the sum of a two digit number and the number formed by interchanging its digits is 110. if 10 is subtracted from the first number new number is 4 more than 5 times the sum of its digits in the first number. find the first number
please give written solution
Answers
Answer:
64
Step-by-step explanation:
Let the digit at units place be 'x' and the digit at ten's place be y.
Thus, the number formed = 10y + x. ---- (*)
Number formed by interchanging the digits = 10x + y.
(i)
Sum of a two digit number and interchanging digits is 110.
⇒ (10y + x) + (10x + y) = 110
⇒ 10y + x + 10x + y = 110
⇒ 11x + 11y = 110
⇒ x + y = 10
(ii)
10 is subtracted from 1st number and new number is 4 more than 5
⇒ (10y + x) - 10 = 5(x + y) + 4
⇒ 10y + x - 10 = 5x + 5y + 4
⇒ -4x + 5y - 14 = 0
⇒ 4x - 5y = -14
On solving (i) * 4 & (ii), we get
⇒ 4x + 4y = 40
⇒ 4x - 5y = -14
---------------------
9y = 54
y = 6
Substitute y = 6 in (ii), we get
⇒ 4x - 5y = -14
⇒ 4x - 30 = -14
⇒ x = 4
Substitute x = 4 and y = 6 in (*), we get
⇒ 10y + x
⇒ 10(6) + 4
⇒ 64
Therefore, the number formed is 64.
Hope it helps!
Answer:
64
Step-by-step explanation:
Digit at ones place = y
Digit at tens place = x
So, original number = 10x + y.
Also, Number formed by reversing the digits =10y + x.
According to the given Question,
10x + y + 10y + x = 110
11x + 11y = 110
11 (x + y ) = 110
x + y = 10
x = 10 - y ----- (i)
According to the given condition,
10x + y - 10 = 5(x + y) + 4
10x + y -10 = 5x + 5y + 4
10x -5x + y - 5y = 10 +4
5x - 4y = 14 ---- (ii)
We have to substitute the value of x in (ii)
5x - 4y = 14
5 * (10 - y) - 4y = 14
50 - 5y - 4y = 14
50 - 9y = 14
-9y = -36
y = 4
Substitute y = 4 in (i)
x = 10 - y
x = 10 - 4
x = 6
Thus, original number = 10x + y = 64.
Hope it helps you!