The ratio of fare of a person between Auto and Bus is 2 : 3.5 and the ratio of number of passengers travelled, on a particular day, by Auto and Bus is 4 : 7. By what fraction the total fare collected by Auto on that particular day is less than the total fare collected by Bus?

The correct answer is 33/49.

Step 1: Understand the given ratios.
We are given two ratios:
1. The ratio of the fare per person between Auto and Bus is 2 : 3.5.
2. The ratio of the number of passengers travelling by Auto and Bus is 4 : 7.

Step 2: Calculate the total fare collected by each mode of transport.
Total fare collected is the product of the fare per person and the number of passengers.
Let the fare per person for Auto be 2 units and for Bus be 3.5 units.
Let the number of passengers for Auto be 4 units and for Bus be 7 units.

Total fare collected by Auto:

${\mathrm{Total}}_{\mathrm{Auto}}=2\times 4=8$

Total fare collected by Bus:

${\mathrm{Total}}_{\mathrm{Bus}}=3.5\times 7=24.5$

Step 3: Find the fraction by which Auto's fare is less than Bus's fare.
First, calculate the difference between the total fare collected by Bus and Auto:

$\mathrm{Difference}=24.5-8=16.5$

Next, find the required fraction by dividing this difference by the total fare collected by Bus:

$\mathrm{Required\; Fraction}=\frac{16.5}{24.5}$

To simplify the fraction, multiply both the numerator and the denominator by 10 to eliminate the decimal points:

$\mathrm{Required\; Fraction}=\frac{165}{245}$

Now, simplify by dividing both the numerator and the denominator by 5:

$\frac{165÷5}{245÷5}=\frac{33}{49}$

Thus, the total fare collected by Auto is less than the total fare collected by Bus by a fraction of 33/49.