A pen costs Rs. 7 each. A scale costs Rs. 5 each. X spends Rs. 38 on these…

Concept: In such 'find the quantity purchased' problems, translate the cost information into a linear equation with two non-negative-integer unknowns (the quantities bought). Because both quantities must be whole numbers that fit the total budget exactly, only specific pairs satisfy the equation — use a divisibility test to find the pair that fits exactly, rather than assuming several solutions exist.

Applying this to the problem:

1. Let the number of pens be a and the number of scales be b.

2. The total cost gives the equation 7a + 5b = 38.

3. Rearranging for a: 7a = 38 − 5b, so a = (38 − 5b)/7.

4. For a to be a whole number, (38 − 5b) must be exactly divisible by 7.

5. Testing every non-negative integer b with 5b ≤ 38 (so b = 0 through 7): only b = 2 gives 38 − 10 = 28, which is divisible by 7, giving a = 4; every other value of b in this range leaves a remainder not divisible by 7.

6. So a = 4 pens and b = 2 scales is the unique non-negative-integer solution.

Cross-check: Substituting back: 4 pens × Rs. 7 + 2 scales × Rs. 5 = Rs. 28 + Rs. 10 = Rs. 38, which matches the total spend exactly, confirming the count is both valid and unique — so the data given is sufficient to pin down a single answer.

∴ The number of pens purchased is 4.