Question

a number consists of two digits, whose sum is 9. If the digits are reversed,the new number is 3/8 of the first number. Find the number.

Answer 1

Given :-

• Sum of digit of two-digit number = 9
• Digits reversed, new number = ⅜ of original number.

To find :-

• Original number

Solution :-

Let the digit at unit's place be m & digit at ten's place be n.

◗ Original number = m + 10n

◗ Reversed number = n + 10m

According to Question :

⇒ m + n = 9

⇒ m = 9 - n ----- Equation (i)

Case 2 :

⇒ n + 10m = ⅜ of (m + 10n)

⇒ n + 10m = (3m + 30n)/8

⇒ 8(n + 10m) = 3m + 30n

⇒ 8n + 80m = 3m + 30n

⇒ 80m - 3m = 30n - 8n

⇒ 77m = 22n

• Putting value from Equation (i)

⇒ 77(9 - n) = 22n

⇒ 693 - 77n = 22n

⇒ 693 = 22n + 77n

⇒ 693 = 99n

⇒ n = 693/99

⇒ n = 7

⋆ Now finding original number :

⇒ Original number = m + 10n

⇒ Original number = (9 - n) + 10(7)

⇒ Original number = (9 - 7) + 70

⇒ Original number = 2 + 70

⇒ Original number = 72

⋆ Now finding reversed number :

⇒ Reversed number = n + 10m

⇒ Reversed number = 7 + 10(2)

⇒ Reversed number = 7 + 20

⇒ Reversed number = 27

Therefore,

Original two-digit number = 72 & reversed number = 27 .

Answer 2

$\tt{\huge{\orange { ------------ }}}$

QUESTION :

$\sf{ \purple{a \: number \: consists \: of \: \: two \: digits, \: whose \: sum \: is \: 9.}} \\ \sf{ \orange{ If \: the \: digits \: are \: reversed, \: the \: new \: number \: is \: }} \: \\ \\ {{ 3/8 \: of \: the \: first \: number. \: Find \: the \: number.}}$

SOLUTION :

Let the original number be 10 x + y

x + y = 9 ....... ( 1 )

=> X = 9 - y

10 y + x = { 3 / 8 } × ( 10x + y )

=> 80 y + 8 x = 30 x + 3 y..... ( 2 )

Solving we get :

X = 7

y = 2

Therefore the { original } number is 72.