Question

In a garden, 10% pink rose plants, 30% red rose plants, 40% white rose plants are present out of 400 plants and the remaining are jasmine plants. The number of jasmine plants are-
A. 320
B. 80
C. 400
D. 160

Answer 1

Hint:This is a simple question of linear equations in one variable. We will begin by assuming the number of jasmine plants as a variable(x). Then, we will find the number of different types of rose plants using the concept of percentages. Finally, we will form a linear equation in x using the information that the sum of all types of plants is 400, which will give us the answer.

Complete step-by-step answer:
We are required to find the number of jasmine plants in this question. We will begin by assuming the number of jasmine plants as x. Also, it has been given that the total number of plants is 400.
We have been given that 10% of the plants are pink rose plants, and we will let them to be p, which can be calculated as-
 $ {\text{p}} = 10\% \;of\;400 = \dfrac{{10}}{{100}} \times 400 = 40 $ ...(1)
Similarly, we have been given the number of red rose plants, say r, to be 30% of the total plants, which can be calculated as-
 $ {\text{r}} = 30\% \,of\;400 = \dfrac{{30}}{{100}} \times 400 = 120 $ ...(2)
Finally, there are 40% of the white rose plants, say w, which will be computed as-
 $ {\text{w}} = 40\% \;of\;400 = \dfrac{{40}}{{100}} \times 400 = 160 $ ...(3)
Now that we know the number of the rest of the types of plants, we can write an equation that the sum of all types of plants will be equal to the total number of plants, which is 400 as-
Using equations (1), (2) and (3),
 $ {\text{p}} + {\text{r}} + {\text{w}} + {\text{x}} = 400 $
 $ 40 + 120 + 160 + {\text{x}} = 400 $
 $ {\text{x}} = 400 - 40 - 120 - 160 = 80 $
These are the required number of jasmine plants, and the correct option is B.

Note: There is an alternative, shorter method to solve this problem. We know that the percentage of pink, red and white rose plants are 10%, 30% and 40% respectively. So, we can write that the rest of the percentage belongs to jasmine plants which is-
100% - 10% - 30% - 40% = 20%
So, the number of jasmine plants are simply 20% of the total, that is 400-
 $ {\text{x}} = 20\% \;of\;400 = \dfrac{{20}}{{100}} \times 400 = 80 $ .