The sum of two natural numbers is 4923. If we write the number 7 to the right side of the first number and erase the last digit of the
second number, the obtained numbers are equal. Find the initial numbers.
2
Answers
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Given : The sum of two natural numbers is 4923.
If we write the number 7 to the right side of the first number and erase the last digit of the second number, the obtained numbers are equal.
To Find : the initial numbers.
Solution:
Let say initial number are
X and Y
X + Y = 4923
write the number 7 to the right side of the first number
X7 = 10X + 7
erase the last digit of the second number,
= [ Y/10]
10X + 7 = [ Y/10]
so Tens place of Y must be 7
as Y is a maximum 4 digit number hence
[ Y/10] would be max 3 digit number
so X can be max 2 digit numbers
X can not be 1 digit number as then Y would be 3 digit number and it would not be possible to get sum 4923
X = AB where A and B represent digits
Y = AB7C
AB7C
+ AB
__________
4923
7 + A = 2 => A must be 4 of 5 depending upon carry over from last operation
Similarly B can be 8 or 9
from last digit A muse be 4 as its not possible to have carry forward from last operation as B is only digit
Using A = 4
4B7C
+ 4B
__________
4923
C + B must be 13
and B + 1 = 9 => B = 8
=> C = 5
4875
+ 48
__________
4923
initial numbers. were 48 and 4875
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sum of two natural numbers is 4923.
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