Question

the sum of a two digit number and the no. obtained by reversing the digits is 66.if the digits differ by 2 . find the number ​

Answer 1

Answer:

the number is 42

Step-by-step explanation:

let the numbers be 10x+y

10x+y+10y+x=66

11x+11y=66

11(x+y)=66

x+y=66/11

x+  y=   6

-x-(+)y=(-)2

2y=4

y=2

x=4

Answer 2

Complete Question :

• The sum of two digit no and number obtained by reversing the digit is 66.if the digits of the no differ by 2 then find the number?

$\rule{200}1$

Given,

• The sum of two digit no and number obtained by reversing the digit is 66.
• The Digits of the number difference by 2.

To Find,

• The Two Digit Number

Solution,

⇒Suppose the digit at the ten's place be a

And,Suppose the digit at the one's place be b

Therefore,

• Two Digit Number = 10a + b
• Reversing Number = 10b + a

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• The sum of two digit no and number obtained by reversing the digit is 66.

$\implies \sf{10a + b + 10b + a = 66}$

$\implies \sf{11a + 11b = 66}$

$\implies \sf{11(a + b) = 66}$

$\implies \sf{a + b = \dfrac{66}{11}}$

$\implies \sf{a + b = 6}$        1)

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• The Digit of Number is Difference by 2.

$\implies \sf{a - b = 2}$       2)

Now Add both Equation :-

$\implies \sf{a + b + a - b = 6 + 2}$

$\implies \sf{2a = 8}$

$\implies \sf{a = \dfrac{8}{2}}$

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

Now Put the Value of a in First Condition :-

$\implies \sf{a + b = 6}$

$\implies \sf{4 + b = 6}$

$\implies \sf{b = 6 - 4}$

$\implies \boxed{\sf{b = 2}}$

Therefore,

$\boxed{\bold{\red{Two \ Digit \ Number = 10a + b = 10(4) + 2 = 42}}}$

$\rule{200}2$