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Two straight roads $\text{R1}$ and $\text{R2}$ diverge from a point A at an angle of $120^{\circ}.$ Ram starts walking from point A along $\text{R1}$ at a uniform speed of $3$ km/hr. Shyam starts walking at the same time from A along $\text{R2}$ at a uniform speed of $2$ km/hr. They continue walking for $4$ hours along their respective roads and reach points B and C on $\text{R1}$ and $\text{R2}$ , respectively. There is a straight line path connecting B and C. Then Ram returns to point A after walking along the line segments BC and CA. Shyam also returns to A after walking along line segments CB and BA. Their speeds remain unchanged. The time interval (in hours) between Ram‟s and Shyam‟s return to the point A is:

1. $\frac{10 \sqrt{19} + 26}{3}$
2. $\frac{2 \sqrt{19} + 10}{3}$
3. $\frac{\sqrt{19} + 26}{3}$
4. $\frac{10 \sqrt{19} + 10}{3}$

1