Question

the sum of the digits of a two digit number is 12.if the new number formed by reversing the digits is greater than the original number by18, find the original number .check your solution And the options are 55 53 59 57

Answer 1

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

• we need to find the original number

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

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

• Sum of digits = 12
• New number formed by revercing the digits is 18 more than the original number

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

• Number = 10x + y

➳ Sum of digits = 12

➳ x + y = 12

➳ x = 12 - y ....1)

• ▶ According to Question :-

the new number formed by reversing the digits is greater than the original number by 18

• New Number formed by reversing the digits is 10y + x

→ 10 y + x = 10x + y + 18

→ 10y - y + x - 10x = 18

→ 9y - 9x = 18

• From equation (1)

→ 9y - 9(12 - y) = 18

→ 9y - 108 + 9y = 18

→ 18y = 18 + 108

→ 18y = 126

→ y = 126/18

→ y = 7

• Putting value of y in eq (1)

➛ x = 12 - y

➛ x = 12 - 7

➛ x = 5

Hence,

• Original number is :-
• 10x + y
• 10 × 5 + 7
• 50 + 7
• 57

▶ Original number = 57

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Answer 2

To find:−

we need to find the original number

$\huge\red{solution: }$

Sum of digits = 12

New number formed by revercing the digits is 18 more than the original number

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

Number = 10x + y

➳ Sum of digits = 12

➳ x + y = 12

➳ x = 12 - y ....1

▶ According to Question :-

the new number formed by reversing the digits is greater than the original number by 18

New Number formed by reversing the digits is 10y + x

→ 10 y + x = 10x + y + 18

→ 10y - y + x - 10x = 18

→ 9y - 9x = 18

From equation (1)

→ 9y - 9(12 - y) = 18

→ 9y - 108 + 9y = 18

→ 18y = 18 + 108

→ 18y = 126

→ y = 126/18

→ y = 7

Putting value of y in eq (1)

➛ x = 12 - y

➛ x = 12 - 7

➛ x = 5

Hence,

Original number is :-

10x + y

10 × 5 + 7

50 + 7

57

▶ Original number = 57

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