Question

The sum of the digits of a two digit number is 5. If the digits are reversed, the number is reduced by 27. Find the number.

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Answer 1

Answer:

Let the digits be x and y respectively.

Therefore, x + y = 5 --------(1)

Original Number = 10x + y

Reversed Number = 10y + x

10 + y - (10y + x) = 27

10x + y - 10y - x = 27

9x - 9y = 27

9(x - y) = 27

x - y = 3 --------(2)

Adding equation (1) and (2)

2x = 8

x = 4

Substituting value for x in equation (1), we get

4 + y = 5

y = 5 - 4

y = 1

The numbers are 41 and 14.

Answer 2

Question:

The sum of the digits of a two digit number is 5. If the digits are reversed, the number is reduced by 27. Find the number.

To find:

• Number

Given :

• The sum of the digits of a two digit number is 5.
• digits are reversed, the number is reduced by 27.

Let:

• unit place = x
• tens place = y

Answer:

Original number = tens place digit × 10 + unit place digit

.°. Original number = 10y+x

Reversed number = 10x+y

A.T.Q

When digits i.e. x and y are are reversed, the number is reduced by 27.

$\therefore \sf10x+y+27=10y+x$

$: \implies{ \sf10x-x+y-10y=-27}$

$: \implies { \sf9y-9x=27}$

$: \implies { \sf{y = \dfrac{27 + 9x}{9} }}$

$: \implies{ \sf{y = 3 + x}}..........................(1)$

A.T.Q

Sum of digits =5

$\therefore \sf x + y = 5..........................(2)$

Now put value of Y in equation 2

$\sf{x + y = 5}$

$\sf : \implies x + 3 + x = 5$

$\sf : \implies 2x = 5 - 3$

$\sf : \implies 2x = 2$

$\sf : \implies x = \cancel{ \dfrac{2}{2}}$

$\sf : \implies \star \boxed{ \sf x = 1} \star$

Now put value of x in equation 1

$: \implies\small{ \sf{y = 3 + x}}$

$: \implies\small{ \sf{y = 3 + 1}}$

$: \implies\small{ \star \boxed{ \sf{y =4}}} \star$

As in question it's asked to find value of number

.°. put value of x and y in this equation:

$\sf{Original \: number = 10y+x}$

$: \implies \sf{Original \: number = 10 \times 4+1}$

$: \implies \sf{Original \: number = 40+1}$

$: \implies \star \pink{ \underline{\boxed{\sf{Original \: number = 41}}}} \star$

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And all we are done! ✔

:D