Data Plan Overage
A student has a mobile data plan with a monthly limit of 2 GB (gigabytes). In a month, they use the following: 14 hours of music streaming at 128 kbps, 3 hours of video streaming at 1.5 Mbps, and 500 MB for web browsing and social media. The plan charges 100 rubles for each additional 100 MB beyond the limit. The student wants to know if they will incur an overage and by how much.
1. Calculate the total data used in MB. Show all steps and conversions.
Read the worked answer
Music: 14 hours × 3600 s/h = 50,400 s. At 128 kbps = 128,000 bits/s, total bits = 50,400 × 128,000 = 6,451,200,000 bits. Convert to bytes: ÷8 = 806,400,000 bytes. To MB (1 MB = 1,000,000 bytes): 806.4 MB. Video: 3 hours × 3600 = 10,800 s. At 1.5 Mbps = 1,500,000 bits/s, total bits = 10,800 × 1,500,000 = 16,200,000,000 bits. To bytes: ÷8 = 2,025,000,000 bytes. To MB: 2,025 MB. Browsing: 500 MB. Total = 806.4 + 2,025 + 500 = 3,331.4 MB.
2. The plan limit is 2 GB. Assuming 1 GB = 1024 MB, determine if the student exceeds the limit and by how many MB.
Read the worked answer
Limit in MB = 2 × 1024 = 2048 MB. Total used = 3331.4 MB. Overage = 3331.4 − 2048 = 1283.4 MB.
3. Calculate the additional charge. The plan charges 100 rubles per 100 MB over the limit. How many 100 MB blocks are charged?
Read the worked answer
Overage = 1283.4 MB. Number of 100 MB blocks = ceil(1283.4 / 100) = ceil(12.834) = 13 blocks. Charge = 13 × 100 = 1300 rubles. Note: If the provider charges proportionally, it would be 1283.4/100 × 100 = 1283.4 rubles, but typically blocks are rounded up.