Question

the sum of the digits of a two numbers is 7. the number obtained by interchanging the digit exceed the original number by 27. find the number please answer this​

Answer 1

Given information,

The sum of the digits of a two numbers is 7. The number obtained by interchanging the digit exceed the original number by 27. Find the original number.

Let,

◓ Ten's digit of a number be m

◓ One's digit of a number be n

◓ So, original number is (10m + n)

◓ Also, Number obtained after interchanging digits is 10n + m

Now,

It is given to us that the sum of the digits of a two numbers is 7. Therefore;

➻ m + n = 7

➻ m = 7 - nㅤㅤㅤㅤㅤㅤ • • • (1)

Also,

The number obtained by interchanging the digit exceed the original number by 27. Therefore;

➻ Interchanged no. = Original no. + 27

➻ 10n + m = (10m + n) + 27

➻ 10n + m = 10m + n + 27

➻ 10n - n = 10m + 27 - m

➻ 9n = 10m - m + 27

➻ 9n = 9m + 27

➻ 9n = 9(m + 3)

➻ 9n/9 = m + 3

➻ (9 × n)/9 = m + 3

➻ (1 × n)/1 = m + 3

➻ n = m + 3

➻ n - 3 = m

➻ m = n - 3ㅤㅤㅤㅤㅤㅤ • • • (2)

From (1) and (2) we get,

➻ 7 - n = n - 3

➻ 7 + 3 = n + n

➻ 10 = 2n

➻ 10/2 = n

➻ 5 = n

➻ n = 5

• Hence, one's digit of a number is 5.

Putting value of n in (1),

➻ m = 7 - n

➻ m = 7 - 5

➻ m = 2

• Hence, ten's digit of a number is 2.

Now,

➻ Original number = 10m + n

Putting value of m and n,

➻ Original number = 10(2) + 5

➻ Original number = (10 × 2) + 5

➻ Original number = (20) + 5

➻ Original number = 20 + 5

➻ Original number = 25

• Hence, original number is 25.

Verification,

The number obtained by interchanging the digit exceed the original number by 27. Therefore;

➻ Interchanged no. = Original no. + 27

➻ 10n + m = (10m + n) + 27

Putting value of m and n,

➻ 10(5) + 2 = [10(2) + 5] + 27

➻ (10 × 5) + 2 = [(10 × 2) + 5] + 27

➻ (50) + 2 = [(20) + 5] + 27

➻ 50 + 2 = (20 + 5) + 27

➻ 52 = 25 + 27

➻ 52 = 52

➻ LHS = RHS

• Hence, Verified ✔

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Answer 2

Question:-

The sum of the digits of a two numbers is 7. the number obtained by interchanging the digit exceed the original number by 27. find the number.

To Find:-

• 2 digit number.

Given:-

• Sum of the digits is 7.

Solution:-

• New number = Original number + 27
• Let x be ones digit and y be the tens digit.

Original number = 10 × y + x

= 10y + x

On interchanging the digits

New number = 10 × x + y

= 10x + y

Now, x + y = 7 ---------> Equation 1

And, 10x + y = 10y + x + 27

=> 10x – x + y – 10y = 27

=> 9x – 9y = 27

=> x – y = 3 ---------> Equation 2

Adding 1 and 2

2x = 10

=> x = 5

Using x = 5 in Equation 1

5 + y = 7

=> y = 7 – 5

=> y = 2

Original number = 10 × 2 + 5

= 20 + 5

= 25

$\sf\small\red{Hence, the \: required \: number \: is \: 25.}$

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