​If the cost of 3 kg of potatoes and 4 kg of tomatoes is Rs.100 and 4 kg of potatoes and 3 kg of tomatoes is Rs.110, then the rate of tomatoes Rs. per kg is :​

Correct option is A

​Given:

Cost of 3 kg potatoes + 4 kg tomatoes = Rs. 100

Cost of 4 kg potatoes + 3 kg tomatoes = Rs. 110

Let the rate of potatoes = Rs. x per kg
Let the rate of tomatoes = Rs. y per kg

Solution:
We solve the two equations:

$$\quad 3x + 4y = 100 \quad \text{(1)} \\\quad 4x + 3y = 110 \quad \text{(2)} \\$$​​

Step 1: Multiply both equations to eliminate one variable
Multiply Eq(1) by 4:
(3x + 4y) × 4 => 12x + 16y = 400

Multiply Eq(2) by 3:
(4x + 3y) × 3 => 12x + 9y = 330

Now subtract:

(12x + 16y) - (12x + 9y) = 400 - 330

12x + 16y - 12x - 9y = 70

7y = 70

y = 10

Now substitute back into Eq(1):
3x + 4(10) = 100
3x + 40 = 100
3x = 60
x = 20

So, rate of tomatoes per kg = Rs. 10

Final Answer:
Rs. 10