Question

A forester wants to plant 44 apple trees, 66 banana trees and 110 mango trees in equal rows. Also, he wants to make distinct rows of different trees. The number of minimum rows that are requires are:
(a) 2
(b) 3
(c) 10
(d) 11

Answer 1

Hint: As a minimum number of rows are asked, so we need to put the maximum number of trees possible in each row. Therefore, the number of trees in each row is equal to the HCF of the number of the three trees. Once we get the number of trees in each row, just divide the total number of trees by the number of trees per row to get the answer.

Complete step-by-step answer:
A minimum number of rows are asked, so we need to put the maximum number of trees possible in each row. Also, it is mentioned that the number of trees in each row is the same and no row consists of more than one type of tree. So, the number of trees in each row must be the factor of the number of trees of each type. So, we can say that the number of trees in each row must be equal to the HCF of the number of trees of each type, i.e., the highest common factor of 44, 66, 110.
Now if we see, 66 is divisible by 11, 3 and 2 while 44 is divisible by 11 and 4, i.e., two 2s. Also, 110 is divisible by 11, 5 and 2. So, the three numbers can be represented as:
$44=2\times 2\times 11$
$66=2\times 3\times 11$
$110=2\times 5\times 11$
$\therefore HCF(44,66,110)=2\times 11=22$
Therefore, the number of trees in each row is 22 trees.
Now let us find the total number of trees by adding the number of each type of tree.
$\text{Total trees}=44+66+110=220$
Now the total number of rows of tree is given by $\dfrac{\text{total trees}}{\text{trees in each row}}$ , which is equal to $\dfrac{220}{22}=10\text{ rows}$ .
Hence, the answer to the above question is option (c).

Note: If in case you are asked to find the LCM of two fractions you must use the formula $HCF=\dfrac{HCF\text{ of numerator of the fractions}}{\text{LCM of the denominator of the fractions}}$ . Also, remember that the key to the above question is realising the fact that the number of trees in each row is equal to the HCF of the number of each type of tree.