**Q) ****A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?**

**Ans:**

Let’s consider the original average speed of the train: X km/hr.

Hence, to cover distance of 63 km, it will take hrs

Next, when its speed increased to (X + 6) km/hr,

the time taken to cover 72 km will be: hrs

Now, total distance covered = 63 + 72 = 135 km

Total Time taken by train = Time taken to cover 63 kms + Time taken to travel 72 Kms

= hrs + hrs

= hrs

= hrs

Given that the total time taken is 3 hours

(135 X + 378) = 3X (X + 6)

135 X + 378 = 3X2 + 18 X

3X2 – 117 X – 378 = 0

X2 – 39 X – 126 = 0

(X – 42) (X + 3) = 0

X = 42 and X = – 3

Since Speed can not be negative, therefore X = 42 will be taken

**Hence, the original speed of the train is 42 km/hr.**

*Check: At 42 kmph, train will take 1.5 hrs to cover 63 km. At 6 kmph higher speed i.e. at 48 kmph, train will cover 72 km in 1.5 hrs. **Total time will be 1.5 + 1.5 = 3 hrs*

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