Question

Anand and Bala started from towns P and Q
simultaneously towards Q and P respectively. After
6 hours, they crossed each other at town R. After
that, Anand took 5 hours more to reach Q than Bala
took to reach P. Find the sum of the times taken by
them to reach their destinations from R (in hours).​

Answer 1

Given :- Anand and Bala started from towns P and Q simultaneously towards Q and P respectively. After 6 hours, they crossed each other at town R. After that, Anand took 5 hours more to reach Q than Bala took to reach P.

To Find :- the sum of the times taken by them to reach their destinations from R (in hours).

Solution :-

Let us assume that,

• Speed of Anand = a km/h .
• Speed of Bala = b km/h .
• Time taken by Bala to reach Q = x hours .

so,

→ In first 6 hours Anand covered = S * T = a * 6 = 6a km = PR .

→ In first 6 hours Bala covered = S * T = b * 6 = 6b km = QR .

now, after crossing each other at R ,

• Distance covered by Anand = QR = 6b km .
• Distance covered by Bala = PR = 6a km .

then,

→ Time taken by Anand to cover QR = D/S = (6b/a) hours .

→ Time taken by Bala to cover PR = (6a/b) hours .

A/q,

→ x = (6a/b)

→ b = (6a/x) ------- Eqn.(1)

and,

→ x + 5 = (6b/a)

→ a = 6b/(x + 5) ------- Eqn.(2)

putting value of Eqn.(1) in Eqn.(2)

→ a = 6(6a/x) / (x + 5)

→ a = 36a/x(x + 5)

→ x² + 5x - 36 = 0

→ x² + 9x - 4x - 36 = 0

→ x(x + 9) - 4(x + 9) = 0

→ (x + 9)(x - 4) = 0

→ x = (-9) or 4 . { - ve value of hours is not possible. }

therefore,

→ The sum of the times taken by them to reach their destinations from R = x + (x + 5) = 2x + 5 = 2*4 + 5 = 8 + 5 = 13 hours (Ans.)

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