Two plants were planted the same day. The change in the height of the first plant after 3 days was the same as the change in the height of the second plant after 7 days. After 12 days the height of the first plant was 4% greater than its initial height and the height of the second plant was 5% greater than its initial height. What was the ratio of initial heights of plants?
Answers
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Given : Two plants were planted the same day.
The change in the height of the first plant after 3 days was the same as the change in the height of the second plant after 7 days. After 12 days the height of the first plant was 4% greater than its initial height and the height of the second plant was 5% greater than its initial height.
To Find : the ratio of initial heights of plants
Solution :
Plant 1 in 3 Days = x
=> plant 1 in 1 day = x/3
=> plant 1 in 12 days = 12x/3 = 4x
Plant 2 in 7 Days = x
=> plant 2 in 1 day = x/7
=> plant 1 in 12 days = 12x/3 =12x/7
1st plant height = A
4 % growth = 4A/100 = 4x => A = 100x
2nd plant height = B
5 % growth = 5B/100 = 12x/7 => B = 240x/7
A : B = 100x : 240x/7
=> 700 : 240
=> 70 : 24
=> 35 : 12
ratio of initial heights of plants = 35 : 12
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