Question

If 10 horses consume 18 bushels in 36 days, how long will 24 bushels last for 30 horses?

Answer 1

Hint: We will first find how many bushels is consumed by 1 horse in 36 days by using a unitary method. So, we can write it as
$\begin{align}
  & 10horses=18bushels \\
 & 1horse=? \\
\end{align}$ .
After solving this, we will similarly find for 24 bushels consumed by 30 horses. So, we will have data for both 1 horse with us. Then we will compare it with days i.e. number of bushels in 36days then in how many days it will consume these bushels. Thus, on solving we will get an answer. Also, we will assume here the number of days to be found as ‘x’.

Complete step-by-step answer:
Here, we are given that 10 horses consume 18 bushels in 36 days. So, we can find how many bushels 1 horse can consume in 36 days. So, we can find this by unitary method, we can be written as
$\begin{align}
  & 10horses=18bushels \\
 & 1horse=? \\
\end{align}$
On further solving, we get as
$=\dfrac{18\times 1}{10}=1.8bushels$
Thus, we can say that 1 horse consume 1.8 bushels in 36 days.
Similarly, we are given that 30horses consume 24 bushels in let say ‘x’ days. So, using unitary method we will find how many bushels are consume by 1 horse in x days.
$\begin{align}
  & 30horses=24bushels \\
 & 1horse=? \\
\end{align}$
On further solving, we get as
$=\dfrac{24\times 1}{30}=\dfrac{8}{10}=0.8bushels$
Thus, from this we can say that 1horse consume 0.8 bushels in x days.
Now, we will compare both the data of 1 horse we have i.e. 1.8 bushels in 36 days and 0.8 bushels in x days.
So, we will again use unitary method to method value of ‘x’. We get as
$\begin{align}
  & 1.8bushels=36days \\
 & 0.8bushels=xdays \\
\end{align}$
Here, we will make x as subject so, we can write it as
$x=\dfrac{0.8\times 36}{1.8}$
On further solving, we get as
$x=0.8\times 20=16days$
Thus, we can say that 24 bushels last for 30 horses for 16 days.

Note: Another method to find number of days is by using the formula $horses1\times bushels\times days1=horses\times bushels1\times days$ where $horses1=10,bushels 1=18,days1=36$ and $horses=30,bushels=24,days=x$ . So, on putting values, we get as
$10\times 24\times 36=30\times 18\times x$
On solving, we get x as
$\dfrac{10\times 24\times 36}{30\times 18}=x=16days$
We are interchanging the value of bushels in order to get an answer. Thus, we will get the same answer.