Question

A and B start moving towards each other from places X and Y, respectively, at the same time on the same day. The speed of A is 20% more than that of B. After meeting on the way, A and B take p hours and $7\frac{1}{5}$ hours, respectively, to reach Y and X, respectively. What is the value of p?

• A. 5.5
• B. 6
• C. 4.5
• D. 5

Answer 1

Answer:

D. 5

Shortcut Trick S1/S2 = √(t2/t1) given S1 = 120% of S2 Let S2 = 5x then S1= 6x given t2 = 7(1/5) = 36/5 t1 = p so, 6x/5x = √(36/5)/p so 36/25 = 36/5p p = 5 Given: A and B start moving towards each other from places X and Y, respectively, at the same time on the same day. The speed of A is 20% more than that of B. After meeting on the way, A and B take p hours and 715 hours, respectively Concept Used: Time taken = Distance covered / Speed Calculation: 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 + 715 ) = (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 Alternate Method Let speed of A and B be 6x and 5x respectively First case When they meet at O, both time is the same ⇒ D1 = S1t, D2 = S2t ⇒ D1 = 5xt ----(1) ⇒ D2 = 6xt ----(2) According to the question after meeting reach final destination B and A take 7(1/5)hr and P hr Then, D1 = 5xt ⇒ D1= 5x × (36/5) ⇒ D1= 36 x ----(3) Put equation 3 in equation 1 ⇒ 36 x = 6xt ⇒ t = 6 ----(4) D2 = 6xt A takes P hour D2 = 6xp ----(5) Put equation 5 in equation 2 ⇒ 5xt = 6xp (Put t = 6) ⇒ p = 30/6 = 5 hours ∴ The value of p is 5