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:

3 : 2

Step by Step explanation:

Define x and y:

Let x be the amount paid for usage during 8am to 8pm.

Let y be the amount paid for usage during 8pm to 8am.

Before the introduction of the 50% benefit:

x + y = 100% of the bill

After the introduction of the 50% benefit:

x + 0.5y = 80%

Solve y:

x + y = 100% ---------------- [ 1 ]

x + 0.5y = 80%  ------------ [ 2 ]

Equation [ 2 ] - [ 1 ]:

0.5y = 20%

y = 40%

Solve x:

x + y = 100%

x + 40% = 100%

x = 60%

Find the ratio:

Day : Night = x : y

Day : Night = 60% : 40%

Simplify by dividing by 20%:

Day : Night = 3 : 2

Answer: 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