RS Aggarwal solution class 8 chapter 10 Profit and Loss Exercise 10C

Exercise 10C

Page-139

Q1 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 1:

The list price of a refrigerator is Rs 14650. If 6% is charged as sales tax, find the cost of the refrigerator.

Answer 1:

List price of the refrigerator = Rs 14650
Sales tax = 6% of ​Rs 14650
            $$\begin{gathered} =\mathrm{Rs} \left(14650\times \frac{6}{100}\right) \\ =\mathrm{Rs} 879 \end{gathered}$$

Bill amount$=\mathrm{Rs} \left(14650+879\right)$
                 $=\mathrm{Rs} 15529$
Hence, the cost of the refrigerator is Rs 15,529.

Q2 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 2:

Reena bought the following articles from a general store:
(i) 1 tie costing Rs 250 with ST @ 6%
(ii) Medicines costing Rs 625 with ST @ 4%
(iii) Cosmetics costing Rs 430 with ST @ 10%
(iv) Clothes costing Rs 1175 with ST @ 8%
Calculate the total amount to be paid by Reena.

Answer 2:

(i)
 $\mathrm{Cost} \mathrm{of} \mathrm{the} \mathrm{tie} =\mathrm{Rs}. 250$
$\mathrm{Sales} \mathrm{tax}=6\% \mathrm{of} \mathrm{Rs} 250$
             $$\begin{gathered} =\mathrm{Rs}.\left(250\times \frac{6}{100}\right) \\ =\mathrm{Rs}.15 \end{gathered}$$
$\mathrm{Hence}, \mathrm{bill} \mathrm{amount} = \mathrm{Rs} \left(250+15\right)$
                          $=\mathrm{Rs}.265$

(ii) $\mathrm{Cost} \mathrm{of} \mathrm{the} \mathrm{medicines}=\mathrm{Rs}. 625$
$\mathrm{Sales} \mathrm{tax}=4\% \mathrm{of} \mathrm{Rs}.625$
             $$\begin{gathered} =\mathrm{Rs}.\left(625\times \frac{4}{100}\right) \\ =\mathrm{Rs}.25 \end{gathered}$$
$\mathrm{Hence}, \mathrm{bill} \mathrm{amount} = \mathrm{Rs} \left(625+25\right)$
                           $=\mathrm{Rs} 650$

$$\begin{gathered} \left(\mathrm{iii}\right) \mathrm{Cost} \mathrm{of} \mathrm{the} \mathrm{cosmetics}=\mathrm{Rs} 430 \\ \mathrm{Sales} \mathrm{tax} =10\% \mathrm{of} \mathrm{Rs} 430 \end{gathered}$$
                      $$\begin{gathered} =\mathrm{Rs} \left(430\times \frac{10}{100}\right) \\ =\mathrm{Rs} 43 \end{gathered}$$

$\mathrm{Hence}, \mathrm{bill} \mathrm{amount}=\mathrm{Rs} \left(430+43\right)$
                          $=\mathrm{Rs}.473$

$$\begin{gathered} \left(\mathrm{iv}\right) \mathrm{Cost} \mathrm{of} \mathrm{clothes}=\mathrm{Rs} 1175 \\ \mathrm{Sales} \mathrm{tax}=8\% \mathrm{of} \mathrm{Rs} 1175 \end{gathered}$$
                 $$\begin{gathered} =\mathrm{Rs} \left(1175\times \frac{8}{100}\right) \\ =\mathrm{Rs} 94 \end{gathered}$$
$\mathrm{Hence}, \mathrm{bill} \mathrm{amount}=\mathrm{Rs} \left(1175+94\right)$
                          $=\mathrm{Rs}.1269$
$\mathrm{Therefore}, \mathrm{total} \mathrm{amount} \mathrm{to} \mathrm{be} \mathrm{paid} \mathrm{by} \mathrm{Reena} = \mathrm{bill} \mathrm{amount} \mathrm{of} \mathrm{all} \mathrm{the} \mathrm{four} \mathrm{items}$
                                                              $$\begin{gathered} =\mathrm{Rs} \left(265+650+473+1269\right) \\ =\mathrm{Rs} 2657 \end{gathered}$$

Q3 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 3:

Tanvy bought a watch for Rs 1980 including VAT at 10%. Find the original price of the watch.

Answer 3:

Let the original price of the watch be Rs x.
VAT = 10% of Rs x
       $$\begin{gathered} =\mathrm{Rs} \left(x\times \frac{10}{100}\right) \\ =\mathrm{Rs} \frac{10x}{100} \end{gathered}$$
∴ Price including VAT = $\mathrm{Rs} \left(x+\frac{x}{10}\right)$
                                     $=\mathrm{Rs} \frac{11x}{10}$
Now, $\frac{11x}{10}=1980$
      $$\begin{gathered} \Rightarrow x=\left(1980\times \frac{10}{11}\right) \\ =1800 \end{gathered}$$

Hence, the original price of the watch is Rs 1,800.

Q4 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 4:

Mohit bought a shirt for Rs 1337.50 including VAT at 7%. Find the original price of the shirt.

Answer 4:

​​Let the original price of the shirt be Rs x.
VAT = 7% of Rs x
       $$\begin{gathered} =\mathrm{Rs}.\left(x\times \frac{7}{100}\right) \\ =\mathrm{Rs}.\frac{7x}{100} \end{gathered}$$
∴ Price including VAT = $\mathrm{Rs}.\left(x+\frac{7x}{100}\right)$
                                     $=\mathrm{Rs}.\frac{107x}{100}$
Now, $\frac{107x}{100}=1337.50$
         $$\begin{gathered} \Rightarrow x=\mathrm{Rs} \left(1337.50\times \frac{100}{107}\right) \\ =\mathrm{Rs} 1250 \end{gathered}$$

Hence, the original price of the shirt is Rs 1,250.

Q5 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 5:

Karuna bought 10 g of gold for Rs 15756 including VAT at 1%. What is the rate of gold per 10 g?

Answer 5:

Let the price of 10 g of gold be Rs x.
$$\begin{gathered} \mathrm{VAT}=1\% \mathrm{of} \mathrm{Rs} x \\ =\mathrm{Rs} \left(x\times \frac{1}{100}\right) \\ =\mathrm{Rs} \frac{x}{100} \end{gathered}$$
∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{x}{100}\right)$
                                     $=\mathrm{Rs} \frac{101x}{100}$
$$\begin{gathered} \mathrm{Now}, \frac{101x}{100}=15756 \\ \Rightarrow x= \mathrm{Rs} \left(15756\times \frac{100}{101}\right) \\ = \mathrm{Rs} 15600 \end{gathered}$$

Hence, the price of 10 g of gold is Rs 15,600.

Q6 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 6:

Mohini purchased a computer for Rs 37960 including VAT at 4%. What is the original price of the computer?

Answer 6:

Let the original price of the computer be Rs x.
$$\begin{gathered} \mathrm{VAT}=4\% \mathrm{of} \mathrm{Rs}.x \\ =\mathrm{Rs}.\left(x\times \frac{4}{100}\right) \\ =\mathrm{Rs}.\frac{4x}{100} \end{gathered}$$
∴ Price including VAT$=\mathrm{Rs}.\left(x+\frac{4x}{100}\right)$
                                    $=\mathrm{Rs}.\frac{104x}{100}$
$$\begin{gathered} \mathrm{Now}, \frac{104x}{100}= 37960 \\ \Rightarrow x=\left(37960\times \frac{100}{104}\right) \\ = 36500 \end{gathered}$$

∴ The original price of the computer is Rs 36,500

Q7 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 7:

Sajal purchased some car parts for Rs 20776 including VAT at 12%. What is the original cost of these spare parts?

Answer 7:

​Let the original cost of the spare parts be Rs x.
$$\begin{gathered} \mathrm{VAT}=12\% \mathrm{of} \mathrm{Rs}.x \\ =\mathrm{Rs}.\left(x\times \frac{12}{100}\right) \\ =\mathrm{Rs}.\frac{12x}{100} \end{gathered}$$
∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{12x}{100}\right)$
                                      $=\mathrm{Rs}.\frac{112x}{100}$
$$\begin{gathered} \mathrm{Now}, \frac{112x}{100}=20776 \\ \Rightarrow x=\left(20776\times \frac{100}{112}\right) \\ =18550 \end{gathered}$$

Hence, ​the original cost of the spare parts is Rs 18,550.

Q8 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 8:

The sale price of a TV set including VAT is Rs 27000. If the VAT is charged at 8% of the list price, what is the list price of the TV set?

Answer 8:

​Let the list price of the TV set be Rs x.
$$\begin{gathered} \mathrm{VAT}=8\% \mathrm{of} \mathrm{Rs}.x \\ =\mathrm{Rs}.\left(x\times \frac{8}{100}\right) \\ =\mathrm{Rs}.\frac{8x}{100} \end{gathered}$$
∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{8x}{100}\right)$
                                     $=\mathrm{Rs}.\frac{108x}{100}$
$$\begin{gathered} \mathrm{Now}, \frac{108x}{100}=27000 \\ \Rightarrow x=\left(27000\times \frac{100}{108}\right) \\ =25000 \end{gathered}$$

Hence, the list price of the TV set is Rs 25,000.

Q9 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 9:

Rohit purchased a pair of shoes for Rs 882 inclusive of VAT. If the original cost be Rs 840, find the rate of VAT.

Answer 9:

Let the rate of VAT be x%. Then, we have:

$$\begin{gathered} 840+x\% of 840=882 \\ \Rightarrow \left(\frac{x}{100}\times 840\right)=882-840 \\ \Rightarrow \frac{84x}{10}=42 \\ \Rightarrow x=\left(42\times \frac{10}{84}\right) \\ =5 \end{gathered}$$

∴ The rate of VAT is 5%.

Q10 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 10:

Malti bought a VCR for Rs 19980 including VAT. If the original price of VCR be Rs 18500, find the rate of VAT.

Answer 10:

Let the rate of VAT be x%. Then, we have:

   $$\begin{gathered} 18500+x\% of 18500=19980 \\ \Rightarrow \left(\frac{x}{100}\times 18500\right)=19980-18500 \\ \Rightarrow 185x=1480 \\ \Rightarrow x=\frac{1480}{185} \\ =8 \end{gathered}$$

∴ The rate of VAT is 8%.

Q11 | Ex-10C | Class 8 | RS AGGARWAL | chapter 10 | Profit and Loss | myhelper

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Question 11:

The value of a car including VAT is Rs 382500. If the basic price of the car be Rs 340000, find the rate of VAT on cars.

Answer 11:

Let the rate of VAT be x%. Then, we have:

$$\begin{gathered} 34000+x\% of 34000=382500 \\ \Rightarrow \left(\frac{x}{100}\times 340000\right)=382500-340000 \\ \Rightarrow 3400x=42500 \\ \Rightarrow x=\frac{42500}{3400} \\ =12.5 \end{gathered}$$

∴ The rate of VAT is 12.5%.