Question

A group of people went to a restaurant.

Answer 1

Answer:

The fraction of the people who choose curry = $\frac{13}{4}$

Step-by-step explanation:

As given,

Starter              Main course

Soup                    Lasagna

Prawns                 Curry

The number of people who choose soup: the number of people who choose prawns = 2 : 3

Of those who chose soup,

The number of people who choose Lasagna : the number of people who chose curry = 5 : 3

Of those who chose prawns,

The number of people who chose Lasagna : the number of people who chose curry = 1 : 5

Let total number of people goes to restaurant = 5x

People who choose soup = $\frac{2}{5}$×5x = 2x

People who choose prawns = $\frac{3}{5}$×5x = 3x

Now, given,

Of those who choose soup,

The number of people who choose Lasagna : the number of people who chose curry = 5 : 3

So,

People who choose Lasagna after choosing soup = $\frac{5}{8}$×2x = $\frac{5}{4}x$

People who choose Curry after choosing soup = $\frac{3}{8}$×2x = $\frac{3}{4}x$

Also, given,

Of those who chose prawns,

The number of people who chose Lasagna : the number of people who chose curry = 1 : 5

So,

People who choose Lasagna after choosing prawns = $\frac{1}{6}$×3x = $\frac{1}{2}x$

People who choose Curry after choosing prawns = $\frac{5}{6}$×3x = $\frac{5}{2}x$

So,

Total number of people who choose curry = $\frac{3}{4}x$ + $\frac{5}{2}x$ = $x ( \frac{3}{4} + \frac{5}{2} ) = x (\frac{3 + 10}{4} ) = x ( \frac{13}{4} ) = \frac{13}{4}x$

So ,

The fraction of the people who choose curry = $\frac{Total number of people who choose curry}{Total number of people who go to restaurant} = \frac{\frac{13}{4} x}{x} = \frac{13}{4}$