What least number must be subtracted from 1739 so that the resulting number when divided by 6, 10 an

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06 Apr 2022 Number System

What least number must be subtracted from 1739 so that the resulting number when divided by 6, 10 and 12 will leave in each case the same remainder 5 ?

OPtion

1) 61
2) 54
3) 39
4) 49
5) 36
6) 59
7) 64
8) 65
9) 44
10) None of these

Solution

LCM of 6, 10 and 12 = 60
⇒ The multiple of 60 are also divisible by 6, 10 or 12.
.'. Nearest number below 1739 divisible by them = 60 x 28 = 1680
Now, 1685 will be the number that will give remainder 5.
Hence, number to be subtracted = 1739 – 1685 = 54

Correct Option: 2 Best Solution (2)