the sum of a number of two digit and the number format by reversing the digit is 110, and the difference of the digit is 6 .find the number
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Let,
The ten's digit of original number be x
The unit's digit of the original number be y
The original number= 10x + y
The Number obtained on reversing the digits = 10y + x
A/q
Add original numbers and reverse number.
So
=>( 10x + y )+( 10y + x )=110 .
=>11x + 11y = 110
=>11( x + y ) = 110
=>x + y = 110/11
x + y = 10...............(i)
x - y = 6 ..................(ii) (given)
On adding equation (i) and (ii), we get
x + y + x - y= 10 +6
2x = 16
X=8
On putting the value of x in equation (i), we get
x + y = 10
8 + y = 10 .
Y = 10 - 8
y= 2
original number = 10x + y .
=>10 × 8 + 2 .
=>80 + 2 .
=>82
Hence,
The required number is 82 .
Hope it helps you
Verified answer
Let be two digit no. 10x+y......bocz tens digit is x n ones digit is y.And its reverse 10y+x
10x+y + 10y+x = 110
11x+11y = 110
11(x+y) = 110............ x+y = 10------------(I)
x-y = 6----------------(ii)
Add eq(I) n (ii)...... We get..
2x=16...........n we get.......... x= 8.....
Put the value of x in eq (i)
x+y = 10
8+y = 10
y = 10-8............... y = 2
So. The two digit no. (Tens digit 8 n ones digit 2)... is 82...... Ans
I hope this is helpful to u..