Question

The sum of a two digit number and a number formed by the reversing the order of digit is 66if the two digits differ by 2 find the number.How many such numbers are there?

Answer 1

Given :

• Sum of a two digit number and a number formed by the reversing = 66
• Digits of the number differ by 2

To Find :

• The number
• and How many such numbers are there

Solution:

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

⇒Number = 10x+ y

According to the Question :

Number + Reversed number = 66

$\sf \implies(10x + y) + (10y + x) = 66$

$\sf \implies10x + 10y + y + x = 66$

$\sf \implies11x + 11y = 66$

$\sf \implies11(x + y) = 66$

$\sf \implies \: x + y = 6...(1)$

and it is also given that

Digits of the no. differ by 2

$\sf \: x - y = 2..(2)$

$\sf \: or \: y - x = 2..(3)$

Solving (1) and (2)

Add equations (1) and (2)

$\implies\sf \: x + y + x - y = 6 + 2$

$\sf \implies2x = 8$

$\sf \implies \: x = 4$

Put x = 4 in Equation (1)

$\sf \implies4 + y = 6$

$\sf \implies \: y = 2$

Hence,Number = 10x+y = 42

Solving (1) and (3)

Add equations (1) and (3)

$\sf \implies \: x + y + y - x = 6 + 2$

$\sf \implies \: 2y = 8$

$\sf \implies \: y = 4$

put y = 4 in Equation (1)

$\sf \implies \: x + 4 = 6$

$\sf \implies \: x = 2$

Hence ,Number = 10x+ y = 24

Therefore ,Two digit numbers are 24 and 42 .

Answer 2

ANSWER:

Given

Sum of 2-digit number and the number formed by reversing = 0

Digits of number differ by 2

TO FIND:

The number

And how many such numbers are there

SOLUTION:

Let the no. at unit place be y & the no. at tens place be x

→ Number = 10x + y

→ Reversed number = 10y + x

____________________________

➳ Number + Reversed number = 66

➳ 10x + y + 10y + x = 66

➳ 11x + 11y = 66

➳ 11(x + y) = 66

➳ x + y = 66/11

➳ x + y = 6

Assuming as equation 1

Given , Digits differ by 2

➱ x - y = 2 _______ ( 2 )

(or)

➱ y - x = 2 _______ ( 3 )

Equation 1 + Equation 2

➱ x + y + x - y = 6 + 2

➱ 2x = 8

➱ x = 4

Substituting x = 4 in equation 1

→ 4 + y = 6

→ y = 6 - 4

→ y = 2

Hence, number = 10x + y = 42

Adding equation 1 + equation 2

→ x + y + y - x = 6 + 2

→ 2y = 8

→ y = 4

Substituting y = 4 in equation 1

→ x + 4 = 6

→ x = 2

Hence, number = 10x + y = 24

Therefore Two digit numbers are 24 & 42