Number System Examples with Explanation:
Model 1:
Example 1:
Explanation: Answer is 58.
Shortcut 1: Follow the Options, if any one of the option is satisfying our requirement choose that option. otherwise follow the tradition method.
in the given options option 3 and 4 are satisfying the condition(it means sum of the digits is 13) but answer is either option 3 or 4. Now here you can think in smart way.. then automatically you can find answer easily and quickly.
After interchanging the number is less than the original number. now go to options, here the approximation answer is either option 3 or option 4.
apply logic for both option 3 and 4.
From option 3 is 85
After interchanging 85 we will get 58, the interchanging number 58 is less than 85 by 27. It's not satisfy the condition then immediately choose option 4. once you get exact answer don't check it for other option. In competitive exams only one option is correct.
Tradition Method for solving Number System Problems:
Note: We can write any two digit number in the form of (10x + y) when 'xy' is the any two digit number.
Now we assume 'xy' is the two digit number and 'yx' is the interchanging number.
we can write xy is in the form of 10x + y.
Similarly yx is in the form of 10y + x.
From the given question the interchanging number is more than 27 by original number.
it means
xy = yx -27
10x + y = 10y + x - 27
9y - 9x = 27 ⇒ y -x = 27 ÷ 9 = 3
y - x = 3 -------------> equation 1
from the given data the sum of digits is 13
x + y = 13 --------------> equation 2
solve equation 1 and equation 2
x + y = 13
-x + y = 03
2y = 16 ⇒ y = 8
y is substitute in equation 1 or equation 2 then we get 'x' value
x = 8.
So the original number is 'xy' where x = 5 and y = 8
xy =58.
Explanation: Answer is 58.
Shortcut 1: Follow the Options, if any one of the option is satisfying our requirement choose that option. otherwise follow the tradition method.
in the given options option 3 and 4 are satisfying the condition(it means sum of the digits is 13) but answer is either option 3 or 4. Now here you can think in smart way.. then automatically you can find answer easily and quickly.
After interchanging the number is less than the original number. now go to options, here the approximation answer is either option 3 or option 4.
apply logic for both option 3 and 4.
From option 3 is 85
After interchanging 85 we will get 58, the interchanging number 58 is less than 85 by 27. It's not satisfy the condition then immediately choose option 4. once you get exact answer don't check it for other option. In competitive exams only one option is correct.
Tradition Method for solving Number System Problems:
Note: We can write any two digit number in the form of (10x + y) when 'xy' is the any two digit number.
Now we assume 'xy' is the two digit number and 'yx' is the interchanging number.
we can write xy is in the form of 10x + y.
Similarly yx is in the form of 10y + x.
From the given question the interchanging number is more than 27 by original number.
it means
xy = yx -27
10x + y = 10y + x - 27
9y - 9x = 27 ⇒ y -x = 27 ÷ 9 = 3
y - x = 3 -------------> equation 1
from the given data the sum of digits is 13
x + y = 13 --------------> equation 2
solve equation 1 and equation 2
x + y = 13
-x + y = 03
2y = 16 ⇒ y = 8
y is substitute in equation 1 or equation 2 then we get 'x' value
x = 8.
So the original number is 'xy' where x = 5 and y = 8
xy =58.
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