Question

The sum of the digits of a 2-digit number is 7. The number obtained by interchanging
the digits exceeds the original number by 27. Find the number.​

Answer 1

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

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Answer 2

Answer:

Let digit at ones place=x

and

digit at tens place=y

So, the number will be 10y+x

x+y=7 ....(1)

reverse digit will be represented as, 10x+y

So,

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

9x-9y=27

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

Adding equation (1) and (2)

2x=10

x=5

substituting in equation (1)

y=7-5

=2

Thus, the number will be 25

Step-by-step explanation:

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