Question

the sum of the digits of two digit number is 7 the number obtained by interchanging the digits exceeds the original number by 27 find the number
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Answer 1

Answer:

let the units place be x

then the tens digit be 7 - x

number formed by these digits = 10 x t's digit+u's digit

=> 10(7-x)+x

70 x -10 x +x

70 x -9x

when the digits are interchanged than,

t's digit= x

u's digit = 7-x

the new no. formed = 10x + 7-x

= 9 x +7

given that the no. exceeds by 27

new no. - given no.

9x +7 - (70-9x)=27

9 x + 7 - 70 + 9x =27

18x -63= 27

18 x = 63+27

18 x= 90

x = 90/18

=5

the no. = 70- 9x

=> 70-45

=> 25 ans

verify : 2+5=7

Answer 2

☆Given Question :-

• The sum of the digits of two digit number is 7. The number obtained by interchanging the digits exceeds the original number by 27. Find the number.

$\huge \orange{AηsωeR} ✍$

☆Given :-

• The sum of the digits of two digit number is 7.
• The number obtained by interchanging the digits exceeds the original number by 27.

☆To Find :-

• The two digit number.

☆Solution :-

$\begin{gathered}\begin{gathered}\bf Let = \begin{cases} &\sf{digit \: at \: ones \: place \: be \: x} \\ &\sf{digit \: at \: tens \: place \: be \: y} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf So = \begin{cases} &\sf{number \: formed \: = 10y + x} \\ &\sf{reverse \: number \: = 10x + y} \end{cases}\end{gathered}\end{gathered}$

$\large \red{\bf \: According \: to \: statement } ✍$

$\bf \:Sum \: of \: the \: digits \: = 7$

$\bf \:  ⟼ x + y = 7 \: ⟼ \: (1)$

$\large \red{\bf \: According \: to \: statement } ✍$

☆The number obtained by interchanging the digits exceeds the original number by 27.

$\bf \:  ⟼ (10x + y) - (10y + x) = 27$

$\bf \:  ⟼ 10x + y - 10y - x = 27$

$\bf \:  ⟼ 9x - 9y = 27$

$\bf \:  ⟼ x - y = 3 \: ⟼ \: (2)$

☆On Adding equation (1) and (2), we get

$\bf \:  ⟼ 2x = 10$

$\bf \:  ⟼ x = 5 \: ⟼ \: (3)$

☆On substituting the value of x = 5, in equation (1), we get

$\bf \:  ⟼ 5 + y = 7$

$\bf \:  ⟼ y = 7 - 5 = 2$

$\bf \:So, \: number \: is \: 10y + x = 10 \times 2 + 5 = 25$

$\large{\boxed{\boxed{\bf{Hence, \: 2 \: digit \: number \: is \: 25}}}}$