Question

A driver of an auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres ?

Answer 1

Hint: First find the profit in rupees for the percentage given in the question. By profit you get the earnings of the driver in the first case. By using the earnings, find the profit in the second case. You must also find the cost that each passenger has to pay. For finding the cost of each passenger use the following formula (by using total earnings)

Complete step-by-step answer:

$\text{Cost of each passenger = }\dfrac{\text{Total earnings}}{\text{No}\text{.of passengers}}$

First, we have to find the earning of driver in first case:

Let the income when number of passengers is 3 was $3x$

Given in the question: the petrol price is 30Re per litre.

By the above condition, we can say the expense is:

Expense = 30Re

Given in the question: the profit percentage per trip is 20%

Profit = 20% of 30 = $\dfrac{20\times 30}{100}$

Profit = (2).(3) = 6 Re

By basic knowledge, we can say that this is true:

Earning = Expense + Profit

By using the above condition, we get earning of driver as:

Earning = 30Re + 6Re = 36Re

Here we assumed income to be $3x$ , by that we get:

$3x=36,x=12$

So, 12Re is the cost for each passenger per trip.

In Next case it is given that no. of passengers is 4.

So, by using that we can find the income in this case

By basic knowledge, we can say the income will be:

Income = (no. of passengers) x (cost for each)

By applying the above formula, we get the income as:

Income = 4 x 12 = 48Re

The cost of passengers is used from the result of the previous case.

Given in the question: the petrol price is 24Re per litre.

By using this we can say the expense will be:

expense = 24

By basic knowledge we can say the profit will be:

Profit = income – expense

By applying this, we can find the profit in this case:

Profit = 48 – 24 = 24

Therefore, profit percentage in second is 24%


Note: The cost of passengers remains the same from case 1 to case 2. This is a crucial observation; don't confuse it, because that point helps to get the result.