The sum of a two-digit number and the number formed by reversing the order of digit is 66. If the two digits differ by 2, find the number. How many such numbers are there?
Answers
Given : The sum of a two-digit number and the number formed by reversing the order of digit is 66. If the two digits differ by 2, find the number.
Solution:
Let the digit in the unit's place be x and the digit at the tens place be y.
Number = 10y + x
The number obtained by reversing the order of the digits is = 10x + y
ATQ :
Condition : 1
x - y = ±2 ………….(1)
Condition : 2
(10x + y) + (10y + x) = 66
10x + y + 10y + x = 66
11x + 11y = 66
11(x + y) = 66
x + y = 66/11
x + y = 6 ………….(2)
Thus , we obtain two following systems of linear equations :
(i) x - y = 2 ………….(3)
x + y = 6………….(4)
(ii) x – y = -2………….(5)
x + y = 6………….(6)
(i) First, we solve eq. (3) & (4) by adding :
x - y = 2
x + y = 6
----------------
2x = 8
x = 8/2
x = 4
On putting x = 4 in eq (3) we obtain :
x - y = 2
4 - y = 2
y = 4 - 2
y = 2
Number = 10y + x = 10 × 2 + 4 = 20 + 4 = 24
Hence, the number is 24.
(ii) Now, we solve eq. (5) & (6) by adding :
x - y = -2
x + y = 6
---------------
2x = 4
x = 4/2
x = 2
On putting x = 2 in eq (5) we obtain :
x - y = - 2
2 - y = - 2
-y = -2 - 2
-y = - 4
y = 4
Number = 10y + x = 10 × 4 + 2 = 40 + 2 = 42
Hence, the number is 24 and 42.
Hope this answer will help you…
Some more questions from this chapter :
The sum of digits of a two number is 15. The number obtained by reversing the order of digits of the given number exceeds the given number by 9. Find the given number.
https://brainly.in/question/17175907
A number consist of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.
https://brainly.in/question/17174191
Step-by-step explanation:
NUMBER IS 42 And 24.
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