Question

There are four kinds of trees in an orchard. Fourth part of the total trees are neem trees. Half of the remaining trees are mango trees. Half of the remaining trees are Drumstick trees and the remaining 6 trees are peepal trees. Find the total number of trees in the orchard.

Answer 1

Hint – In this particular type of question use the concept that assume any variable be the number of trees then after constructing one equation the remaining number of tees is the difference of the variable and the first equation so use these concepts to reach the solution of the question.

Complete step by step solution:
There are four types of trees in an orchard.
Let the total number of trees in an orchard be X.
Now it is given that Fourth part of the total trees are neem trees.
So the total number of trees divided by 4 is equal to neem trees.
Therefore, neem trees = (X/4).
Now it is given that half of the remaining trees are Mango trees.
So the remaining trees are = X – (X/4) = (3X/4)
So half of the remaining trees is = $\dfrac{1}{2}\left( {\dfrac{{3X}}{4}} \right) = \dfrac{{3X}}{8}$
So the number of mango trees = (3X/8)
Now the remaining trees are = $\dfrac{{3X}}{4} - \dfrac{{3X}}{8} = \dfrac{{3X}}{8}$
Now it is again given that half of the remaining trees are Drumstick trees.
So the number of Drumstick trees = $\dfrac{1}{2}\left( {\dfrac{{3X}}{8}} \right) = \dfrac{{3X}}{{16}}$
So the remaining trees are = $\dfrac{{3X}}{8} - \dfrac{{3X}}{{16}} = \dfrac{{3X}}{{16}}$
Now it is given that the remaining 6 trees are people.
Therefore, number of peepal trees are 6 = $\dfrac{{3X}}{{16}}$
Now simplify this equation we have,
$ \Rightarrow X = \dfrac{{16\left( 6 \right)}}{3} = 32$
So the total number of trees in the orchard is 32 trees.
So this is the required answer.

Note – Whenever we face such types of question first find out the neem trees by dividing the variable by 4 as above, then find out the remaining trees as above then find out the mango trees by divide by 2 in the remaining trees as above, then again find the remaining trees then again divide by 2 in the remaining trees, then again find the remaining trees as above then equate this number of trees to 6 and simplify we will get the total number of trees in an orchard.