Refer `Q.95`. If the man takes `t_1 and t_2` to move to and fro journey respectively, the time taken by him to go downstream (while the man does not swim) is :A. `(2 t_1 t_2)/(t_(1)+t_(2))`B. `sqrt(t_1^2 + t_2^2)`C. `sqrt(t_1 t_2)`D. `(2 t_1 t_2)/(t_1 - t_2)`

Refer `Q.95`. If the man takes `t_1 and t_2` to move to and fro journe

1.	Refer `Q.95`. If the man takes `t_1 and t_2` to move to and fro journey respectively, the time taken by him to go downstream (while the man does not swim) is :A. `(2 t_1 t_2)/(t_(1)+t_(2))`B. `sqrt(t_1^2 + t_2^2)`C. `sqrt(t_1 t_2)`D. `(2 t_1 t_2)/(t_1 - t_2)`
Answer» Correct Answer - D velocity of man relative to water = v Velocity of water flow = u Velocity of man relative to ground in upstream `= v - u` Velocity of man relative to ground in downstream `= v + u` Now for to and fro motion, time taken to cover distance `d` in upstream `t_1 = (d)/(v - u)` `1/t_(1)=v/d-u/d` ...(i) And time taken to cover distance `d` in downstream `t_2 = (d)/( v+ u)` `(1)/(t_2) = (v)/(d) + (u)/(d)` ...(ii) Now time taken to cover distance `d` in downstream When ` v= 0` `t_3 = (d)/(u)` Subtracting equation (i) from equation (ii) we get `(1)/(t_2) - (1)/(t_1) = (2u)/(d)` Now put value of `u//d` from equation (iii) `(t_1 - t_2)/(t_1 t_2) = (2)/(t_3) rArr t_3 = (2 t_1 t_2)/(t_1 - t_2)`.

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Refer `Q.95`. If the man takes `t_1 and t_2` to move to and fro journey respectively, the time taken by him to go downstream (while the man does not swim) is :A. `(2 t_1 t_2)/(t_(1)+t_(2))`B. `sqrt(t_1^2 + t_2^2)`C. `sqrt(t_1 t_2)`D. `(2 t_1 t_2)/(t_1 - t_2)`

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