Question

The sum of the two digits of a two-digit number is 7. If 27 is added to the number the digits are interchanged.
Find the number.
please slove ..​

Answer 1

Given:

• The sum of the two digits of a two-digit number is 7
• If 27 is added to the number the digits are interchanged.

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To find:

• Numbers?

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Solution:

☯ Let the digit in unit's place be "y" and the digit in ten's place be "x".

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Then,

• The two digit number is 10x + y

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

• The sum of the two digits of a two-digit number is 7.

$:\implies\sf x + y = 7\qquad\qquad\bigg\lgroup\bf eq.\;(1)\bigg\rgroup$

Also,

• If 27 is added to the number the digits are interchanged.

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When digits are interchanged = 10x + y

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$:\implies\sf 10x + y + 27 = 10y + x$

$:\implies\sf 10x + y + 27 - 10y - x$

$:\implies\sf 9x - 9y + 27$

$:\implies\sf 9(x - y + 3) = 0$

$:\implies\sf x - y + 3 = 0$

$:\implies\sf x - y = - 3\qquad\qquad\bigg\lgroup\bf eq.\;(2)\bigg\rgroup$

Adding eq. (1) and eq. (2), we get,

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$:\implies\sf 2x = 4$

$:\implies\sf x = \cancel{ \dfrac{4}{2}}$

$:\implies{\boxed{\sf{\pink{x = 2}}}}\;\bigstar$

Now, Putting value of x in eq. (1),

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$:\implies\sf 2 + y = 7$

$:\implies\sf y = 7 - 2$

$:\implies{\boxed{\sf{\pink{y = 5}}}}\;\bigstar$

Therefore, the required number is,

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$:\implies\sf 10 \times 2 + 5$

$:\implies{\boxed{\sf{\purple{25}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;the\; required\;two\;digit\;number\;is\; \bf{25}.}}}$

Answer 2

$\huge {\underline {\mathfrak{ \red q \blue u\green e \pink s \orange t\purple i\red o\orange n: - }}} </p><p></p><p>$

The sum of the two digits of a two-digit number is 7. If 27 is added to the number the digits are interchanged

$\huge {\underline {{ \mathfrak Find - }}}</h2><h2></h2><h2>$

Find the number.

$\huge {\underline {\mathfrak{ \red a \blue n \green \pink s \orange w\purple e\red r\: - }}} </p><p></p><p>$

Suppose the two digit original number is 10x+y.

The sum of digits of original number is

7 →x+y = 7 —equation(1)

If 27 is added to original number its digits are interchanged .

So,

10x + y +27 =10y+ x

→ 9x +27 = 9y

→ 9(x+3) = 9(y)

→ x+3 = y — equation(2)

Substituting value of y from equation (2) in equation (1)

x + x+3 = 7

2x + 3 = 7

2x =4

x= 2

Substituting x= 2 in equation (2)

y= 5

So original number is 10 (2) + 5

i.e. 20 +5 → 25.

$\huge {\underline {\mathfrak \star{ \red verification: - }}} </p><p></p><p>$

In order to check the answer..

• 25 is original number and 52 is the number formed by interchanging the digits.

25 +27 = 52.