Answer : Option D

Explanation :

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Solution 1
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Let Vikas, Vijay and Viraj gets Rs.x, Rs.y and Rs.z respectively.
Simple Interest on x at 5% for 1 year
= Simple Interest on y at 5% for 2 year
= Simple Interest on z at 5% for 3 year
$MF#%\begin{align}&\Rightarrow \dfrac{x \times 5 \times 1}{100} = \dfrac{\text{y} \times 5 \times 2}{100} = \dfrac{\text{z} \times 5 \times 3}{100}\\\\ &\Rightarrow5x = 10\text{y} = 15\text{z}\\\\ &\Rightarrow x = 2\text{y} = 3\text{z}\\\\ &\Rightarrow \text{y} = \dfrac{x}{2} \text{ and }\text{z} = \dfrac{x}{3} \quad \color{#F00}{\text{--- (1)}}\\\\ &\text{x + y + z = 7700 } \quad \color{#F00}{\text{(∵ the total amount is Rs. 7700)}} \\\\ &\Rightarrow x +\dfrac{x}{2}+\dfrac{x}{3} = 7700 \quad \color{#F00}{(∵ \text{substituted the values of y and z from from equation 1)}}\\\\ &\Rightarrow \dfrac{11x}{6} = 7700\\\\ &\Rightarrow \dfrac{x}{6} = 7000\\\\ &\Rightarrow x = 4200\\\\ &\text{z} = \dfrac{x}{3} = \dfrac{4200}{3} = 1400\end{align}$MF#%
i.e, Vikas gets Rs.4200 and Viraj gets Rs.1400
Share of Vikas is more than that of Viraj by (4200 - 1400) = 2800
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Solution 2
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If a certain sum of money is lent out in n parts in such a manner that equal sum of money is obtained at simple interest on each part where interest rates are R₁, R₂, ... , R_n respectively and time periods are T₁, T₂, ... , T_n respectively, then the ratio in which the sum will be divided in n parts can be given by
$MF#%\dfrac{1}{\text{R}_1\text{T}_1} : \dfrac{1}{\text{R}_2\text{T}_2} : \cdots \dfrac{1}{\text{R}_\text{n}\text{T}_\text{n}}$MF#%