Question

BA
-
Find the number,
In a two digit number, the sum of the digits is 9. If the digits are reversed, the number is
increased by 9. Find the number.​

Answer 1

let the digit in one place is =X

and the digit in 2nd place is =y

therefore the number is =10y+X

now condition 1

X+y=9.....,.(I)

now condition 2

10x+y=10y+X+9

9x=9y+9

x-y=1......(ii)

solving equations (I) and (ii)...

X=5 and y=4

therefore the original number is =45

Answer 2

$\bold{\Huge{\underline{\boxed{\sf{\orange{ANSWER\::}}}}}}$

$\bold{\Large{\underline{\sf{\green{Given\::}}}}}$

In a two digit number, the sum of the digits is 9. If the digits are reversed the number is increased by 9.

$\bold{\Large{\underline{\rm{\red{To\:find\::}}}}}$

The number.

$\bold{\Large{\underline{\sf{\purple{Explanation\::}}}}}$

Let the ten's digit be R &

Let the one's digit be M

A/q

The sum of the digit is 9;

→ R+M = 9.......................(1)

&

• The original number= 10R + M
• The reversed number= 10M + R

If the digits are reversed the number is increased by 9;

→ 10M + R = 10R + M +9

→ 10M - M +R - 10R = 9

→ 9M - 9R = 9

→ 9(M - R) = 9

→ M - R = $\bold{\cancel{\frac{9}{9} }}$

→ M - R = 1

→ M = 1 + R.............................(2)

Putting the value of M in equation (1), we get;

→ R + 1 + R = 9

→ 2R + 1 = 9

→ 2R = 9 -1

→ 2R = 8

→ R = $\bold{\cancel{\frac{8}{2} }}$

→ R = 4

Putting the value of R in equation (2), we get;

→ M = 1 + 4

→ M = 5

Thus,

The original number is 10(4) + 5

The original number is 40 + 5 = 45