Question

The ratio of daily wages of two workers is $4:3$ and one gets $Rs.9$ more than the other. What are their daily wages?

Answer 1

Hint: Here we have been given the ratio between the daily wages of two workers and also that one get $Rs.9$ more than the other . We have to find their daily wages. Firstly we will let our ratio values by multiplying them with an unknown variable. Then we will subtract the bigger value by smaller value and put it equal to $Rs.9$ and solve. Finally we will put the variable value obtained in the ratio we let and get our desired answer.

Complete step by step answer:
The ratio of daily wages of two workers is given as $4:3$. Also one gets $Rs.9$ more than the other.So let us take the wages of the workers as follows,
Daily wages of first worker $=4x$…..$\left( 1 \right)$
Daily wages of second worker $=3x$……$\left( 2 \right)$
As for any value of $x$ the value $4x$ will be greater than $3x$ so the difference between the two wages can be written as follows,
$4x-3x=Rs.9$

Now we will simplify it as follows,
$\Rightarrow x=Rs.9$
We have got the value of $x=Rs.9$ substitute it in equation (1),
Daily wages of first worker $=4\times Rs.9$
Daily wages of first worker $=Rs.36$
Substitute $x=Rs.9$ in equation (2) we get,
Daily wages of second worker $=3\times Rs.9$
Daily wages of second worker $=Rs.27$

Hence the daily wages of two workers is $Rs.36$ and $Rs.27$.

Note: While comparing two quantities the method of division is very useful and this division is given a name known as ratio. Ratio is the number which expresses one quantity as a fraction of the other one. It always exists between the quantities of the same kind and the unit of the both quantities should be the same. We can cross check our answer as below,
The ratio between $Rs.36$ and $Rs.27$ is,
$\Rightarrow \dfrac{Rs.36}{Rs.27}$
Divide numerator and denominator by $9$ ,
$\Rightarrow \dfrac{4}{3}$
This can be written as $4:3$
Also the difference between the two values is,
$\Rightarrow ~Rs.36-Rs.27$
$\therefore Rs.9$
Hence our answer is correct.