Question

sum of two digits of a two digit number is 7 if the digits are reversed the new number so formed is increased by 27. Find the number​

Answer 1

Let the -

• one's digit number be N
• ten's digit number be M

$\sf{Number\:=\:10M\:+\:N}$

Sum of two digits of a two digit number is 7. (Means, the sum of one's digit number and ten's digit number is 7)

According to question,

⇒ M + N = 7

⇒ M = 7 - N ...(1)

If the digits are revered. In actual number is 10M + N. If we revered then M will take the place of N and vice-versa.

So,

$\sf{Interchanged\:number\:=\:10\:\times\:N\:+\:M}$

$\rightarrow\:\sf{10N\:+\:M}$

If the digits are reversed the new number so formed is increased by 27.

According to question,

⇒ 10M + N + 27 = 10N + M

⇒ 10M - M + N - 10N = - 27

⇒ 9M - 9N = - 27

Take 9 common from both sides

⇒ 9(M - N) = -9(3)

⇒ M - N = - 3

⇒ 7 - N - N = - 3 [From (1)]

⇒ 7 - 2N = - 3

⇒ - 2N = - 3 - 7

⇒ -2N = - 10

⇒ N = 5

Substitute value of N = 5 in (1)

⇒ M = 7 - 5

⇒ M = 2

$\therefore$ Number = 10M + N

Substitute value of M = 2 and N = 5 above

⇒ 10(2) + 5

⇒ 20 + 5

⇒ 25

•°• Number is 25.

___________________

Verification :-

From above we have -

• ten's digit number = M = 2
• one's digit number = N = 5

Substitute value of M and N in eq (1)

→ 5 = 7 - 2

→ 5 = 5

Answer 2

Answer:

The original number is 25.

Step-by-step explanation:

Let the unit digit be y and tens digit be x.

Given :

◐ Sum of the digits of the number or the the sum of x and y is 7.

◐ By reversing the digits, the new number which is formed is 27 more than the original.

As we know,

Any two digit no. can be written in the form of 10a + b ( ab ).

So,

The number is 10x + y... (original)

And its reversed form is 10y + x.

since x + y = 7

y = 7 - x ___ ( I )

Solution :

[ 27 is added in the original to balance the equation ]

(10x + y) + 27 = (10y + x)___( II )

[Substituting the value of equation i in equation ii]

10x + (7 - x) + 27 = 10(7 - x) + x

9x + 34 = 70 - 10x + x

9x + 34 = 70 - 9x

18x = 36

x = 2

We got our tens digit as 2 (x)

And acc. to the equation 1 y = 7 - x

so our unit digit is 5.

So, the number is 25.