Amplitude Modulation:
Amplitude modulation (AM) is a technique used in communication systems to transmit information by varying the amplitude of a carrier signal in accordance with the variations in the message signal. It is a commonly used modulation scheme in radio broadcasting.

Modulation Index:
The modulation index is a parameter that determines the extent of modulation in an AM signal. It is defined as the ratio of the peak amplitude of the message signal to the peak amplitude of the carrier signal. Mathematically, it can be expressed as:
Modulation Index (m) = (Amplitude of Message Signal) / (Amplitude of Carrier Signal)

Given Information:
In this question, we are given that the carrier signal is amplitude modulated by a single-tone sinusoidal message signal with a modulation index of 50%.
Modulation Index (m) = 50%

Suppression of Carrier and Sidebands:
In AM modulation, the modulated signal consists of the carrier signal and two sidebands - the upper sideband (USB) and the lower sideband (LSB). These sidebands contain the information from the message signal. When the carrier and one of the sidebands are suppressed, it means that either the carrier and the USB or the carrier and the LSB are removed from the modulated signal.

Calculation of Power Saved:
To calculate the percentage of power saved, we need to determine the power in the suppressed carrier and sideband and compare it to the power in the original modulated signal.

Power in the Original Modulated Signal:
The power in the original modulated signal can be calculated as the sum of the powers in the carrier and the two sidebands. Since the modulation index is given as 50%, the power in each sideband is 25% of the total power. Therefore, the power in the original modulated signal is:
Power in Original Modulated Signal = Power in Carrier + Power in USB + Power in LSB
= Power in Carrier + 0.25 * Power in Carrier + 0.25 * Power in Carrier
= Power in Carrier + 0.5 * Power in Carrier
= 1.5 * Power in Carrier

Power in the Suppressed Carrier and Sideband:
When the carrier and one of the sidebands are suppressed, the power in the suppressed components becomes zero. The power in the modulated signal with suppressed carrier and USB is then:
Power in Suppressed Carrier and USB = Power in LSB
= 0.25 * Power in Carrier

Calculation of Power Saved:
The percentage of power saved can be calculated as the ratio of the power saved to the power in the original modulated signal, multiplied by 100.
Percentage of Power Saved = (Power Saved / Power in Original Modulated Signal) * 100
= (Power in Carrier + 0.25 * Power in Carrier) / (1.5 * Power in Carrier) * 100
= (1.25 * Power in Carrier) / (1.5 * Power in Carrier) * 100
= (5/6) * 100
= 83.33%

Rounded-off Answer:
The percentage of power saved, rounded off to one decimal place, is 83.3%.