Question

The heights of three plants A,B AND C in a gardan are in the ratio 2:3:5. Their mean height is 30cm.
I) find the height of plant B
ii) if another plant D is added to the garden such that the mean height of the four plants is now 33cm find the height of plant D

Answer 1

Answer:

I) 27

ii)42

Step-by-step explanation:

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Answer 2

Answer :-

i) Height of plant B is 27 cm.

ii) Height of plant D is 42 cm.

Explanation :-

Ratio of heights of 3 plants A, B, C = 2 : 3 : 5

Let the heights of 3 plants A, B, C be 2x, 3x, 5x

Mean of heights of 3 plants = 30 cm

Mean = Sum of observations/Number of observations

30 = (2x + 3x + 5x)/3

30 = 10x/3

30 * 3 = 10x

90 = 10x

90/10 = x

9 = x

x = 9

Height of the plant B = 3x = 3(9) = 27 cm

Sum of 3 observations = 2x + 3x + 5x = 10x = 10(9) = 90

Let the height of the plant D be 'x' cm

Sum of 4 observations = 90 + x

Number of observations = 3 + 1 = 4

Mean of heights 4 plants = 33 cm

Sum of observations/Number of obervations = 33

(90 + x)/4 = 33

90 + x = 33(4)

90 + x = 132

x = 132 - 90

x = 42

Height of plant D = 42