Question

The difference between the two digits of a number
is 2. If the digits are reversed and the number added
to original number then, the result is 132. Find the
original number.​

Answer 1

Given:-

• The difference between the two digits of a number is 2.
• If the digits are reversed and the number is added to the original number, then the result is 132.

To Find:-

• The original number.

Solution:-

Let the digit in the ones place be y and the digit in the tens place be x.

Hence,

$\dag{\boxed{\green{\rm{The\:original\:number = 10x + y}}}}$

Now,

On reversing the digits:-

$\dag{\boxed{\blue{\rm{The\:new\:number = 10y + x}}}}$

Now,

We are given that the difference between the two digits of the number is 2.

Hence,

$\blue{\rm{10x - y = 2 \longrightarrow(i)}}$

Also it is given that, the sum of original number and the new number is 132.

Hence,

$\red{\rm{(10x + y) + (10y + x) = 132}}$

$= \red{\rm{10x + y + 10y + x = 132}}$

$= \red{\rm{11x + 11y = 132}}$

$:\implies \red{\rm{11(x + y) = 132}}$

$:\implies \red{\rm{x + y = \dfrac{132}{11}}}$

$= \red{\rm{x + y = 12 \longrightarrow(ii)}}$

Now,

On subtracting equation (i) from equation (ii)

= (x + y) - (x - y) = 12 - 2

= x + y - x + y = 10

= 2y = 10

$= \sf{y = \dfrac{10}{2}}$

= y = 5

Putting the value of y in equation (i)

= x - y = 2

= x - 5 = 2

= x = 2 + 5

= x = 7

Therefore the original number becomes:-

• $\rm{\orange{10x + y = 10\times 7 + 5 = 75}}$

$\boxed{\underline{\red{\rm{\therefore\:The\:original\:number\:is\:75}}}}$

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