If each of the two numbers 516 and 525 are divided by 6, the remainders are R1 and R2 respectively. What is the value of R_1 + R_2 R_2?

Answer: Option D

Given:
Two numbers 5¹⁶ and 5²⁵ are divided by 6, the remainders are R₁ and R₂ respectively.
Concept used:
If a number in the form of (b - 1)ⁿ is divided by b
Then,
Remainder = 1 if n is even number
Remainder = (b - 1) if n is an odd number
Calculation:
$$\begin{array}{rl}& 5^{16}={\left(6-1\right)}^{16}\\ & \text{So, remainder}=\frac{{\left(6-1\right)}^{16}}{6}=1\text{i}\text{.e}\text{.,}{\text{R}}_{\text{1}}\\ & \text{Again, }{5}^{25}={\left(6-1\right)}^{25}\\ & \text{So, remainder}=\frac{{\left(6-1\right)}^{25}}{6}=\left(6-1\right)=5\text{i}\text{.e}\text{.,}{\text{R}}_{\text{2}}\\ & \text{Now,}\\ & \frac{{\text{R}}_1+{\text{R}}_2}{{\text{R}}_2}=\frac{1+5}{5}=\frac{6}{5}\\ & \therefore \text{Required answer is }\frac{6}{5}\end{array}$$