Question

The sum of digits of a two-digit number is 13. If the number is subtracted from the one obtained by interchanging the digits, the result it 45. What is the number?

Class 10th

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Answer 1

in a two digit number the sum of the digits is 13, if the number is subtracted from the one obtained by reversing the digits the result is 45. find the number
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let u=units digit
let t=tens digit
..
t+u=13
t=13-u
..
10u+t-(10t+u)=45
10u+t-10t-u=45
10u+13-u-10(13-u)-u=45
10u+13-u-130+10u-u=45
18u=162
u=9
t=13-u=4
number=49
does this work 

Answer 2

hey dear,

here is your answer,

__________ ^-^

Let the ten 's place digit be x and one 's place digit be y.

therefore, ATQ, x+y=13.

Original no.= 10x+y.

Reversed no.= 10y+x

ATQ,

10y+x-(10x+y)=45

10y+x-10x-y=45

-9x+9y=45   ....(1)

Now,

(x+y=13)*9

9x+9y=117   ....(2)

adding (1) and (2)

(-9x+9y)+(9x+9y) = 45 + 117

18y=162

y=162/18

hence, y=9.

x+y=13

x+9=13

x=13-9

hence x=4

Original no.= 10x+y

10*4+9=40+9

=49....answer.
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