The sum of a two digit number and the number formed by interchanging t

1.	The sum of a two digit number and the number formed by interchanging the digits is 110. If 10 is subtracted from the original number the new number is 4 more than 5 times the sum of its digits in the original number. Find the original two digit number
Answer» Answer: 64 Step-by-step explanation: $\textbf{Let\: the\: digit\: at\: ones\:= \:M}$ and $\textbf{Digit \:at \:tens \:= \:N}$ ☞ The sum of two digit number and the number formed by interchanging the digits is 110. Let the original number be $\underline{\bold{<klux>10N</klux>\: +\: M}}$ Number formed by reversing the digit is $\underline{\bold{10M\:+\:N}}$ 10N + M + 10M + N = 110 ________ [AS SAID IN QUESTION] 11N + 11M = 110 11 (N + M) = 110 N + M = 10 N = 10 - M _______(eq 1) ☞ If 10 is SUBTRACTED from original number i.e. 10N + M 10N + M - 10 ☞ The new number is (equal to) 4 more than 5 times the sum of it's digit in the original number. 5(M + N) + 4 • A.T.Q. 10N + M - 10 = 5(M + N) + 4 10N + M - 10 = 5M + 5N + 4 10N - 5N + M - 5M = 4 + 10 5N - 4M = 14 _______(eq 2) 5(10 - M) - 4M = 14 ___[From eq 1] 50 - 5M - 4M = 14 - 9M = 14 - 50 - 9M = - 36 9M = 36 M = 4 • Put value of M in eq 1 N = 10 - (4) N = 6 ☞ We have to FIND the original two digit numbers. So, the original number is 10N + M 10(6) + 4 64 _______________________________ The original two digit number is 64. ___________________[ANSWER]

The sum of a two digit number and the number formed by interchanging the digits is 110. If 10 is subtracted from the original number the new number is 4 more than 5 times the sum of its digits in the original number. Find the original two digit number

Answer»

Answer:

Step-by-step explanation:

$\textbf{Let\: the\: digit\: at\: ones\:= \:M}$

and $\textbf{Digit \:at \:tens \:= \:N}$

☞ The sum of two digit number and the number formed by interchanging the digits is 110.

Let the original number be $\underline{\bold{<klux>10N</klux>\: +\: M}}$

Number formed by reversing the digit is $\underline{\bold{10M\:+\:N}}$

10N + M + 10M + N = 110

________ [AS SAID IN QUESTION]

11N + 11M = 110

11 (N + M) = 110

N + M = 10

N = 10 - M _______(eq 1)

☞ If 10 is SUBTRACTED from original number i.e. 10N + M

10N + M - 10

☞ The new number is (equal to) 4 more than 5 times the sum of it's digit in the original number.

5(M + N) + 4

• A.T.Q.

10N + M - 10 = 5(M + N) + 4

10N + M - 10 = 5M + 5N + 4

10N - 5N + M - 5M = 4 + 10

5N - 4M = 14 _______(eq 2)

5(10 - M) - 4M = 14 ___[From eq 1]

50 - 5M - 4M = 14

- 9M = 14 - 50

- 9M = - 36

9M = 36

M = 4

• Put value of M in eq 1

N = 10 - (4)

N = 6

☞ We have to FIND the original two digit numbers.

So, the original number is 10N + M

10(6) + 4

_______________________________

The original two digit number is 64.

___________________[ANSWER]