Train ‘A’ takes 2 hours more than train ‘B’ to cover certain distance ‘X’ while train ‘A’ can cover (X + 160) is 8 hours. If speed of train ‘B’ is 1.5 times of speed of train ‘A’, then find the speed of train ‘B’.

The correct answer is 120 km/hr.

Step-by-Step Explanation:

Step 1: Define variables for speed and time

Let the speed of train A be _SA and the speed of train B be _SB.

According to the question, the speed of train B is 1.5 times the speed of train A:

$S_B=1.5\times S_A=\frac{3}{2}{S}_A$

Step 2: Express time taken to cover distance X

Let the time taken by train A to cover distance X be _TA, and the time taken by train B to cover distance X be _TB.

Since time = distance / speed:

$T_A=\frac{X}{S_A}$

$T_B=\frac{X}{S_B}=\frac{X}{1.5S_A}=\frac{T_A}{1.5}=\frac{2}{3}{T}_A$

Step 3: Use the time difference condition

We are given that train A takes 2 hours more than train B to cover distance X:

$T_A-T_B=2$

Substitute _TB = (2/3)_TA into the equation:

$T_A-\frac{2}{3}{T}_A=2$

$\frac{1}{3}{T}_A=2$

$T_A=6\text{hours}$

Step 4: Find the relationship between X and S_A

Since train A takes 6 hours to cover distance X:

$X=S_A\times T_A=6S_A$

Step 5: Use the condition for distance (X + 160)

We are given that train A covers distance (X + 160) in 8 hours:

$X+160=S_A\times 8$

Substitute X = 6_SA into this equation:

$6S_A+160=8S_A$

$8S_A-6S_A=160$

$2S_A=160$

$S_A=80\text{km/hr}$

Step 6: Calculate the speed of train B

Now, calculate _SB using the ratio given in the problem:

$S_B=1.5\times S_A=1.5\times 80=120\text{km/hr}$

Thus, the speed of train B is 120 km/hr.