Question

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?

Answer 1

Answer:

The ratio of calls and sms during day and night time is 3 : 2

Step by Step explanation:

Let Suppose,

A be the amount paid for usage between 8 am to 8 pm.

B be the amount paid for usage between 8 pm to 8 am.

Given Data,

Before the applying the benefits of 50%:

A + B = 100% of the bill  ................. (1)

After the applying the benefits of 50%:

(Bill reduced by 20% = 100% - 20% = 80% of previous bill)

A + (1/2)B = 80%  ................ (2)

We have to find the value of A and B.

Equation (2) - (1)

(A + (1/2)B) - (A + B) = 80% - 100%

-(1/2)B = -20%

B = 40%

Put the value of B in Equation (1)

A + B = 100%

A + 40% = 100%

A = 60%

The Ratio between A and B is :

Day : Night = A : B

Day : Night = 60% : 40%

Day : Night = 3 : 2

Answer 2

$\huge\bf{Answer:-}$

• Let (x) and (y) be the amount.

$x + y = 100 \: percent$

$x + 0.5 = 80$

Solving (y)

$x + y = 100 - - (eq - 1)$

$x + 0.5y = 80 - - (eq - 2)$

Equation (2) subtracting (1)

$0.5y = 20$

$y = 40$

Solving (x)

$x + y = 100$

$x + 40 = 100$

$x = 60$

Ration = x : y

60 : 40

Simplifing we get 20%

Therefore, the ratio is 3 : 2