The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45. What is the number?
Answers
Given : The sum of digits of a two digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result is 45.
Solution:
Let the digit in the unit's place be x and the digit at the tens place be y.
Number = 10y + x
The number obtained by reversing the order of the digits is = 10x + y
ATQ :
Condition : 1
x + y = 13 ………….(1)
Condition : 2
(10x + y) - (10y + x) = 45
10x + y - 10y - x = 45
9x - 9y = 45
9(x – y) = 45
(x – y) = 45/9
x - y = 5 ………..(2)
On adding equations (1) and (2) :
x + y = 13
x - y = 5
-----------------
2x = 18
x = 18/2
x = 9
On putting x = 9 in eq (1) we obtain :
x + y = 13
9 + y = 13
y = 13 – 9
y = 4
Now, Number = 10y + x = 10 × 4 + 9 = 49
Hence, the number is 49.
Hope this answer will help you…
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Answer:
Step-by-step explanation:
Solution :-
Let the tens place digit be x
And the ones place digit be y.
Number = 10x + y
Changed Number = 10y + x
According to the Question,
⇒ x + y = 13 .... (i)
⇒ 10y + x − 10x - y = 45
⇒ 9(y - x) = 45
⇒ y - x = 5 ..... (ii)
Solving Eq (i) & (ii), we get
⇒ 2y = 18
⇒ y = 18/2
⇒ y = 9
Putting y's value in Eq (i), we get
⇒ x + y = 13
⇒ x = 4
Hence, the required number is 49.