Question 39

Two men—Pand start from two points—X and Y on opposite banks of still river towards Y and X respectively. They meet at 340 m from one bank 'X' and proceed on their respective onward journey. After that they meet at 170 m from the other bank 'Y' on their return journey. What is the width of the river?

Solution

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,

$$340 (D + 170) = (D - 170) (D - 340)$$

$$340D + 57800 = D^2 - 170D - 340D + 57800$$

$$D^2 - 850D = 0$$

By Factorizing,

D(D - 850) = 0

D = 850

Hence the width of the river = 850 m.

C is correct choice.

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