Rahul travels from point P to S via Q. The fare per km for the vehicle from Q to S is 20\% higher than the fare per km from P to Q. If the total fare collected for the journey from P to S via Q is Rs. 72,000, find the fare per km of the taxi.

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**Solution:**

1. Let the fare per km from P to Q be Rs. *x*.
2. Since the fare from Q to S is 20\% more, the fare per km from Q to S will be Rs. *1.2x*.
3. From the given data, the distance from P to Q is 240 km and from Q to S is 400 km.
4. Total fare collected is given as Rs. 72,000.

Using the formula for total fare:

$$	ext{Total Fare} = (	ext{Fare per km from P to Q} 	imes 	ext{Distance P to Q}) + (	ext{Fare per km from Q to S} 	imes 	ext{Distance Q to S})$$

Substitute the values:

$$72000 = x 	imes 240 + 1.2x 	imes 400$$

Simplify:

$$72000 = 240x + 480x = 720x$$

Divide both sides by 720:

$$x = \frac{72000}{720} = 100$$

Therefore, the fare per km of the taxi is Rs. 100.

**Answer:** Rs. 100

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