Solution

Let, speed of B be 10v km/h Speed of a is 12v km/h Let the distance be d Time taken to cover the whole distance by A is (d/12v) hours Time taken to cover the whole distance by B is (d/10v) hours Relative speed (10v + 12V) ⇒ 22v km/h When they meet each other together they covered d distance Time taken to meet d/22v hours Then time taken by A to cover the whole journey is (d/22v + P) hours d/22v + p = d/12v ⇒ p = d/12v - d/22v ⇒ p = (d/v)(1/12 - 1/22) ⇒ p = 5/132.(d/v) ⇒ d/v = 132p/5 ----(1) Time taken by B to cover the whole journey is (d/22v + 7 (1/5) ) = (d/22v + 36/5) d/22v + 36/5 = d/10v ⇒ 36/5 = d/10v - d/22v ⇒ 36/5 = (d/v).(1/10 - 1/22) ⇒ 36/5 = (6/110).(d/v) ⇒ d/v = 6 × 22 ----(2) From (1) and (2) get, 132p/5 = 6 × 22 ⇒ p = 5 ∴ The value of p is 5