Question

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Answer 1

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$\huge{\mathtt{QUESTION}}$

The sum of the digits of a two - digit number is 15 .The no. obtained by interchanging the digits exceeds the given number by 9 . The number is ?

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$\huge{\mathtt{SOLUTION}}$

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

Required number = (10x + y)

NOW , ATQ →

x + y = 15 ---------- equation 1

☯ No. obtained on reversing its digits = (10y + x)

∴ (10y + x) = (10x + y) + 9

⇒ 10y + x – 10x – y = 9

⇒ 9y – 9x = 9

⇒ y – x = 1 --------- equation 2

☯ Now adding equation 1 and equation 2

↪ x + y + y - x = 15 + 1

↪ 2y = 16

↪ y = $\dfrac {16}{2}$

⇒ y = 8

On substituting y = 8 in equation 1 →

↪ x + 8 = 15

⇒ x = (15 – 8) = 7

Number →

↪ (10x + y)

↪ 10 × 7 + 8

↪ 70 + 8

↪78

$\:\:\:\:\:\:\:\:\large{\mathtt{\red{Required\:Number\:=\:78}}}$

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Answer 2

Given :

• The sum of the digits of a two - digit number is 15 .The no. obtained by interchanging the digits exceeds the given number by 9 .

To Find :

• The number is ?

Procedure :

Let the tens digits of required number be x and units digits of required number be y.

Required number = (10x + y)

☢ According to question :

➨ x + y = 15.....(1)

The number obtained by reversing its digit = (10y + x)

Therefore,

➨ (10y + x) = (10x + y) + 9

➨ 10y + x - 10x - y = 9

➨ 9y - 9x = 9

➨ y - x = 1.....(2)

On adding equation (1) and (2) we get :

➨ 2y = 16

➨ y = 16/2

➨ y = 8

On substituting y = 8 in equation (1) we get :

➨ x + 8 = 15

➨ x = 15 - 8

➨ x = 7

★ Number = (10x + y)

★ Number = (10 × 7 + 8)

★ Number = (70 + 8)

★ Number = 78

Hence, the required number is 7.