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Ans. let x is distance from A to B
and y is initial speed.
30/y+(x-30)5/4y -x/y = 3/4
=> 4x-12y=120 —-(1).
45/y + (x-45)5/4y -x/y=3/5
=> 5x-12y=225 ——-(2).
From equ (1) and equ (2) we will get.
x=25 and y=105
so initial speed is 25 km/hr
and Distance From A to B is 105 km

140 cents

Required Ratio=3:2

x

Son in law

Reduction of 40% or 4/10th in price of bananas will lead to an increase of 4/(10 – 4) = 2/3rd part in quantity if expenditure is constant.
If original quantity is q, then :
2q/3 = 64
=> q = 64 x 3/2 = 96 = 8 dozens.
=> Original price per dozen = 40/8 = Rs 5

time = distance / speed
speed = 36*(5/18) m/s=10m/s
distance = 100m
time=100/10s = 10sec

C

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.

5x/4

Nice

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

So as to prevent unauthorized persons from entering and reducing vandalism

c