The sum of a two-digit number and the number | vedclass

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Question

(C) Let the tens digit be $x$ and the units digit be $y$. The original number is $10x + y$.The number obtained by interchanging the digits is $10y + x

Vedclass · Accepted Answer

$64$

Vedclass · Answer

(C) Let the tens digit be $x$ and the units digit be $y$. The original number is $10x + y$.The number obtained by interchanging the digits is $10y + x$.According to the first condition: $(10x + y) + (10y + x) = 110$.$11x + 11y = 110 \implies x + y = 10$ (Equation $1$).According to the second condition: $(10x + y - 10) = 5(x + y) + 4$.Substitute $x + y = 10$ into the equation: $10x + y - 10 = 5(10) + 4$.$10x + y - 10 = 54 \implies 10x + y = 64$ (Equation $2$).From $x + y = 10$ and $10x + y = 64$,we subtract the equations: $(10x + y) - (x + y) = 64 - 10$.$9x = 54 \implies x = 6$.Substituting $x = 6$ into $x + y = 10$,we get $y = 4$.Thus,the original number is $10(6) + 4 = 64$.

The sum of a two-digit number and the number obtained by interchanging its digits is $110$. If the number obtained by subtracting $10$ from the original number exceeds five times the sum of the digits of the original number by $4$,then find the original number.

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