This option is correct because the formula for simple interest is I = PRT/100. When P and R are fixed, the interest I varies directly with T. Doubling the time doubles the interest, and halving the time halves the interest. Therefore, simple interest is directly proportional to the time period.
Option A:
The time period appears as a direct factor in the simple interest formula. If P and R stay constant, any change in T results in a proportional change in I. This shows a clear direct proportionality between interest and time, so this option correctly identifies the varying quantity.
Option B:
Compound amount includes both principal and interest in compound interest problems and is not part of the simple interest formula in this way. Simple interest is not directly proportional to compound amount. Thus, this option is not appropriate.
Option C:
Discount allowed refers to the reduction from the marked price in sales, which belongs to commercial arithmetic. It does not appear in the simple interest formula and is unrelated to the direct proportionality mentioned. Therefore, discount is not the correct answer.
Option D:
Selling price is determined by cost, profit or loss and discount, not directly by simple interest. While interest can affect selling price in some credit contexts, the simple interest formula itself does not express any direct relationship with selling price. Hence, this option is incorrect.
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