Question

find the smallest number which when divided by 25 ,45 ,55 leaves the remainders 17, 27 and 37 respectively.

Answer 1

Given :   number which when divided by 25,45,55 leaves the remainders 17,27,37 respectively. ​

To Find :  the smallest number  

Solution:

N  = 25A  + 17

N =  45B  + 27   = 45(B + 1)  - 18

N  = 55C  + 37  =  55(C + 1) - 18

=>  N + 18  =  45(B + 1)   = 55(C + 1)

Find LCM of 45 & 55

= 495

=> N + 18  =  495K

=> N =  495K - 18

495K - 18   = 25A  + 17

=> 495K  = 25A + 35

=> 99K = 5A  + 7

=> 99K = 5(A+1)  + 2

=> K = 3    

N =  495K - 18

= 495 * 3 - 18

= 1467

1467  is the smallest number  which when divided by 25,45,55 leaves the remainders 17,27 , 37 respectively. ​

Verification :

1467 = 25 * 58  + 17

1467 = 45*32  +27

1467 = 55*26  + 37

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Answer 2

Answer:

The answer if this question is 3437