Let’s assume the length of each train is ‘L’ and the speeds of the two trains are ‘V₁’ and ‘V₂’ respectively.
When the trains are moving in the opposite direction, their relative speed is the sum of their individual speeds. The total distance they need to cover is the sum of their lengths. Since they cross each other completely in 5 seconds, we can set up the following equation:
(V₁ + V₂) × 5 = 2L
When the trains are moving in the same direction, their relative speed is the difference between their individual speeds. The total distance they need to cover is the difference between their lengths. Since they cross each other completely in 15 seconds, we can set up the following equation:
(V₁ – V₂) × 15 = 2L
Now, let’s solve these equations to find the ratio of their speeds.
From the first equation, we have:
(V₁ + V₂) × 5 = 2L
V₁ + V₂ = (2L) / 5
From the second equation, we have:
(V₁ – V₂) × 15 = 2L
V₁ – V₂ = (2L) / 15
Let’s add these two equations together:
V₁ + V₂ + V₁ – V₂ = (2L) / 5 + (2L) / 15
2V₁ = (6L + 2L) / 15
2V₁ = (8L) / 15
V₁ = (4L) / 15
So, the speed of the first train is (4L) / 15.
Now, let’s substitute this value back into the first equation to find V₂:
(4L) / 15 + V₂ = (2L) / 5
V₂ = (2L) / 5 – (4L) / 15
V₂ = (6L – 4L) / 15
V₂ = (2L) / 15
Therefore, the speed of the second train is (2L) / 15.
The ratio of their speeds is given by:
(V₁ / V₂) = ((4L) / 15) / ((2L) / 15)
(V₁ / V₂) = 4L / 2L
(V₁ / V₂) = 2
So, the ratio of their speeds is 2:1.
9 AND 3
Complete step-by-step answer:
Investment made by A for 1 year, IA=2000
Investment made by B for 2 year,
IB=2×3000IB=6000
Investment made by C for 2 year,
IC=2×4000IC=8000
The ratio of their investment is given by
IA:IB:IC=2000:6000:8000
To simplify the ratio divide it by 1000,
IA:IB:IC=2:6:8
Now again to simplify divide the ratio by 2,
IA:IB:IC=1:3:4
The total parts of this investment =1+3+4=8
A’s share in the investment is 1 out of the 8 parts; B’s share is 3 out of 8 while C’s share is 4.
Therefore, the profit share of A’s investment of Rs. 2000=18×3200=400.
it is based on the right shift operation on the perticular digit
163
270
Speed of train = 54km/hr
= 54 x (5/18) m/s
= 15 m/s
Length of train = 165m
Time required to cross a bridge of 660m in length = (660+165) / 15
= 55 seconds
total distance to travel the end of the train = 360 + 140 = 500 m
speed of train 45000m/60min = 750m/min or 750m/60sec
(500m*60sec)/750m=40sec the time will take to pass
No loss no gain.