Question

In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?​

Answer 1

There are two methods to solve the given problem.

1. Unitary method
2. Cross multiplication method

Unitary method:

We know that 3 computers are given for 6 students.

This written in ratio form :

$\longrightarrow{\sf{3 : 6}}$

For finding number of computers for 1 student we will make it into fraction form and simplify it .

$\longrightarrow{\sf{\dfrac{3}{6}}}$

Simplification gives :

$\longrightarrow{\sf{\cancel{\dfrac{3}{6}} \implies \dfrac{1}{2}}}$

$\longrightarrow{\sf{\dfrac{1}{2} = 2 \: students = 1 \: computer}}$

Now we are given the number of computers and asked number of students.

So we will divide 24 computers among the students in such a way that 2 students get 1 computer.

$\longrightarrow{\sf{\dfrac{24}{2}}}$

$\longrightarrow{\sf{\cancel{\dfrac{24}{2}} \implies 12}}$

So 12 computers will be needed for 24 students .

Cross multiplication method :

$\longrightarrow{\sf{3 = 6}}$

$\longrightarrow{\sf{24 = ?}}$

So :

$\longrightarrow{\sf{\dfrac{3}{6} \times 24}}$

$\longrightarrow{\sf{\dfrac{1}{2} \times 24}}$

$\longrightarrow{\sf{\dfrac{1}{\cancel{2}} \times \cancel{24} \implies 12}}$

So , 12 computers are needed for 24 students.

Answer 2

Using Unitary Method, we have

6 students require 3 computers

∴ 1 student will require =

$\frac{3}{6} computers$

c

∴ 24 students will require

$=\frac{3}{6} x 24 \: computers$

= 3 × 4 computers = 12 computers

Hence the number of computers required = 12.