Question

The highest of three plants A,B and C in a garden are in the ratio $\text{2:3:5}$ Their mean height is $\text{30 cm}$. Find the height of plant B.

If another plant D is added to the garden, the mean height of the four plants becomes $\text{33 cm}$, find the height of plant D.

Answer 1

Step 1: Finding the height of plant B

Ratio of heights of three plants $\text{= 2:3:5 = 2x:3x:5x}$

Mean of heights of three plants $\text{= 30 cm}$

$\frac{\text{2x + 3x+ 5x}}{\text{3}}\text{=30}$

$\text{10 x= 90}$

$\text{x = 9 cm}$

Height of A plant $\text{= 2x = 2×9 = 18 cm}$

Height of B plant $\text{= 3x = 3×9 = 27 cm}$

Height of C plant $\text{= 5x = 5×9 =45 cm}$

Step 2: Finding the height of plant D

Let the height of D plant be $\text{y}$

Mean of four plants $\text{= 33 cm}$

$\frac{\text{18+27+45+y}}{\text{4}}\text{=33}$

$\text{90+ y=132}$

$\text{y = 132-90}$

$\text{y = 42 cm}$

Height of the D plant is $\text{42 cm}$

Hence the height of the plant B and D is $\text{27 cm and 42 cm}$.