Question

a number consists of 2 digits whose sum is 7.if 45 is added to the number the digits are reversed.Find the number

Answer 1

Given :

• A number consists of 2 digits whose sum is 7.
• If 45 is added to the number the digits are reversed.

To calculate :

• The number.

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Explication of steps :

As the number consists of 2 digits, so let the number be 10x + y. Now according to the question, the sum of its digits is 7. Hence,

$\twoheadrightarrow$⠀⠀x + y = 7

Or, we can say that,

$\twoheadrightarrow$⠀⠀x = 7 ― y

Let this be equation ( 1 ).

Now, according to the question, if 45 is added to the number the digits are reversed. Writing this statement in the form of an equation,

$\twoheadrightarrow$⠀⠀10x + y + 45 = 10y + x

$\twoheadrightarrow$⠀⠀10x ― x + 45 = 10y ― y

$\twoheadrightarrow$⠀⠀9x + 45 = 9y

Substitute the value of x from equation ( 1 ).

$\twoheadrightarrow$⠀⠀9(7 ― y) + 45 = 9y

$\twoheadrightarrow$⠀⠀63 ― 9y + 45 = 9y

$\twoheadrightarrow$⠀⠀108 = 9y + 9y

$\twoheadrightarrow$⠀⠀108 = 18y

$\twoheadrightarrow$⠀⠀6 = y

Now, substitute the value of y in equation ( 1 ) to find the value of x.

$\twoheadrightarrow$⠀⠀x = 7 ― y

$\twoheadrightarrow$⠀⠀x = 7 ― 6

$\twoheadrightarrow$⠀⠀x = 1

Therefore,

• Number = 10x + y = 10(1) + 6 = 16

∴ The number is 16.

Answer 2

UNDERSTANDING CONCEPT :-

• For solving this problem, let x and y be the unit and tens digit of a number respectively. We obtain the first equation by using the sum of digits. Another equation is formed by using the second statement. In this way, we have two variables and two equations, so we can easily obtain the answer.

QUESTION :-

• a number consists of 2 digits whose sum is 7 if 45 is added to the number the digits are reversed.Find the number

GIVEN :-

• number consists of 2 digits

• 45 is added to the number the digits

TO FIND :-

• Find the number = ?

SOLUTION :-

Let the unit digit of a number be x and

tens digit of a number be y. According to the problem statement, the sum of digits of a

two-digit number is 7 This can be mathematically expressed as :-

x + y = 7

and

y = 7 - x

Also, we are given that if 45 is added to

the number, its digits get interchanged. The initial number is 10y + x and the interchanged number is 10x + y.

By using this information,we form

equation (2) as :-

Let the two digit number be

10x + y

A number consists of two digits whose sum is 7

x + y = 7

y = 7 - x

The two digit number 10x + y = 10x + 7 - x = 9x + 7

According to the condition, we get :-

9x + 7 + 45 = 10(7 - x) + x

Replacing the value of y from equation (1)

into equation (2), we get :-

9x + 52 = 70 - 9x

18x = 18

x = 1

y = 7 - 1 = 6

So, the required number

= 10(1) + 6 = 16

ADDITIONAL INFORMATION :-

• steps involved in solving this problem is the manipulation of problem statements into equations. This problem can also be simplified by assuming digits as x and (7 - x) and then proceeding for solution. Substitution must be done carefully after obtaining the general form of numbers.