⇢ x - y = 1

• From equation 1)

⇢ 17 - y - y = 1

⇢ -2y = 1 - 17

⇢ - 2y = -16

⇢ y = 8

• Substituting value of y in Equation ..1)

↠ x = 17 - y

↠ x = 17 - 8

↠ x = 9

So,

• Original number 10x + y

= 10 × 9 + 8

= 90 + 8

= 98

• Number formed on revercing the digits is 10 y + x

= 10 × 8 + 9

= 80 + 9

= 89

Hence,

• Original number = 98

✫Verification :-

Sum of digits of a two digit number = 17.

So,

= x + y = 17

= 8 + 9 = 17

= 17 = 17

LHS = RHS

Hence, verified

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