Question

The sum of the digits of a two-digit number is ten. Twice its tens digit is one less than its units digit. Find the two-digit number.

Answer 1

Step-by-step explanation:

GVEN :-

• Sum of two digit number is ten .
• Twice the tens digit is one less than unit digit

SOLUTION :-

• Let unit digit be. x and tens digit is y

• Hence the two digits number = (10y + x)

According To the First case(i) :-

$\sf \: Sum \: of \: digits \: of \: 2 \: digit \: number \: =10$

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

$\sf \implies \: \: y = 10 - x \: \: \: \: \: \: ..(i)$

Second Case ( ii )

$\sf \: Twice \: the \: tens \: digit \: is \: one \: \: less \: than \: its \: \\ \: \ \sf \: \: units \: digit. \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

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

$\implies \sf \: 2(10 - x) = x - 1$

$\implies \sf \: 20 -2 x = x - 1$

$\sf \implies \: 2x + x = 20 + 1$

$\sf \implies \: 3 x = 21$

$\sf \implies \: x = 7$

Here x = 7 then

y = 10-x = 10 - 7 =3

$\sf \: hence \: no. \: \: is \: (10 \times 3 + 7) \\ \sf \: = 37$