Explanation:

Given: 3798125P369 is divisible by 7
Let’s express the given number in terms of triplets of digits, starting from the right, as follows.
(37) (981) (25P) (369)
Now, 369 – 25P + 981 – 37 = 1350 – 25P – 37 = 1313 – 25P
By dividing 1313 by 7 we get 4 as remainder.
25P in the above equation should be in between 250 to 259. Now, 252 and 259 are divisible by 7. So,
the number must be 252 + 4 = 256. Hence, value of P = 6
Let’s double check it:
1313 – 256 = 1057
It is divisible by 7.
Hence, option (2) is the correct answer