Bertha buys electricity from a company that offers a choice of two tariffs. Both have a daily charge of $0.20 regardless of how much electricity is used. The 'standard' tariff charges $0.10 for each unit used, while the 'day/night tariff' charges $0.12 for each unit consumed between 06:00 and 22:00 but only $0.05 for each unit consumed between 22:00 and 06:00, when total demand on the electricity network is low. Bertha is currently on the standard tariff. What is the highest proportion of her total electricity consumption that Bertha's daytime use can be, so that she would not be paying more if she switched to the 'day/night' tariff?

A. 5/17

B. 2/5

C. 5/7

D. 17/20

Question

Mathematics

Bethany

28 April, 17:19

Bertha buys electricity from a company that offers a choice of two tariffs. Both have a daily charge of $0.20 regardless of how much electricity is used. The 'standard' tariff charges $0.10 for each unit used, while the 'day/night tariff' charges $0.12 for each unit consumed between 06:00 and 22:00 but only $0.05 for each unit consumed between 22:00 and 06:00, when total demand on the electricity network is low. Bertha is currently on the standard tariff. What is the highest proportion of her total electricity consumption that Bertha's daytime use can be, so that she would not be paying more if she switched to the 'day/night' tariff?

A. 5/17

B. 2/5

C. 5/7

D. 17/20

+3

Answers (1)

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Fields · Answer 1

Answer: D (17/20)

Step-by-step explanation:

The two choices are:

The 'standard' tariff charges = $0.10 per unit

The 'day/night tariff' = $0.12 per unit for each unit consumed between 06:00 and 22:00 but only $0.05 for each unit consumed between 22:00 and 06:00

The day time is between 22:00 and 06:00

Time = 22 - 6 = 16 hours

Let assume that the charges are unit per hour.

For standard tariff = (16 * 0.10) + 0.2

Standard tariff = 1.6 + 0.2 = 1.8

For day/night = (16 * 0.12) + 0.2

= 1.92 + 0.2

= 2.12

The proportion will be

1.8/2.12 = 17/20 (approximately)