The ones digit of a 2-digit number is twice the tens digit. When the number
formed by reversing the digits is added to the original number, the sum is 99. Find
the original number.
Answers
Required Answer:-
Given:
- The ones digit of a two digit number is twice the tens digit.
- When the number formed by reversing thr digits is added to the original number,the sum is 99.
To find:
- The number.
Answer:
- The number is 63.
Solution:
➡Let the ones digit of the number be y.
➡ Let the tens digit of the number be x.
Therefore,
Number = 10x + y
Reversed number = 10y + x.
It's given that,
Ones digit = 2 × tens digit.
➡ y = 2x
➡ 2x - y= 0 ......(i)
Sum of the number + reversed number
= 10x + y + 10y + x
= 11(x + y)
It's given that,
Sum of the number + reversed number = 99
➡ 11(x + y) = 99
➡ x + y = 9 ......(ii)
Adding equations (i) and (ii), we get,
➡ 2x - y + x + y = 0 + 9
➡ 3x = 9
➡ x = 3
Hence, we got the value of x.
Now,
y = 2x
= 6
Hence, the number is
= 10x + y
= 10 × 3 + 6
= 30 + 6
= 36
Verification:
Let us verify our result.
Number = 36
Ones Digit = 6
Tens Digit = 3
Here, we can see that ones digit is twice the tens digit.
Reversed number
= 63
Sum = 63 + 36 = 99 which is true.
Therefore, answer is correct. (Verified)
Answer:
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