If a body moving along a straight line travels distance $S_{1}$ with speed $V_{1}$ , distance $S_{2}$ with speed $V_{2}$ , distance $S_{3}$ with $V_{3}$ ,................ $S_{n}$ , with $V_{n}$ then average speed is

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$\frac{S_{1} + S_{2} + S_{3} + \dots \dots + S_{n}}{\frac{S_{1}}{V_{1}} + \frac{S_{2}}{V_{2}} + \frac{S_{3}}{V_{3}} + \dots \dots + \frac{S_{n}}{V_{n}}}$

$\frac{S_{1} - S_{2} - S_{3} - \dots \dots - S_{n}}{\frac{S_{1}}{V_{1}} + \frac{S_{2}}{V_{2}} + \frac{S_{3}}{V_{3}} + \dots \dots + \frac{S_{n}}{V_{n}}}$

$\frac{S_{1} + S_{2} + S_{3} + \dots \dots + S_{n}}{\frac{S_{1}}{V_{1}} - \frac{S_{2}}{V_{2}} - \frac{S_{3}}{V_{3}} - \dots \dots - \frac{S_{n}}{V_{n}}}$

$\frac{S_{1} + S_{2} - S_{3} + \dots \dots - S_{n}}{\frac{S_{1}}{V_{1}} - \frac{S_{2}}{V_{2}} + \frac{S_{3}}{V_{3}} - \dots \dots + \frac{S_{n}}{V_{n}}}$

answer is A.

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Detailed Solution

$t_{1} = \frac{s_{1}}{v_{1}}, t_{2} = \frac{s_{2}}{v_{2}}, t_{3} = \frac{s_{3}}{v_{3}}$

Average speed= $\frac{total distance}{total time taken}$ = $\frac{S_{1} + S_{2} + S_{3} + \dots \dots + S_{n}}{\frac{S_{1}}{V_{1}} + \frac{S_{2}}{V_{2}} + \frac{S_{3}}{V_{3}} + \dots \dots + \frac{S_{n}}{V_{n}}}$