Question

the sum of the digits of a two-digit number is 7.if the digits are reversed ,the number formed is 9 less than the original number.Find the number​

Answer 1

Answer:

• Original number is 43.

Explanation:

It is given that the sum of the digits of a two-digit number is 7. If the digits are reversed, the number formed is 9 less than the original number.

We have to find the original number.

• Let ten's digit of a number be m
• And one's digit of a number be n
• So, original number is (10m + n)
• Also, number obtained after reversing digits (reversed number) is (10n + m)

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Now, we know that the sum of the digits of a two-digit number is 7. Therefore;

➻ m + n = 7

➻ m = 7 - n ㅤㅤㅤ• • • (1)

Again, we know that if the digits are reversed, the number formed is 9 less than the original number. Therefore;

➻ Reversed no. = Original no. - 9

➻ 10n + m = (10m + n) - 9

➻ 10n + m = 10m + n - 9

➻ 10n - n = 10m - m - 9

➻ 9n = 9m - 9

➻ 9n = 9(m - 1)

➻ 9n/9 = m - 1

➻ n = m - 1

➻ n + 1 = m

➻ m = n + 1 ㅤㅤㅤ• • • (2)

From (1) and (2) we get,

➻ 7 - n = n + 1

➻ - n - n = 1 - 7

➻ - 2n = - 6

➻ 2n = 6

➻ n = 6/2

➻ n = 3

• Hence, one's digit of number is 3.

Putting value of n in (2),

➻ m = n + 1

➻ m = 3 + 1

➻ m = 4

• Hence, ten's digit of a number is 4.

Now, let's find the original number,

➻ Original number = 10m + n

Putting value of m and n,

➻ Original number = 10(4) + 3

➻ Original number = (10 × 4) + 3

➻ Original number = 40 + 3

➻ Original number = 43

• Hence, original number is 43.

Verification:

We know that, if the digits are reversed, the number formed is 9 less than the original number. Therefore;

➻ Reversed no. = Original no. - 9

➻ 10n + m = (10m + n) - 9

➻ 10n + m = 10m + n - 9

Putting value of m and n,

➻ 10(3) + 4 = 10(4) + 3 - 9

➻ (10 × 3) + 4 = (10 × 4) - 6

➻ 30 + 4 = 40 - 6

➻ 34 = 34

➻ LHS = RHS

• Hence, verified.

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Answer 2

Given:-

↦The sum of the digits of a two-digit number is 7.

↦If the digits are reversed, the number formed is 9 less than the original number.

To find:-

The original number.

Solution:-

Let the first digit of the number be n and the second digit of the number be m.

⇛ Original number is (10m + n)

⇛ Reversed number is (10n + m)

The sum of the digits of a two-digit number is 7. [ Given ]

m + n = 7

m = 7 - n _____ (1)

If the digits are reversed, the number formed is 9 less than the original number. [ Given ]

⇒Reversed no. = Original no. - 9

⇒10n + m = (10m + n) - 9

⇒10n + m = 10m + n - 9

⇒10n - n = 10m - m - 9

⇒9n = 9m - 9

⇒9n = 9(m - 1)

⇒9n/9 = m - 1

⇒n = m - 1

⇒n + 1 = m

⇒m = n + 1 _____ (2)

From (1) and (2),

7 - n = n + 1

- n - n = 1 - 7

- 2n = - 6

2n = 6

n = 6/2

n = 3

Therefore, the first digit of the number is 3.

Substituting the value of n in the equation (2),

m = n + 1

m = 3 + 1

m = 4

Therefore, te second digit of the number is 4.

Thus,

Original number = 10m + n

Substituting the value of m and n, we get,

Original number = 10(4) + 3

= (10 × 4) + 3

= 40 + 3

= 43

Hence, the original number is 43.