Once you attempt the question then PrepInsta explanation will be displayed.
Let the two opposite ends of the river be X and Y and the distance
between them be D meters.(i.e., width = D meters)
Let P and Q be the two men starting from the opposite banks
(i.e., from X and Y respectively).
Let the speed of P and Q be A and B m/hr .
I meet :
During I meet, P travels 340m from X while Q travels
(D - 340)m from Y.
Therefore, Time taken for P to travel 340m = Time taken for
Q to travel (D - 340)
Or 340 / A = (D - 340) / B
Or 340 / (D - 340) = A / B ...(1)
II meet :
After crossing spot I, both of them proceed in their respective directions,
reach banks and return back to cross each other at
Spot II which is 170m from Y.
From Spot I to Spot II, P would had travelled a distance of
(D - 340) + 170 m
From Spot I to Spot II, Q would had travelled a distance of
340 + (D - 170) m
Time taken by P to travel from Spot I to Spot II will be the same
as that of Q from Spot I to Spot II
Therefore, A / (D - 340) + 170 = B / 340 + (D - 170)
(D - 340) + 170 / 340 + (D - 170) = A / B ...(2)
From equations I and II, we get,
340 / (D - 340) = (D - 340) + 170 / 340 + (D - 170)
340 / (D - 340) =
D - 170 / D + 170
By Cross- Multiplying,
340 (D + 170) = (D - 170) (D - 340)
340D + 57800 =
D2 - 170D - 340D + 57800
D2 - 850D = 0
D(D - 850) = 0
D = 850
Hence the width of the river = 850 m
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