Question

10. Two men simultaneously left two places A and B. One
of them left A for B and the other left B for A. Both
travelled each with his own uniform velocity. Having
arrived at their destinations, they turned back without
stopping and proceeded to their starting points. First
time, they met on their onward journey 18 km from B;
the second time on their return journey 9 km from A.
Find the distance between A and B.
(A) 30 km
(B) 45 km
(C) 60 km
(D) Cannot be determined​

Answer 1

The distance between A and B is 45 km.

Step-by-step explanation:

We are given that two men simultaneously left two places A and B. One of them left A for B and the other left B for A.

First  time, they met on their onward journey 18 km from B;  the second time on their return journey 9 km from A.

Let the distance between A and B be 'x km'.

So, according to the first situation that first  time, they met on their onward journey 18 km from B, means that;

Distance traveled by B = 18 km

Distance traveled by A = x km - 18 km   {because total distance is x km}

Now, according to the second situation that they met the second time on their return journey 9 km from A, means that;

Distance traveled by B = x km + 9 km

Distance traveled by A = 2x km - 9 km  {because first time A completed the whole distance and the second time only 9 km}

Now, representing the above situation in ratios;

$\frac{\text{Distance traveled by B}}{\text{Distance traveled by A}} =\frac{\text{Distance traveled by B}}{\text{Distance traveled by A}}$

$\frac{18}{x-18}=\frac{x+9}{2x-9}$

$18 \times (2x-9)=(x+9)\times (x-18)$

$36x-162=x^{2}-9x -162$

$x^{2}-9x -36 x=0$

$x^{2} -45x=0$

$x(x-45)=0$

x = 45 km

Hence, the distance between A and B is 45 km.

Answer 2

Step-by-step explanation:

When they meet for the first time at the man starting from B has covered 18 km and both men have together covered x km. By the time they meet at D. The two men have together covered 3x km.

the man starting from B would have covered

3 x 18 = 54 km

But we know he had gone to A and come back 9 km

i.e. (x + 9)km

:x + 9 = 54 = x= 45 km