If the sum of two digits number and the number formed after interchanging the digits is 110 then find the number if the difference of their digits is 4
Soln Date / Update:-08-Aug-2025 01:12PM
Solution:-
Exrecise - 2 ( B ) Real Numbers
Q-20. If the sum of two digits number and the number formed after interchanging the digits is 110 then find the number if the difference of their digits is 4.
Solution:-
Let the two digits x and y
Unit place number = X
Tens place number = 10Y
Then, Make Original Number = 10Y + X -------(i)
After interchanging the digits ,
Unit place number = Y
Tens place number = 10X
Then, Make nterchanging number = 10X + Y ----(ii)
A/Q, sum of original number + interchanging number = 110
Or, ( 10Y + X ) + ( 10X + Y ) 110
Or, 10Y + X + 10X + Y = 110
Or, 11X + 11Y = 110
Or, 11( X + Y ) 110
Or, X + Y = 110 / 11
X + Y = 10 ------(iii)
Difference of their digits = 4 [Given in Question]
X - Y = 4 ------(iv)
Sum Equation (iii) And Equation (iv)
2X = 14
X = 7
Putting the value of X in Eq(iii)
X + Y = 10
7 + Y = 10
Y = 10 - 7
Y = 3
Now, Make Possible number,
10X + Y 10Y + X
10 * 3 + 7 =10 * 7 + 3
30 + 7 = 70 + 3
= 37 Ans. = 73 Ans.
Solution image given Below,
