Question

5. In an apple orchard, trees of variety A are
25% more than the trees of variety B. Trees of
variety C are 50% of the total trees of variety
A and B. Find the percentage of variety C
trees relative to the variety B trees.​

Answer 1

Answer:

$\sf{The \ percentage \ of \ variety \ C \ trees}$

$\sf{relative \ to \ the \ variety \ B \ trees \ is \ 112.5\%.}$

Given:

• In an apple orchard, trees of variety A are 25% more than the trees of variety B.

• Trees of variety C are 50% of the total trees of variety A and B.

To find:

• The percentage of variety C
• trees relative to the variety B trees.

Solution:

$\sf{Let \ the \ number \ of \ trees \ of \ variety \ B}$

$\sf{be \ x.}$

$\sf{\leadsto{25\% \ of \ x}}$

$\sf{=\dfrac{25}{100}\times \ x}$

$\sf{\therefore{25\% \ of \ x=\dfrac{x}{4}}}$

$\sf{But, \ trees \ of \ variety \ A \ are \ 25\% \ more}$

$\sf{than \ trees \ of \ variety \ B.}$

$\sf{\longmapsto{Trees \ of \ variety \ A=x+\dfrac{x}{4}}}$

$\sf{\longmapsto{Trees \ of \ variety \ A=\dfrac{5x}{4}}}$

$\sf{According \ to \ the \ given \ condition.}$

$\sf{The \ total \ trees \ of \ variety \ A \ and \ B}$

$\sf{=x+\dfrac{5x}{4}}$

$\sf{=\dfrac{9x}{4}}$

$\sf{But, \ Trees \ of \ variety \ C \ is \ 50\% \ of}$

$\sf{the \ total \ trees \ of \ variety \ A \ and \ B.}$

$\sf{\therefore{Trees \ of \ variety \ C=\dfrac{1}{2}\times\dfrac{9x}{4}}}$

$\sf{\therefore{Trees \ of \ variety \ C=\dfrac{9x}{8}}}$

$\sf{Now,}$

$\sf{Percentage \ of \ variety \ C \ trees}$

$\sf{relative \ to \ the \ variety \ B \ trees}$

$\sf{=\dfrac{9x}{8}\times\dfrac{100}{x}}$

$\sf{=\dfrac{900}{8}}$

$\sf{=112.5\%}$

$\sf\purple{\tt{\therefore{The \ percentage \ of \ variety \ C \ trees}}}$

$\sf\purple{\tt{relative \ to \ the \ variety \ B \ trees \ is \ 112.5\%.}}$