Question

sum of two digited 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

${\huge{\overbrace{\underbrace{\purple{SoluTion }}}}}$

Let the 1st digit be x and 2nd digit be y

First no. = 10x + y

When the digits are reversed,

It becomes = 10y + x

Then,

$\mathrm {(10x + y) + (10y + x) = 66}\\\\\\\mathrm {11(x + y) = 66}\\\\\\\mathrm {x + y = 6 \ .....(1)}$

According to the question, digits differ by 2

$\mathrm {x - y = 2 \ ..... (2)}\\\\\\\mathrm {Or \ y - x = 2 \ ..... (3)}$

If x - y = 2, then, {By elimination, solving (1) and (2)}

x = 4

y = 2

∴ Number = 42

If y – x = 2, then, {By elimination, solving (1) and (3)}

x = 2

y = 4

∴ Number = 24

There are two such numbers = 42 and 24

Answer 2

Step-by-step explanation:

$\bf \: Question \:$

sum of two digited 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

$\bf \: solution$

GIVEN

sum of two digited number and the number obtained by reversing the digits is 66.If the digits of the number differ by 2.

$\bf \: Find \: it$

$\bf \red{how \: many \: such \:\: number\: are \: there }$

$\bf \: Let \: the \: two \: digit \: be \: x \: and \: y$

∴ Number (2−digit) =10×x+y

Sum of 2−digit and reverse of it

$\bf \: given$

$\bf</p><p>10x+y+10y+x=66 \\ \bf</p><p></p><p>∴x+y=6 \red{.......equation \: 1 }$

Digits differ by 2

$\bf \: ∴ \: x - y=2 ..... \red{equation \: 2 }\\ \\ </p><p></p><p> \bf \: On \: adding, \\ \\ </p><p> \bf \: 2x=8 \\ \bf \: x = \frac{8}{2} \\ \\ </p><p> \bf \: \red{x=4 }\\ \\ </p><p> \bf∴ \red{y=2 }\\ \\ </p><p> \bf \: or, x+y=6 \: From \: ..1 \: equation</p><p>$

$\bf \red{and} \\ \\ \bf \: y - x=2 \: From \: 2 \: equation \\ </p><p></p><p> \bf \red{On \: adding:} \\ </p><p> \bf \: 2y=8 \\ \\ \bf \: y = \frac{8}{2} \\ \bf \red{</p><p>y=4} \\ \\ \bf \red{</p><p>x=2} \\ \bf \: ∴x - y=2.. \red{ equation \: 2}</p><p></p><p></p><p></p><p></p><p></p><p>\\ \bf \: ∴ Two \: digit \: numbers \: are: \red{\: 42 \: and \: 24.}$