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Answers
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★ Question :-
Sum of the digits of a two digit number is 9. When we interchange the digits, it is found that the resulting number is greater than the original number by 63. Find the numbers .
★ Solution :-
Given,
» Sum of the digits = 9
» New number after interchanging the digits = Original number + 63
• Let the unit digit be 'x' and the tens place digit be 'y'. Then,
Now using the given things, we form equations as :-
~ Case I :-
➮ x + y = 9
➮ x = 9 - y ... (i)
~ Case II :-
➮ 10x + y = 10y + x + 62
➮ 10x + y - 10y - x = 62
➮ 9x - 9y = 62 ... (ii)
From equations (i) and equations (ii), we get,
➮ 9(9 - y) - 9y = 63
➮ 81 - 9y - 9y = 63
➮ -18y = 62 - 81
➮ -18y = -18
➮ 18y = 18
➮ y = 1
• So, tens place digit = y = 1
Now using equation (i) and value of y, we get,
➮ x = 9 - y
➮ x = 9 - 1
➮ x = 8
• So, unit place digit = x = 8
Then, using bot values of x and y, we get,
»Original number = 10y + x = 10(1) + 8 = 18
» New Number = 10x + y = 10(8) + 1 = 81
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For verification, we must simply apply the values we got into the equations we formed.
~Case I :-
:⟹ x + y = 9
:⟹ 8 + 1 = 9
:⟹ 9 = 9
Clearly, LHS = RHS
Here the condition satisfies, so our answer is correct.
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• Linear Equations in One Variable is the form of equations where we use to find the value of one variable using constant terms.
• Linear Equations are the form of linear polynomial with degree is equal to 1.