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)

Or

(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

By Factorizing,

D(D - 850) = 0

D = 850

Hence the width of the river = 850 m

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