Question

Question !!

The sum of the digits of a two digit number is 12. The number obtained by interchanging the digits exceeds the original number by 36. Find the number ?

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Answer 1

Answer :

• Required original number is 48.

Given :-

• The sum of the digits of a two digit number is 12.
• The number obtained by interchanging the digits exceeds the original number by 36.

To Find :-

• Find the original number ?

Solution :-

• Let the 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 interchanging digits (interchanging number) is (10n + m).

Now,

It is given that the sum of the digits of a two digit number is 12.

Therefore,

➻ m + n = 12

➻ m = 12 - n (Eqⁿ - 1)

Also,

The number obtained by interchanging the digit exceeds the original number by 36.

Therefore,

➻ Interchanged no. = Original no. + 36

➻ 10n + m = (10m + n) + 36

➻ 10n + m = 10m + n + 36

➻ 10n - n = 10m + 36 - m

➻ 9n = 10m - m + 36

➻ 9n = 9m + 36

➻ 9n = 9(m + 4)

➻ 9n/9 = m + 4

➻ (9 × n)/9 = m + 4

➻ (1 + n)/1 = m + 4

➻ n = m + 4

➻ n - 4 = m

➻ m = n - 4 (Eqⁿ - 2)

From (1) and (2) we get,

➻ m = 12 - n = n - 4

➻ 12 - n = n - 4

➻ 12 + n = n + n

➻ 16n = 2n

➻ 16/2 = n

➻ 8/1 = n

➻ 8 = n

➻ n = 8

• Hence, one's digit of a number is 8.

Now,

➻ Original number = 10m + n

• Putting values of m and n,

➻ Original number = 10(4) + 8

➻ Original number = (10 × 4) + 8

➻ Original number = (40) + 8

➻ Original number = 40 + 8

➻ Original number = 48

• Hence, original number is 48.

Verification :-

• The number obtained by interchanging the digit exceeds the original number by 36.

Therefore,

➻ Interchanged no. = Original no. + 36

➻ 10n + m = (10m + n) + 36

• Putting values of m and n,

➻ 10(8) + 4 = [10(4) + 8] + 36

➻ (10 × 8) + 4 = [(10 × 4) × 8] + 36

➻ (80) + 4 = [(40) + 8] + 36

➻ 80 + 4 = (40 + 8) + 36

➻ 84 = 84

➻ LHS = RHS

• Hence, verified.

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Answer 2

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