Question

5. The price of a T.V. set inclusive of tax of 9%
is 13,407. Find its marked price. If tax is
increased to 13%, how much more does the
customer has to pay for the T.V. set ?​

Answer 1

Answer:

Price of T.V. Set = Rs. 13,407 inclusive of tax.

Price of TV set is calculated as:

→ Final Price = Marked Price + Tax

→ Tax = x% of Marked Price, where 'x' is the percentage.

According to question,

• Final Price = Rs. 13,407
• Tax % = 9 %
• Marked Price = ? (m)

Substituting in the formula, we get:

⇒ 13,407 = m + 9% of m

⇒ 13,407 = m +9m/100

Taking LCM we get:

⇒ 13,407 = (100m + 9m)/100

⇒ 13,407 = 109m/100

Cross multiplying we get:

⇒ m = ( 13,407 × 100 ) / 109

⇒ m = 12,300

Hence the marked price of the T.V. is Rs. 12,300.

Now, the tax percentage is increased from 9 to 13. Hence we need to find the excess to be paid for purchasing the T.V.

Substituting the new values in the formula we get:

⇒ Final Price = 12,300 + 13% of 12,300

⇒ Final Price = 12,300 + (13 × 12,300)/100

⇒ Final Price = 12,300 + (13 × 123)

⇒ Final Price = 12,300 + 1599

⇒ Final Price = Rs. 13,899

Hence the amount required to be paid in excess is:

⇒ Excess = New Final Price - Old Final Price

⇒ Excess = 13,899 - 13,407

⇒ Excess = Rs. 492

Hence the excess required to be paid by the customer is Rs. 492.

Answer 2

Answer:

• It's marked price is 12,300 Rupees.

• Rupees 492 is the price that the customer have to pay more for the T.V set.

Step-by-step explanation:

Correct question: The price of a T.V. set inclusive of tax of 9% is Rupees 13,407. Find its marked price. If tax is increased to 13%, how much more does the customer has to pay for the T.V. set?

Given that: (1) The TV's price including the tax is Rupees 13,407. (2) The tax on TV is 9 percentage (3) Tax is increased to 13 percentage.

To find: (1) The marked price. (2) How much price that the customer have to pay more for the T.V set.

Assumption: (1) Let the marked price be a

Full solution:

~ As it's already given that the price of a T.V. set inclusive of tax of 9% is Rupees 13,407. Have to find marked price. So, according to the this the formed equation is given below. We just have to solve it and it is very easy. Let's do it!

${\small{\underline{\boxed{\sf{\therefore \: a + 9 \% \: of \: a \: = 13,407}}}}}$

${\sf{:\implies a + 9 \% \: of \: a \: = 13,407}}$

${\sf{:\implies a + 9 \% \: \times \: a \: = 13,407}}$

${\sf{:\implies a + \dfrac{9}{100} = 13,407}}$

~ Now let us take the lowest common multiple (LCM) and let's carry on! As LCM of 1 and 100 is 100.

${\sf{:\implies \dfrac{a}{1} + \dfrac{9}{100} = 13,407}}$

${\sf{:\implies \dfrac{109a}{100} \: = 13,407}}$

~ Now let us solve the value for a. As we already know that (÷ = ×) and (× = ÷). Let us solve this question!

${\sf{:\implies 109a \: = 13,407 \times 100}}$

${\sf{:\implies 109a \: = 13,40,700}}$

${\sf{:\implies a \: = \dfrac{13,40,700}{109}}}$

${\sf{:\implies a \: = 12,300 \: Rupees}}$

${\underline{\pmb{\sf{Henceforth, \: marked \: price \: is \: 12,300 \: Rupees}}}}$

~ Now as it's given that tax is increased to 13%, henceforth according to this the formed equation be the given. We just have to put the values according to this and have to solve. It is very easy too. Let us solve!

${\small{\underline{\boxed{\sf{\therefore \: Rs. \: 12,300 + 13 \% \: of \: 12,300}}}}}$

${\sf{:\implies Rs. \: 12,300 + 13 \% \: of \: 12,300}}$

${\sf{:\implies Rs. \: 12,300 + 13 \% \: \times \: 12,300}}$

${\sf{:\implies 12,300 + \dfrac{13}{100} \times \: 12,300}}$

${\sf{:\implies 12,300 + 0.13 \times \: 12,300}}$

${\sf{:\implies 12,300 + 1599}}$

${\sf{:\implies 13899 \: Rupees}}$

${\underline{\pmb{\sf{Henceforth, \: 13899 \: Rupees \: is \: the \: new \: price \: of \: TV}}}}$

~ Now at last let us find that how much more does the customer has to pay for the T.V. set.

${\sf{:\implies (13899-13407) \: Rupees}}$

${\sf{:\implies Rupees \: 492}}$

${\underline{\pmb{\sf{Henceforth, \: Rupees \: 492 \: is \: our \: final \: result}}}}$