Question

The cost of 2 kg apples and 1 kg of grapes on a day was found to be ₹ 320. The cost of 4 kg apples and 2 kg grapes was found to be ₹ 600. If cost of 1 kg of apples and 1 kg of grapes is ₹ x and ₹ y respectively, represent the given situation algebraically as a system of equations and check whether the system so obtained is consistent or not.

Answer 1

Given: Let x = cost of 1 kg apples (₹), y = cost of 1 kg grapes (₹). From 2x + y = 320, 4x + 2y = 600.

Step-wise calculation:

1. Write the system:

2x + y = 320

4x + 2y = 600

2. Multiply the first equation by 2:

2 × (2x + y) = 2 × 320 

⇒ 4x + 2y = 640

3. Compare with the second equation:

4x + 2y = 640 and 4x + 2y = 600

This gives the contradiction 640 = 600, which is impossible.

Hence no pair (x, y) can satisfy both equations simultaneously.

The system 2x + y = 320 and 4x + 2y = 600 is inconsistent (has no solution).