Question

A worker is paid Rs $200$ for $8$ days work. If he works for $20$ days, how much will he get?

Answer 1

Hint: In this type of question let us suppose that the amount he will pay in $20$ days is $x$ then the question become as Rs $200$ for $8$ days of work and Rs $x$ for the $20$ days of work .So by direct variation we can find out the value of $x$

Complete step-by-step answer:
It is given that the person is Paid as Rs $200$ for $8$ days of work . We have to find what amount he should be paid for $20$ days of work .
Let us suppose that $x$ is the amount that he would pay for $20$ days of work .
So Now

Income in Rs	$200$	$x$
Number of days	$8$	$20$

So the income and the number of days is directly varied means that the Income of in Rs is directly proportional to Number of days the man can work .
By the proportionality we know it becomes that ;
$\dfrac{{200}}{8} = \dfrac{x}{{20}}$
Now by cross multiplication
$200 \times 20 = 8 \times x$
$8x = 4000$
By dividing by $8$ on the both side we get ;
$x = \dfrac{{4000}}{8}$
$x = 500$
Hence the person will get Rs $500$ for the work of $20$ days

Note: This Question we can solve in a few steps by Unitary Method . In this we will try to find out what amount a worker will pay in $1$ day of work .
In one day the amount he will get is equal to $\dfrac{{200}}{8}$ . Now for the $20$ days of work this is equal to $\dfrac{{200}}{8} \times 20$ . This will equal to Rs $500$ and it is your required answer.
In Inverse variation the one number is increase and the other one is decreases