Question

The sum of the digit of a two digit number is seven if the number formed by reversing the digit is less than Original number by seve original number by 27 what is the Original number

Answer 1

Answer:

Let the two numbers be a and b

Given :

sum of digit of number = 7 ➪ a + b = 7

And ,

the number formed by reversing the digit is less than original number by 27 .

For this , the equation formed will be

$\bf{\pink{\implies{10a+b=10b+a+27}}}$

$\displaystyle{\implies 10a-a+b-10b=27}$

$\displaystyle{\implies 9a-9b=27}$

$\displaystyle{\implies 9(a-b)=27}$

$\displaystyle{\implies a-b =\frac{27}{9} \implies a-b=\frac{\cancel 27}{\cancel 9}}$

✈︎ a-b = 3

✈︎ a=3+b

Now , putting the value of a in equation :

a + b = 7 , we get :

☞︎︎︎ 3 + b + b = 7

☞︎︎︎ 3 + 2b = 7

☞︎︎︎ 2b = 7- 3

☞︎︎︎ 2b = 4

☞︎︎︎ b = 4/2

☞︎︎︎ b = 2

Now, putting the value of b in a + b = 7

a = 7-b

a = 7- 2

a = 5

❥︎ a = 5

❥︎b = 2

Hence, the number formed is

10a+b ➪ 10 × 5 + 2

➪ 52

Answer 2

✪ Question Correction :

The sum of the digit of a two digit number is seven .If the number formed by reversing the digit is less than Original number by 27 .What is the Original number ?

✫ Answer :

Let the two digit number be x and y

According to the given question :

$x + y = 7....(1)$

Let the original number be 10x + y

Now ,

$10x + y - 27 = 10y + x$

$\implies \: 10x - x + y - 10y = 27$

$\implies \: 9x - 9y = 27$

$\implies \: 9(x - y) = 27$

$\implies \: (x - y) = \frac{ \cancel 27}{ \cancel9}$

$\implies \: x - y = 3$

$x = 3 + y.....(2)$

Now , putting the value of equation (2) in equation (1) ,we get :

$(3 + y)+ y = 7$

$\implies \: 3 + 2y = 7$

$\implies \: 2y = 7 - 3$

$\implies \: 2y = 7 - 3$

$\implies \: 2y = 4$

$\implies \: y = \frac{ \cancel4}{ \cancel2}$

➪ y = 2

Our equation was :

x + y = 7

so ,the value of x is

➪ x = 7 - 2

➪ x = 5

and y = 2

Therefore , the given number is $\bf{\red{\underline{52}}}$