Question 77

A Telecom Service operator announced that between 8 PM and 8 AM all outgoing calls and text messages shall be charged @ 50 % of the charge rate as applicable from 8 AM to 8 PM. After availing of this benefit, my bill dues reduced by 20 %. What is the ratio of my calls and SMS during day and night time?

Solution

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Let the ratio of messages during day and night be x:y.

Let the charge of messages during the day be 100, so the charge of messages during the night will be 50.

Initial total bill=100*(x+y)

New total bill= 100*x + 50*y = 50*(2x+y)

Now, $$\frac{50\times\ \left(2x+y\right)}{100\times\ \left(x+y\right)}=\frac{80}{100}$$

$$10x+5y=8x+8y$$

x:y=3:2

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