18) The sum of two digit number is 15. If the number obtained by
reversing the order of digit is less than the original number by 27.
Find the original number.
Answers
Answer: 96
Step-by-step explanation:
let the tens place digit be x
let the units place digit be y
therefore, the number = 10x + y
the number is reversed .
now , the ten's place digit is y
the unit's place digit is x
therefore, the number becomes = 10y + x
according to the question,
x + y = 15 -------------- eqn. 1
again,
(10x+y)-(10y+x)=27
⇒10x+y-10y-x=27
⇒9x-9y=27
⇒9(x-y)=9x3
⇒x-y=3 -------------- eqn. 2
using elimination method.
from eqn. 1 and eqn. 2 we get...
x + y = 15
x - y = 3
____________
2x = 18
⇒ x = 9
putting x = 9 in eqn. 1
x + y = 15
9 + y = 15
y = 15 - 9
y = 6
therefore the original number is = 10x9 +6 =96