# Two persons A and B start moving from point P towards Q which are 1400 Km apart. Speed of A is 50 Krn/hr and that of B is 20 Km/hr. How far is A from Q when he meets B for the 22nd time?

Arun
25750 Points
5 years ago

Total distance travelled by both of them for 22nd meeting = 1400 + (21 * 2 * 1400) = 43 * 1400
Distance travelled by each will be in proportion of their speed :
Therefore, distance travelled by A = 50/(50 + 20) * 43 * 1400 = 43000 (Note - Always do complicated calculations at last because things cancel out generally)
Now, for every odd multiple of 1400, A will be at Q and for every even multiple of 1400 A will be at P. So, at 42000 Km (1400 x 30, even multiple) A will beat P. So at their 22 meeting, A will be 1000 Km from P, therefore, 400 Km from Q.

The question is "How far is A from Q when he meets B for the 22nd time?"

##### Hence, the answer is 400 km
Vikas TU
14149 Points
5 years ago
Distance travelled byA / Distance travelled byB = 50/20 = 5/2 .
Dividing 1400 in the ratio 5: 2, we get 1000 : 400.
First time they meet at 400 km from Q.
On 22nd time , 22*800 - 400 = 17,200 km from **Q**
One to and fro motion from Q is 2800 km
17,200 = 6 *2800 + 1000 km
Therefore, they meet at 1000 km from Q.