Question

The Sum of digits of a 2 digit no is 7.If digits are reversed the new number decreases by twice the original number. Find the number.​

Answer 1

AnswEr :

Let us Consider that x & y be two digits numbers.

And, Original Number be = 10x + y.

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⠀⠀⠀⠀⠀As Per Given Question -

Sum of two digits numbers is = 7.

$:\implies\sf x + y = 7$ -eq. (1)

Now, Reversing the Digits.

$:\implies\sf 10y + x$

$:\implies$ 2( Original Number) = Reversed Number - 2.

[Reversed Number is Decreased by 2 (Given) ]

$:\implies\sf 2(10x + y) = 10y + x - 2 \\ \\ \\ \implies\sf 20x + 2y = 10y + x - 2 \\ \\ \\ \implies\sf 19x + 2 = 8y \\ \\ \\ \implies\sf 8y - 2 = 19x \\ \\ \\ \implies\sf -2 = 19x = 8y$ -eq. (2)

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From eq(1) & (2).

$:\implies\sf x + y = 7$

$:\implies\sf 19x - 8y = -2$

⠀⠀⠀⠀Multiplying eq(1) with 19 & eq(2) with 1

$:\implies\sf 19x + 19y = 133$

$:\implies\sf 19x - 8y = -2$

$:\implies\sf 27y = 135$

$:\implies\sf y = \cancel\dfrac{135}{27}$

$:\implies\sf\red{y \: = \: 5}$

We get value of y = 5

$:\implies\sf x + y = 7$⠀⠀⠀⠀⠀⠀[From eq(1)]⠀⠀

$:\implies\sf x + 5 = 7$

$:\implies\sf\red{x \: = \: 2}$

Hence, Value of x & y is 2 & 5

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⠀⠀⠀⠀Now, Original Number -

$:\implies\sf 10x + y$

$:\implies\sf 10(2) + y$

$:\implies\sf 20 + 5$

$:\implies\sf\pink{25}$

Thus, the orignal Number is 25.

Answer 2

Given :

Sum of digits of a 2 digit no is 7.

If digits are reversed the new number decreases by twice the original number.

To Find :

Original Number

Solution :

Let the original number = 10y+x.

and

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

According to question :

Sum of digits of a 2 digit no is 7

So x + y = 7

The second condition gives

10x + y − 2 = 2( 10y + x)

Thus we have two equations:

x + y = 7 ...(1)

8x − 19y = 2 ...(2)

Multiplying the equation 1 by 19 and we get

19x+19y=133.

Adding this to equation 2, we get

=> 27x=135

=> x=5

=> y = 7−x =7−5 = 2

Thus the required number is 25.