The digits of a two-digit number differ by 3. If digits are interchanged and the resulting number is added to the original number, we get 121. Find the original number.
Answers
Answer:
74
here it is not given that which digit is greater whether ones place or tens place , therefore answer may also be 47
Step-by-step explanation:
Let the original number be xy
value = 10x +y
reversed number = 10y +x
given that x-y = 3
now add the original number and reversed number
11x + 11y = 121
x+y = 11
and we know
x-y= 3
x= 7
y= 4
number is 74
Let us take the two digit number such that the digit in the units place is x. The digit
in the tens place differs from x by 3. Let us take it as x + 3. So the two-digit number is
10 (x + 3) + x = 10x + 30 + x = 11x + 30.
With interchange of digits, the resulting two-digit number will be 10x + (x + 3) = 11x + 3
If we add these two two-digit numbers, their sum is
(11x + 30) + (11x + 3) = 11x + 11x + 30 + 3 = 22x + 33
It is given that the sum is 121.
Therefore, 22x + 33 = 121
22x = 121 – 33
22x = 88
x=4
The units digit is 4 and therefore the tens digit is 4 + 3 = 7.
Hence, the number is 74 or 47.