Ali buys a glass, a pencil box and a cup and pays ₹ 21 to the shopkeeper.…

Concept

When several purchases combine the same items, assign one variable to each unit price. Each purchase becomes a linear equation, and subtracting equations can isolate a variable by cancelling common terms.

Application

1. Let g, p and c be the prices of one glass, one pencil box and one cup, respectively.

2. Ali’s purchase gives g + p + c = 21.

3. Rakesh’s purchase gives g + 2p + c = 28. Subtracting the first equation gives p = 7.

4. Preeti’s purchase gives 2g + 2p + c = 35. Subtracting Ali’s equation gives g + p = 14, so g = 7.

5. Substitute g = 7 and p = 7 into g + p + c = 21: 7 + 7 + c = 21, so c = 7.

6. Therefore, 10c = 10 × 7 = ₹70.

Cross-check

Using g = p = c = 7, the three totals are 21, 28 and 35, exactly as stated. Hence the cost of 10 cups is ₹70.