Question

find the smallest number which when divided by 25,45,55 leaves the remainders 12,17,27 respectively. ​

Answer 1

Given :   number which when divided by 25,45,55 leaves the remainders 12,17,27 respectively. ​

To Find :  the smallest number  

Solution:

N  = 25A  + 12

N =  45B  + 17   = 45(B + 1)  - 28

N  = 55C  +  27  = 55(C + 1) - 28

=>  N + 28  =  45(B + 1)   = 55(C + 1)

Find LCM of 45 & 55

= 495

=> N + 28  =  495K

=> N =  495K - 28

495K - 28   = 25A  + 12

=> 495K  = 25A + 40

=> 99K = 5A  + 8

=> K = 2   & A = 38

N =  495K - 28

= 495 * 2 - 28

= 990 - 28

= 962

962  is the smallest number  which when divided by 25,45,55 leaves the remainders 12,17,27 respectively. ​

962 = 25 * 38  + 12

962 = 45*21  + 17

962 = 55*17  + 27

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