Question

the sum of a two digit number and the number formed by interchanging the digit is 110.if 10 is subtracted from the original number ,the new number is 4 more than 5 times the sum of the digits of the original number.find the original number .​

Answer 1

Answer:

64

Step-by-step explanation:

Let the original number be xy

So, original number = 10x + y

No. formed by interchanging digits = 10y + x

If we add them up:

11x + 11y = 110

so, x+y = 10

If we subtract 10 From og no. i.e

10x + y - 10 = 5(x+y) + 4

10x + y = 5(10) + 4 + 10

10x + y = 64

Answer 2

• Let digit at one's be M and digit at ten's be N.

》 The sum if two digit number and the number formed by interchanging the digits is 110.

Original number = 10N + M

Revered number = 10M + N

According to question,

=> 10N + M + 10M + N = 110

=> 11N + 11M = 110

=> N + M = 10

=> N = 10 - M ____ (eq 1)

》 If 10 is subtracted from the original number, than the new number is 4 more than 5 times the sum of the digits of original number.

According to question,

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

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

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

=> 5N - 4M = 14

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

=> 50 - 5M - 4M = 14

=> - 9M = 14 - 50

=> - 9M = - 36

=> M = 4 (one's digit)

Put value of M in (eq )

=> N = 10 - 4

=> N = 6 (ten's digit)

So,

Original number = 10N + M

=> 10(6) + 4

=> 60 + 4

=> 64

$\underline{\bold{Original\:number\:is\:64}}$

☆ Verification :

From above calculations we have M = 4 and N = 6

Put value of M and N in (eq 1)

=> N = 10 - M

=> 6 = 10 - 4

=> 6 = 6