Test Index

Decimals and Fractions Practice Test 1

© examsnet.com

Question : 20 of 40

Marks: +1, -0

A theatre consists of 4 auditoriums running 4 different evening movie shows in parallel. When the senior manager asked his assistant to calculate the number of people watching the movie in Auditorium 1, he replied that out of a total of 560 people, Auditorium2 has 24 people more than one-third of people in Auditorium 1. Auditorium 3 has twice those of Auditorium 2, and Auditorium 4 consists of 20 people more than

\frac{2}{5}

of people in Auditorium 3. Find the number of people in Auditorium.

210
200
198
195
350

Solution: 👈: Video Solution

Let the number of people in Auditorium 1 = x

Then, the number of people in Auditorium 2

=\frac{x}{3}+24

Number of people in Auditorium 3

=\frac{2x}{3}+48

Number of people in Auditorium 4

=\frac{2}{5}\left(\frac{2x}{3}+48\right)+20=\frac{4x}{15}+\frac{196}{5}

∴ Total number of people

=x+\frac{x}{3}+24+\frac{2x}{3}+48+\frac{4x}{15}+\frac{196}{5}

\Rightarrow 560=\frac{15x+5x+360+10x+720+4x+588}{15}

\Rightarrow 560=\frac{34x+1668}{15}

\Rightarrow 34x+1668=8400

\Rightarrow 34x=6732

\Rightarrow x=198

© examsnet.com

Go to Question:

Prev Question

Next Question