Question

There are three types of tickets, economy, business and first class. The price of these tickets is in the ratio, economy: business: first class= 2:5:9.
The price of a business ticket is Rs. 2350. Calculate the price of a first class ticket.
Work out the price of an economy ticket as a percentage of the price of a first class ticket.

Answer 1

Hint: Take the ratios in proportion of x and then calculate the value of using the business class ticket price. Obtain the price of the other two classes and then simply divide the price of the economy ticket by that of a first class ticket and then multiply by 100 to get the percentage.

Complete step-by-step solution:
Proportion defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
The comparison of two quantities by the method of division is called the ratio. One can say that the comparison or simplified form of two quantities of the same kind is referred to as ratio.
There are no specific formulas to solve such questions, just some simple assumptions are made and then proceed with those assumptions.
Taking the ratios in proportion of x-
$2x: 5x: 9x$
Now, as the ratios are that of the prices of different classes so 2x becomes the price of the economy class. Similarly, 5x is the price of the business class and 9x is that of the first class.
As the price of the business ticket is stated as 2350, we have
$5x = 2350$
$x = 470$
From this value of x we calculate the price of the first class ticket.
The ratio value of first class ticket is given by $9x$, so the price is $9\times 470$ =$\text{Rs.} 4230$
The ratio value of economy class is $2x$, so the price becomes $2\times 470$ = $\text{Rs.} 940$
 Working out the price of an economy ticket as a percentage of the price of a first class ticket.
For this divide the prices of economy class with first class.
$\dfrac{{940}}{{4230}} \times 100 = 22.22\% $.

Note- In these types of questions, always assume the given in proportion of x to get the answers. This quest is a simple application of proportionality problems.