Sum of digits of a two digit number is 8. If the number obtained by reversing the digits is 18 more than the original number, then the original number is______
Answers
Answer:
okay.
sum of two digits be a+ b. = 8.
reversing the digits is 18.
original number is = 18+8
=26.
answer - The original number is 35.
Step-by-step explanation:
Let the digits in tens place be x and the digits in unit place be y.
therefore, the original two digit number is 10x+y.
Given that sum of digits of a two digit number is 8
= x + y = 8 -----------(1)
Given that the new number increases by 18, when the digits are reversed .
= 10y + x = 10x + y + 18
= 10y - y = 10x - x+ 18
= 9y = 9x + 18
= 9y - 9x = 18
= y - x = 2
= x - y = -2 ------------(2)
on solving (1)&(2) equations ,we get
= x+y = 8
= x-y = -2
=2x = 6
= x = 3
Substitute x = 3 in (1), we get
= x+y = 8
= 3+y = 8
= y= 8-3
= y = 5
so, 10x + y = 10(3) + 5 = 35
therefore, the original number is 35