The answer should be- B.
Just divide each option both by 7 and 14. Then get the reminders and check their difference is 7!
Here, 53 satisfies the condition. Therefore, the answer is B.

Theory: Dividend = Divisor*Quotient + Remainder

Given that the remainder when the positive integer m is divided by 7 is x and the remainder when m is divided by 14 is x + 7. And we need to find which of the following could be the value of m

Let's solve the problem using Substitution

We will take each option choice and find out the remainder with 7 and 14 and see which one has remainder by 14, 7 greater than the remainder by 7.

(A) 45
45 when divided by 7 gives 3 remainder
45 when divided by 14 gives 3 remainder
Clearly, Remainder by 14 is NOT 7 greater than Remainder by 7 => NOT POSSIBLE

(B) 53
53 when divided by 7 gives 4 remainder
53 when divided by 14 gives 11 remainder
Clearly, Remainder by 14 IS 7 greater than Remainder by 7 => POSSIBLE
In Test, we don't need to solve further, but I am solving to complete the solution.

(C) 72
72 when divided by 7 gives 2 remainder
72 when divided by 14 gives 2 remainder
Clearly, Remainder by 14 is NOT 7 greater than Remainder by 7 => NOT POSSIBLE

(D) 85
85 when divided by 7 gives 1 remainder
85 when divided by 14 gives 1 remainder
Clearly, Remainder by 14 is NOT 7 greater than Remainder by 7 => NOT POSSIBLE

(E) 100
100 when divided by 7 gives 2 remainder
45 when divided by 14 gives 2 remainder
Clearly, Remainder by 14 is NOT 7 greater than Remainder by 7 => NOT POSSIBLE

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Remainders