Question

2. 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.​

Answer 1

Answer:

• Required original number is 48.

Explanation:

Given information,

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 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 (interchanged 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 ㅤㅤㅤㅤ• • • (1)

Also,

The number obtained by interchanging the digits 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 ㅤㅤㅤㅤ• • • (2)

From (1) and (2) we get,

➻ m = 12 - n = n - 4

➻ 12 - n = n - 4

➻ 12 + 4 = n + n

➻ 16 = 2n

➻ 16/2 = n

➻ 8/1 = n

➻ 8 = n

➻ n = 8

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

Putting value of n in (2),

➻ m = n - 4

➻ m = 8 - 4

➻ m = 4

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

Now,

➻ Original number = 10m + n

Putting value 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 digits exceeds the original number by 36. Therefore;

➻ Interchanged no. = Original no. + 36

➻ 10n + m = (10m + n) + 36

Putting value 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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