Question

the sum of two digit number and the number obtained by reversing the digits is 66 if the digits of the number differ by 2 find the number. how many such numbers are there

Answer 1

Hey there !!

Let the ten's digit of the required number be x ,

And, the unit's digit be y .

Now, A/Q

The, the number = ( 10x + y ) .

The number obtained on reversing the digits = ( 10y + x ) .

∴ ( 10y + x ) + ( 10x + y ) = 66.

⇒ 11x + 11y = 66.

⇒ 11( x + y ) = 66.

⇒ x + y = 66/11 .

⇒ x + y = 6 ...........(1) .

Also, x - y = 2..........(2) .

On substracting equation (1) and (2), we get

x + y = 6.

x - y = 2.

-   +     -

________

⇒ 2y = 4 .

⇒ y = 4/2 .

∴ y = 2 .

On putting the value of y in equation (1), we get

x + y = 6.

⇒ x + 2 = 6.

⇒ x = 6 - 2 .

∴ x = 4 .

∵ Number = 10x + y .

= 10 × 4 + 2 .

= 40 + 2.

= 42 .

Hence, the required number is 42 or 24  .

THANKS

#BeBrainly.

Answer 2

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Let the digit in the unit’s place be x and the digit in the tens place be y.

Then, the number = 10y + x

The number obtained by reversing the order of the digits = 10x + y

According to given conditions,

(10y + x) + (10x + y) = 66

⇒ 11(x + y) = 66

⇒ (x + y) = 6

According to second situation, digits differ by 2

So, either x – y = 2 or y – x = 2

Thus , we have the following sets of simuntaneous equations

x + y = 6 …I

x – y = 2 …II

or,

x + y = 6 …III

x – y = 2 …IV

solving equation I and II, we get x = 2 and y = 4

solving equation III and IV , we get x = 4 and y = 2

When x = 4 and y = 2,

Two digit number = (10y + x) = 10(4) + 2 = 42

When x = 2 and y = 4,

Two digit number = (10y + x) = 10(2) + 4 = 24

Hence, the required number is either 24 or 42.