A person covers 132 km distance in ‘t’ hours by travelling some distance by car and some by train and speed of train is 20% more than Speed of car. If ratio of distance travelled by car and train is 4 : 7 and car covers 48 km distance with 24 km/h speed in (t+0.5) hours ,then find speed of train(approximately) ?

The correct option is 94 km/h.

Let's break down the problem and solve it step-by-step to find the approximate speed of the train.

Step 1: Analyze the given information

• Total distance covered = 132 km
• Ratio of distance covered by car to train = 4 : 7
• Car covers 48 km distance with a speed of 24 km/h in (t + 0.5) hours

Step 2: Find the distance covered by car and train from the total distance

The ratio of distance travelled by car to train is 4 : 7. The total number of parts in the ratio is:

$4+7=11$

Since total distance is 132 km:

Distance covered by car =

$\frac{4}{11}\times 132=48\text{ km}$

Distance covered by train =

$\frac{7}{11}\times 132=84\text{ km}$

Step 3: Calculate the value of time 't'

We are given that the car covers 48 km distance at 24 km/h in (t + 0.5) hours.

Using the formula Time = Distance / Speed:

$t+0.5=\frac{48}{24}$

$t+0.5=2$

$t=2-0.5=1.5\text{ hours}$

Step 4: Express the speed of train in terms of speed of car

Let the speed of the car be S_c and the speed of the train be S_t.

Since the speed of the train is 20% more than the speed of the car:

$S_t=1.2\times S_c$

Step 5: Set up the total time equation to find the speed of the car and train

The total time taken to cover 132 km (48 km by car + 84 km by train) is 't' hours = 1.5 hours.

Total Time = Time by car + Time by train

$\frac{48}{S_c}+\frac{84}{S_t}=1.5$

Substitute S_t = 1.2 S_c into the equation:

$\frac{48}{S_c}+\frac{84}{1.2S_c}=1.5$

Simplify 84 / 1.2 = 70:

$\frac{48}{S_c}+\frac{70}{S_c}=1.5$

$\frac{118}{S_c}=1.5$

$S_c=\frac{118}{1.5}=78.67\text{ km/h}$

Step 6: Calculate the speed of the train

$S_t=1.2\times 78.67=94.4\text{ km/h}$

Rounding off to the nearest whole number gives approximately 94 km/h.