Question

: The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is

Answer 1

Answer:

let first digit be x

second digit is 9-x

that is

10(x)+9-x +27 = 10(9-x)+x

10x+9-x+27=90-10x+x

9x+36=90-9x

9x+9x=90-36

18x=54

x=54/18

x=3

therefore the number is 39

Answer 2

☞ To Find :

➝ The original number...

☞ Given :

Let the digits of the number be a and b...

So, the two-digit number is (10a + b) and the number obtained on reversing the digits is (10b + a)...

ATQ

• $\mathtt{a + b = 9}$[Equation...(i)]

• In the question , it said that when 27 is added to the number ,the number is reversed...

so, we get :

$\mathtt{27 + (10a + b) = (10b + a)}$

☞ Concept :

By finding the second equation, and solving it linearly, we can find the value of a & b and the original number...

Equation...(ii)

Given Equation :

$\mathtt{27 + (10a + b) = (10b + a)}$

$\mathtt{\Rightarrow 27 = (10b + a) - (10a + b)}$

$\mathtt{\Rightarrow 27 = 10b + a - 10a - b}$

$\mathtt{\Rightarrow 27 = 9b - 9a}$

Taking the common digit 9 ,we get :

$\mathtt{\Rightarrow 27 = 9(b - a)}$

$\mathtt{\Rightarrow \cancel{\dfrac{27}{9}} = (b - a)}$

$\mathtt{\Rightarrow 3 = b - a}$

Hence , equation...(ii) is :

$\mathtt{-a + b = 3}$

☞ Solution :

Equation...(i)

• $\mathtt{a + b = 9}$

Equation...(ii)

• $\mathtt{-a + b = 3}$

Putting the equation (i) and (ii) together ,we get :

$\mathtt{\cancel{a} + b = 9}$

$\mathtt{\cancel{-a} + b = 3}$

________[By adding]

$\mathtt{2b = 12}$

By Solving it , we get :

$\mathtt{\Rightarrow 2b = 12}$

$\mathtt{\Rightarrow b = \cancel{\dfrac{12}{2}}}$

$\mathtt{\Rightarrow b = 6}$

Putting the value of b in the equation (i) ,we get :

$\mathtt{\Rightarrow a + 6 = 9}$

$\mathtt{\Rightarrow a = 6 - 9}$

$\mathtt{\Rightarrow a = 3}$

Hence , the value of a is 3 and b is 6..

Putting the value of a and b in original number (10a + b) ,we get :

$\mathtt{10a + b}$

$\mathtt{\Rightarrow 10 \times 3 + 6}$

$\mathtt{\Rightarrow 36}$

Hence ,the original number is 36...

Verification :

Sum of digits :

$a + b = 9$

Putting the value of a and b ,we get :

$\Rightarrow 3 + 6 = 9$

$\Rightarrow 9 = 9$

Proved :)

Since ,we know 27 is added to the number ,the number is reversed...

Original no. is 36

and adding 27 in it ,we get :

36 + 27 = 63

and 63 which is the reverse of the original number (36)...

Proved :)