Malati bought 5 rose plants and 9 jasmine plants for ₹1,410 and her friend Rani bought 6 rose plants and 5 jasmine plants for ₹1,170.

Let the price of 1 rose plant = ₹x
Let the price of 1 jasmine plant = ₹y

From the problem:

1. Malati bought 5 rose and 9 jasmine plants for ₹1,410:

$5x + 9y = 1410 \quad ...(1)$

2. Rani bought 6 rose and 5 jasmine plants for ₹1,170:

$6x + 5y = 1170 \quad ...(2)$

Step 1: Solve the equations

Multiply (1) by 5 and (2) by 9 to equalize the coefficients of $y$:

$5(5x + 9y) = 25x + 45y = 7050$

$9(6x + 5y) = 54x + 45y = 10530$

Subtract the first from the second:

$(54x + 45y) - (25x + 45y) = 10530 - 7050$

$29x = 3480$

$x = \frac{3480}{29} = 120$

Step 2: Find y

Substitute $x = 120$ into (1):

$5(120) + 9y = 1410$

$600 + 9y = 1410$

$9y = 810$

$y = 90$

✅ Answer:

• Price of 1 rose plant = ₹120

• Price of 1 jasmine plant = ₹90