Q) 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 the cost of 1 kg of apples is x and 1 kg of grapes is y, represent the given situation algebraically as a system of equations and check whether the system so obtained is consistent or not.

PYQ: Q 22 – CBSE 2025 – Code 30 – Series 5 – Set 1

Ans:

It is given that: `x` is the price of 1 kg of apples and `y` is the price of 1 kg of grapes

Step 1: Next, we are given two conditions – let’s try to write them in terms of x and y:

1. Buying 2 kg of apples and 1 kg of grapes costs ₹320

∴ we can write it as 2x + y = 320 …………. (i)

2. Buying 4 kg of apples and 2 kg of grapes costs ₹600

∴ we can write it as 4x + 2y = 600 ………… (ii)

These 2 equations represent the system of equations algebraically.

Step 2: Next, by simplifying equation (ii), we get:

2x + y = 300 …………… (iii)

Now, we have two equations:

2x + y = 320 ………….. (i)

and 2x + y = 300 ……… (iii)

We can see that the same combination (2x + y) is giving two different values: 320 and 300. This can’t happen!

Step 3: Decision: It is clear that the given set of system is wrong. By solving these two equations, we can’t get any unique solution of x and y  that will satisfy both equations at the same time. Therefore, the system is Inconsistent.

Please press the “Heart” button if you like the solution.