The sum of two digit number and the number formed by interchanging the digit is 132. if 12 is added to the number ,the new number become 5 times the sum of digits ,find the number .
Answers
Step-by-step explanation:
Given :-
The sum of two digit number and the number formed by interchanging the digit is 132. if 12 is added to the number ,the new number become 5 times the sum of digits.
To find :-
Find the number?
Solution :-
Let the digit at tens place in the two digit number be X
The place value of X = 10×X = 10X
Let the digit at ones place in the two digit number be Y
The place value of Y = 1×Y = Y
The two digit number = 10X+Y
The two digit number obtained by reversing the digits = 10Y+X
Given that
The sum of two digit number and the number formed by interchanging the digit = 132
=> (10X+Y) +(10Y+X) = 132
=> 10X+Y+10Y+X = 132
=> (10X+X) +(10Y+Y) = 132
=> 11X+11Y = 132
=> 11(X+Y) = 132
=> X+Y = 132/11
=> X+Y =12----------------(1)
and
X = 12-Y------------(2)
and
If 12 is added to the number ,the new number become 5 times the sum of digits
=>(10X+Y)+12 = 5(X+Y)
=> 10X+Y+12 = 5X+5Y
=> 10X+Y+12-5X-5Y = 0
=> (10X-5X)+(Y-5Y) +12 = 0
=> 5X-4Y+12 = 0
=> 5(12-Y)-4Y +12 = 0
=> 60-5Y-4Y +12 = 0
=> 72-9Y = 0
=> 9Y = 72
=> Y = 72/9
=> Y = 8
On Substituting the value of Y in (2)
=> X = 12-8
=> X = 4
The digit at tens place = 4
The digit at ones place = 8
The number = 48
Answer:-
The required two digit number for the given problem is 48
Check:-
The original number = 48
The number obtained by reversing the digits = 84
If 12 is added to 48 then
=> 48+12
=> 60
Sum of the digit = 5+7 = 12
5× Sum of the digits = 5×12 = 60
If 12 is added to the number ,the new number become 5 times the sum of digits
48+84 = 132
The sum of two digit number and the number formed by interchanging the digit = 132
Verified the given relations in the given problem