What is the least number when divided by 8, 12, 20 and 30 leaves a remainder 4 and when divided by 21 leaves a remainder 7 ?

Solution (By Examveda Team)

Lcm of 8, 12,20,30 is 120. As they leave a remainder 4
So it should be 120 + 4. But when being divided by 21, remainder is 7
So the number will be exactly divisible by (21 + 7) = 28.
The number will be in the form of (120k + 4) which is divisible by 28
Where k is any positive integer. Now, if we divide 120 by 28, the remainder is 8
We need a remainder of 24, because (24 + 4) = 28
Now (8 × 3) = 24
Thus, k = 3
Hence, the number would be (120 × 3) + 4 = 364