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
therefore,
x-y=3
x=y+3
10x+y+10y+x=121
11x+11y=121
x+y=11
now x=y+3
y+3+y=11
2y=8
y=4.
also x=y+3=4+3=7.
therefore the original no. is 47(Ans)
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.
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.
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.