In the standard 555 timer astable multivibrator, the capacitor C charges through the series combination R_A + R_B and discharges through R_B alone, producing a continuous train of pulses. Two design equations govern its behaviour:

Frequency: f = 1.44 / ((R_A + 2R_B) × C)

Duty cycle: D = (R_A + R_B) / (R_A + 2R_B)

The crucial observation is that frequency depends on both the resistors and the capacitor, but the duty cycle depends only on the resistor ratio — the capacitor C cancels out of the duty-cycle expression. This gives the designer a clean way to shift frequency without disturbing the pulse shape.

• Why decreasing C (with R_A and R_B fixed) is correct: reducing C makes the denominator (R_A + 2R_B) × C smaller, so f increases. Because C is absent from the duty-cycle formula and the resistors are unchanged, the duty cycle stays exactly the same. This meets both requirements — higher frequency, unchanged duty cycle.
• Increasing R_A would raise the denominator and lower the frequency, and it would also change the resistor ratio, altering the duty cycle — so it fails on both counts.
• Increasing C moves the frequency in the wrong direction (it lowers f), so it cannot increase frequency.
• Decreasing the supply voltage does not appear in either formula (the charge/discharge thresholds scale with V_CC), so it does not change the frequency or duty cycle in the ideal case.

Therefore, decreasing C while holding R_A and R_B constant is the right approach.