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.
c
Answer: 10
Reason:
The best case happens ONLY when each rat dies just as they
taste the FIRST bottle given to them (you can imagine it a
miracle 😀 )
In this case, the very first 10 attempts reveal the
poisonous bottles. So the answer is 10.
cost price(c.p) of one fruit = 24/16
(c.p) = Rs 1.50
selling price(s.p) of one fruit = 18/8
(s.p) =Rs 2.25
profit for one fruit = 2.25 – 1.50 = 0.75
profit
profit % = ———– * 100
cost price
0.75
= ——- * 100
1.50
= 50%
38 years
Let Rajan’s present age be x years. Then, his age at the time of marriage = (x – 8) years.
x = 65(x−8)
⇒5x=6x−48
⇒x=48 years
Rajan’s sister’s age at the time of his marriage = (x – 8) – 10 = (x – 18) = 30 years
∴ Rajan’s sister’s present age = (30 + 8) years = 38 years
let’s say the Cost Price is 1000x. (CP)
The selling price is also the same as the Cost price. So, here SP=CP (But he sells 950gm instead of 1000gm)
Instead of 1000gm, he is selling 950 grams at the CP. So he sells 050 gms @1000x price. So his net profit is 50gm.
Now 1000gm is 1000x Rs
So, 50gms is 50x rs. [Apllied Unitary Method]
So his profit percentage is:
Profit Percentage Formula: {(Profit/CP)*100%}
So, Here profit is 50x;
CP is 1000x;
so putting the value in the formula we get, Profit Percentage is: (50x/1000x)*100% =(5000x/1000x)%=5%.
789, 645, 545, 481, 440, 429, 425
b
9/32
35000
15km/hr
I have been teaching some students for 1 year.