Question

the sum of the digits of a two digit number is 7.on reversing the digits, the new number obtained is 9 more than the original number. Find the number.

Answer 1

Answer:

Step-by-step explanation:

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

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Answer 2

Let the two digit no be 10xa+1×b
=10a+b
According to question,
a+b=7.....1 no equation
number obtained by reversing the digits
=10xb+a
=10b+a
According to question,
(10a+b)-(10b+a)=9
or, 10a-a+b-10b=9
or, 9a-9b=9
or, 9(a-b)=9
or, (a-b)=9÷9
or, (a-b)=1...2 no equation
1+2
a+b+a-b=7+1
or, 2a = 8
or, a=8÷2
or, a=4
b=7-a
b=7-4
b=3
the no is = 10a+b
=4×10+5
=40+5
=45