Question

exceeds the sum of its digits by 18. Find the number.
13. A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to the
number, its digits are reversed. Find the number.
4. The sum of the digits of a two-digit number is 15. The number obtained by interchanging its​

Answer 1

Step-by-step explanation:

SOLUTION :-

Let unit digit of number =x

then tenths digit = y

Now

Two digits no. = 10y+x

$\sf \: According \: \: to \: \: Question$

Two digits no. = 4(Sum of the digits )+3 ......(i)

$\sf \: 10y +x = 4(x + y) + 3 \\ \implies \: \sf10y + x = 4x + 4y + 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: \sf \: 10y - 4y - 4x + x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: \sf6y - 3x = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: \sf3 \{2y - x \} = 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: \sf2y - x = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\implies \sf \: x = 2y - 1 \: \: \: \: \: \: \: \: \: .......(ii)$

When digits are reversed then new no. =10x+y......(iii)

$\sf \large \green{ \sf \: Case \: ii}$

18 is added to the no. =Reverse the digits

$\sf \:( 10y + x) + 18 = 10x + y$

$\implies \sf \: 10y + x + 18 = 10x + y$

$\implies \sf \: 10y - y + 18 = 10x - x$

$\implies \sf \: 9y + 18 = 9x$

$\implies \sf \: y + 2 = x$

$\sf \: put \: the \: value \: of \: x$

$\implies \sf \: y + 2 = 2y - 1$

$\implies \sf \: 2y - y = 2 + 1$

$\implies \sf \: y = 3$

$\sf \: putting \: the \: value \: in \: e. \: (ii)$

$\sf \: x = 2y - 1$

$\implies \sf \: x = 2(3) - 1$

$\implies \sf \: x = 6 - 1$

$\implies \sf \: x = 5$

Here unit digit is x= 5 and tenth digit is y=3

$\sf \: number \: is \: = 10y + x \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 10 \times 3 + 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf = 30 + 5 \\ \: \: \: \: \: \sf= 35$