The total cost of 3 kg of potatoes and 4 kg of tomatoes is ₹100, while the…

Concept

When two totals depend on the same two unknown unit prices, represent the prices by variables and form one linear equation from each total. Solving the simultaneous equations gives the unique unit prices.

Application

1. Let p be the price of potatoes per kilogram and t be the price of tomatoes per kilogram. The two totals give 3p + 4t = 100 and 4p + 3t = 110.

2. Subtract the first equation from the second: (4p + 3t) − (3p + 4t) = 110 − 100, so p − t = 10 and therefore p = t + 10.

3. Substitute p = t + 10 into 3p + 4t = 100: 3(t + 10) + 4t = 100, so 7t + 30 = 100, 7t = 70, and t = 10.

Cross-check

The corresponding potato price is p = 20. Then 3(20) + 4(10) = 100 and 4(20) + 3(10) = 110, so both original totals are satisfied.

Therefore, the price of tomatoes is ₹10 per kilogram.