Question

There are four kinds of trees in the orchard. Four parts of the total tree are neem trees. Half of the remaining trees are mango trees. Half of the remaining are drumstick trees and remaining six trees are peepal trees. Find the total number of trees in the orchard.

Answer 1

Hint- By assuming that the total number of trees are $x$, after that find the value of all the trees one by one in the form of $x$. After calculating all numbers of trees, we will find exact numbers of anyone of the number of trees. Then compare this value with anyone of the $x$ term value. Thus we can find the total number of trees which is assumed as $x$.

Complete step-by-step answer:
Let the total number of tree $ = x$
According to the question –
Neem trees$ = \dfrac{x}{4}$
Remaining number of trees $ = x - \dfrac{x}{
  4 \\
}$
$
   \Rightarrow \dfrac{{4x - x}}{4} \\
   \Rightarrow \dfrac{{3x}}{4} \\
$
Again according to the question-
Mango trees are half of remaining trees
\[
   \Rightarrow \left( {\dfrac{{3x}}{4}} \right)/2 \\
   \Rightarrow \dfrac{{3x}}{8} \\
\]
  Again according to the question
Half of the remaining trees are drumstick trees
$
   \Rightarrow \left( {\dfrac{{3x}}{8}} \right)/2 \\
   \Rightarrow \dfrac{{3x}}{{16}} \\
$
Now the remaining 6 trees are peepal trees
So peepal trees are$ = \dfrac{{3x}}{{16}}$
And according to the question peepal trees$ = 6$
$
   \Rightarrow 6 = \dfrac{{3x}}{
  16 \\
} \\
   \Rightarrow 96 = 3x \\
   \Rightarrow x = \dfrac{{96}}{3} \\
   \Rightarrow x = 32 \\
$
Hence the total number of trees is 32.

Note- We have used the subtraction process for calculation of number of trees one by one according to the question. After calculating a sufficient number of trees, at last compare the final number of trees with the given remaining number of trees. This we will find the total number of trees which is 32 and assumed as the value of $x$ . Hence $x = 32$