Question

5. બે અંકની એક સંખ્યાના અંકોનો તફાવત 2 છે. તે સંખ્યા તથા
તેના અંકો અદલબદલ કરવાથી મળતી સંખ્યાનો સરવાળો
132 થાય છે. તે સંખ્યા / સંખ્યાઓ શોધો.​

Answer 1

Given:

The two digits differ by 2.

The sum of a two-digit number and the number obtained by interchanging the digits is 132.

To find:

The numbers

Solution:

Let's assume,

"x" → represents the ten's digit

"y" → represents the one's digit

So,

The 2-digit number = 10x + y

After reversing, the new number so obtained = 10y + x

Since the two differ by 2, so we can form the equation as:

$x - y = 2$ ...... (i)

Also, the sum of a two-digit number and the number obtained by interchanging the digits is 132, so we can form the equation as:

$10x + y + 10y + x = 132$

$\implies 11x + 11y = 132$

$\implies x + y = \frac{132}{11}$

$\implies x + y = 12$ ...... (ii)

On adding eq. (i) & (ii), we get

x + y = 12

x - y = 2

----------------

2x = 14

----------------

∴ x = $\frac{14}{2}$ = 7

On substituting the value of x in eq. (i), we get

x - y = 2

⇒ 7 - y = 2

⇒ y = 7 - 2

⇒ y = 5

Thus,

The 2-digit number → 10x + y = 7×10 + 5 = 75

and

The number obtained by interchanging the digits → 10y + x = 10×5 + 7 = 57

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Answer 2

Answer:

2x= 14

x=7

y=5

so the number is

10x +y

10(7)+5

70+5

75