Question

The sum of the digits of a two digits number is 7 . When the digits are reserved then number is decreased by 9.find the number.
and answer is 43​

Answer 1

Given :

• The sum of the digits of a two digits number is 7 .

• When the digits are reserved then number is decreased by 9.

To calculate :

• The original number.

Calculation :

Let the original number be 10a + b.

According to the question :

$\implies$ a + b = 7

[ Since, sum of the digits of a two digits number is 7.]

So,

$\implies$ a + b = 7

$\implies$ b = 7 - a . . . . . . . . . . . ( Eq. 1 )

Also, according to the question :

$\implies$ 10b + a = 10a + b - 9 . . . . . . ( Eq. 2 )

[ Since, when the digits are reserved then number is decreased by 9. ]

Calculating the value of 'a' :

Now, substitute the value of b from the equation 1 in the equation 2 in order to find the value of digit a.

$\implies$ 10b + a = 10a + b - 9

$\implies$ 10 (7-a) + a = 10a + ( 7 - a ) - 9

$\implies$ 70 - 10a + a = 10a + 7 - a - 9

$\implies$ 70 - 9a = 9a - 2

$\implies$ 70 + 2 = 9a + 9a

$\implies$ 72 = 18a

$\implies$ a = $\sf{\dfrac{72}{18}}$

$\implies$ $\boxed{\sf \red{ a = 4} }$

Calculating the value of 'b' :

Now, substitute the value of a the equation 1 in order to find the value of digit b.

$\implies$ b = 7 - a

$\implies$ b = 7 - 4

$\implies$ $\boxed{\sf \red{ b = 3} }$

Calculating the original number :

→ Original number = 10a + b

Substitute the value of a and b.

$\implies$ Original number = 10(4) + 3

$\implies$ Original number = 40 + 3

$\implies$ $\boxed{\sf \green{ Original \: number= 43} }$

Therefore, the number is 43.