Question

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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

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Answer 1

Answer :

• Original number is 43.

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 :-

• Find the number ?

Solution :-

• 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).

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

Therefore,

➻ m + n = 7

➻ m = 7 - n (Eqⁿ - 1)

Again, we know that if the digits are reversed, the number is 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 (Eqⁿ - 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 values 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 values 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 is 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 all values 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

$\huge{\mathcal{\underline{\orange{Given}}}}$

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

•Sum of the digits is 9

$\huge{\mathcal{\underline{\orange{To Find }}}}$

•The original Number

$\huge{\mathcal{\underline{\orange{Solution}}}}$

Let one's digit be y

Ten's digit be x

Original Number - 10x+y

Reversed number - 10y+x

Also x+y=7

x=7-y---(1)

According to Question:

10y+x+9=10x+y

Put the value of x

10y +7-y+9=10(7-y)+y

9y+16=70-9y

18y=54

y=3

Put value of y in eq(1)

x=4

Therefore,

Number will be 10×4+3 = 43

Required number is 43