Examveda

# Jay wants to buy a total of 100 plants using exactly a sum of Rs. 1000. He can buy Rose plants at Rs. 20 per plant or marigold or Sun flower plants at Rs. 5 and Rs. 1 per plant respectively. If he has to buy at least one of each plant and cannot buy any other type of plants, then in how many distinct ways can Jay make his purchase?

A. 2

B. 3

C. 4

D. 5

E. None of these

### Solution(By Examveda Team)

Let the number of Rose plants be a.
Let number of marigold plants be b.
Let the number of Sunflower plants be c.
According to question,
20a + 5b + 1c = 1000 - - - - - - (1)
a + b + c = 100 - - - - - - - - - - (2)
Solving the above two equations by eliminating c, 19a + 4b = 900
b = $$\frac{{900 - 19a}}{4}$$   = $$225 - \frac{{19a}}{4}$$   - - - - - - - (3)
b being the number of plants, is a positive integer, and is less than 99, as each of the other two types have at least one plant in the combination i.e .
0 < b < 99 - - - - - - - (4)
Substituting (3) in (4),
0 < 225 - $$\frac{{19a}}{4}$$ < 99
⇒ 225 < -$$\frac{{19a}}{4}$$ < (99 - 225)
⇒ 4 × 225 > 19a > 126 × 4
⇒ $$\frac{{900}}{{19}}$$ > a > 504
a is the integer between 47 and 27 - - - - - - - - (5)
From (3), it is clear, a should be multiple of 4.
Hence, possible values of a are (28,32,36,40,44)
For a=28 and 32, a+b>100
For all other values of a, we get the desired solution:
a=36,b=54,c=10
a=40,b=35,c=25
a=44,b=16,c=40
Three solutions are possible.