Question
Two trains, P and Q, are moving
in opposite directions. The speed of train P is 32.4 km/h faster than that of train Q, and they pass each other in 10 seconds. Train P passes a tunnel that is 60 meters long in 10 seconds, while train Q takes 18 seconds to pass the same tunnel. Quantity I: Determine the difference in lengths between the two trains. Quantity II: Determine the time it will take for train P to cross a 540-meter-long bridge. In the question, two quantities I and II are given. You have to solve both the quantities to establish the correct relation between Quantity-I and Quantity-II and choose the correct option.Solution
ATQ, Let the speed of train Q = ‘p’ m/s So, the speed of train P = p + 32.4 × (5/18) = (p + 9) m/s Also let the lengths of trains P and Q are ‘a’ m and ‘b’ m respectively. Since, both the trains cross each other in 10 seconds. So, (a+b)/(2p+9)=10 a + b = 20p + 90 ------------- (1) Since, train P crosses the 60 m long tunnel in 10 seconds. So, (a+60)/(p+9)=10 a + 60 = 10p + 90 ------------- (2) Since, train Q crosses the 60 m long tunnel in 18 seconds. So, (b+60)/p=18 p = (b+60)/18--------(3) From equations (1) and (3): 18a + 18b = 20b + 1200 + 1620 9a – b = 1410 -------------- (4) From equations (2) and (3): 18a + 1080 = 10b + 600 + 1620 9a – 5b = 570 --------------- (5) By equation (4) — equation (5): 9a - b - 9a + 5b = 1410 - 570 b = 210 From equation (4): a = 180 From equation (3): p = 15 Quantity l: Difference between the lengths of both the trains = 210- 180 = 30 m Quantity II: Speed of train P = 180 m Speed of train P = 15 + 9 = 24 m/s So, the time, in which train P will cross the 540m long bridge: (180+540)/24 = 30 seconds Hence, Quantity I = Quantity II
Referring to a little girl, a woman says, "She is the daughter of my sister's sister's sister. How is the woman related to that little girl?
If A denotes ‘+’, B denotes ‘×’, C denotes ‘−’, and D denotes ‘÷’, then what will be the value of the following equation?
94 ...
Three of the following four are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group?
(Note: The odd...
10 is related to 15 following certain logic. Following the same logic, 42 is related to 63. To which of the following numbers is 22 related, following t...
The following Venn diagram shows Men's profession as Doctors and Chess Players.
Select the number from among the given options that can replace the question mark (?) in the following series.
0, 1, 2, 5, 26, ?
Seven boxes A, B, C, D, E, F and G are kept one over the other, but not necessarily in the same order. There are exactly 3 boxes between A and C. Box E ...
127.08 – [17.02 + 3 of (6.50 – 0.5 × 2.02)] = ?
MW 13 is related to NQ 11 in a certain way. In the same way, KE 19 is related to LY 17. To which of the following is GD 17 related, following the same l...
What approximate value should come in place of the question mark (?) in the following equation?
48.09% of 1698 + 59% of 2387.98 - ? = 1225
