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 us solve the problem step-by-step.

Step 1: Understand the given information
- Total distance = 132 km
- Total time taken = t hours
- Ratio of distance covered by car to train = 4 : 7
- Speed of train is 20% more than the speed of car.
- Car covers 48 km distance with speed of 24 km/h in (t + 0.5) hours.

Step 2: Find the value of t
Using the formula:

$\text{Time}=\frac{\text{Distance}}{\text{Speed}}$

For the car's secondary condition:
Time taken = (t + 0.5) hours
Distance = 48 km
Speed = 24 km/h

$t+0.5=\frac{48}{24}=2$

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

Step 3: Calculate the distance travelled by car and train in the main journey
Total distance = 132 km, divided in the ratio 4 : 7.
Sum of ratio parts = 4 + 7 = 11 parts.

Distance travelled by car:

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

Distance travelled by train:

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

Step 4: Relate the speeds of car and train
Let the speed of the car be S_car = S km/h.
Since the speed of the train is 20% more than the speed of the car:

${\text{S}}_{\text{train}}=S+0.20S=1.2S$

Step 5: Set up the total time equation
Total time for covering 132 km is t = 1.5 hours.

${\text{Time}}_{\text{car}}+{\text{Time}}_{\text{train}}=1.5$

Substitute distance and speed values:

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

Simplify the second fraction:

$\frac{84}{1.2}=70$

So the equation becomes:

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

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

$S=\frac{118}{1.5}=\frac{236}{3}\text{ km/h}$

Step 6: Find the speed of the train

${\text{S}}_{\text{train}}=1.2\times S=\frac{6}{5}\times \frac{236}{3}$

${\text{S}}_{\text{train}}=\frac{2\times 236}{5}=\frac{472}{5}=94.4\text{ km/h}$

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