NCERT Solutions for Class 8 Maths Chapter 8: Comparing Quantities - Exercise 8.2

Exercise 8.2

1. A man got a 10% increase in his salary. If his new salary is Rs1,54,000, find his original salary.

Ans: Let $x$ be the original salary.

Given. New salary = Rs 1,54,000 And Increment = 10% of the original salary.

We know that, Original salary + Increment = New salary

 Thus,
$x + \dfrac{{10}}{{100}} \times x = 154000$

$\text{ }\!\!~\!\!\text{  }\!\!~\!\!\text{ }\dfrac{110x}{100}=154000\text{ }\!\!~\!\!\text{ }$

$\begin{align} & x=\left( 154000\times \dfrac{100}{110} \right) \\ & x=140000 \\ \end{align}$

Therefore, the original salary was ${\text{Rs }}1,40,000$.

2. On Sunday 845 people went to the Zoo. On Monday only 169 people went. What is the percent decrease in the people visiting the zoo on Monday?

Ans: Number of people who went zoo on Sunday = 845

Number of people who went zoo on Monday = 169

Decrease in number of people = 845 – 169 = 676

Percentage decrease 

=$\left( {\dfrac{{{\text{Decrease}}\,{\mkern 1mu} {\text{in}}{\mkern 1mu} \,{\text{the}}{\mkern 1mu} \,{\text{number}}{\mkern 1mu} \,{\text{of}}\,{\mkern 1mu} {\text{people}}{\mkern 1mu} \, \times {\mkern 1mu} \,{\text{100}}}}{{{\text{Number}}\,{\mkern 1mu} {\text{of}}\,{\mkern 1mu} {\text{people}}\,{\mkern 1mu} {\text{who}}{\mkern 1mu} \,{\text{went}}\,{\mkern 1mu} {\text{to}}\,{\mkern 1mu} {\text{zoo}}{\mkern 1mu} \,{\text{on}}\,{\mkern 1mu} {\text{Sunday}}}}} \right)\% $

= $\left( {\dfrac{{676}}{{845}} \times 100} \right)\%  = 80\% $

3. A shopkeeper buys 80 articles for Rs 2,400 and sells them for a profit of 16%. Find the selling price of one article.

Ans: Given. Shopkeeper buys 80 articles for Rs. 2400

Therefore, Cost of 1 article = $\dfrac{{2400}}{{80}}$= Rs. 30

Profit percent = 16%

Profit Percent= $1\dfrac{1}{2}$

\[\Rightarrow \text{ }\!\!~\!\!\text{  }\!\!~\!\!\text{ }16=\dfrac{\text{profit}}{\text{Rs}.30}\times 100\text{ }\!\!~\!\!\text{ }\]

\[\begin{align} & \text{Profit}=\text{Rs}\left( \dfrac{16\times 30}{100} \right) \\ & =\text{Rs }4.80 \end{align}\]

Selling price = C.P. + Profit = Rs (30 + 4.80) = Rs.34.80 

4. The cost of an article was Rs 15,500. Rs 450 were spent on its repairs. If it is sold for a profit of 15%, find the selling price of the article.

Ans: Given. Cost = Rs. 15,500

Expenses on repairs = Rs. 450

Total cost = Cost + Overhead expenses = Rs 15500 + Rs 450 = Rs 15950 

Profit % =$\text{ }\!\!~\!\!\text{  }\!\!~\!\!\text{ }\dfrac{\text{Profit}}{\text{C}\text{.P}\text{.}}\times 100\text{ }\!\!~\!\!\text{ }$

$\begin{align} & 15=\dfrac{\text{Profit}}{\text{Rs 15950}}\times 100 \\ & \text{Profit = Rs}\left( \dfrac{\text{15950}\times \text{15}}{\text{100}} \right)\text{ } \\ & \text{= Rs 2392}\text{.50} \end{align}$

Therefore, Selling price = C.P. + Profit = Rs$(15950 + 2392.50) = {\text{Rs }}18342.50$ 

5. A VCR and TV were bought for Rs 8,000 each. The shopkeeper made a loss of 4% on the VCR and a profit of 8% on the TV. Find the gain or loss percent on the whole
transaction.

Ans: Given. C.P. of VCR = Rs. 8000

Loss = 4% on VCR

This implies if C.P. is Rs.100 then, S.P. is Rs.96.

Therefore, when C.P. is Rs.8000, 

S.P. ${\text{ = Rs}}{\text{.}}\left( {\dfrac{{{\text{96}}}}{{{\text{100}}}} \times {\text{8000}}} \right){\text{  =  Rs}}{\text{.7680}}$

C.P. of Tv = Rs 8000

Profit = 8% on TV

This implies if C.P. is 100 then, S.P. is Rs. 108

Therefore, when C.P. is Rs.8000, S.P. ${\text{ = Rs}}{\text{.}}\left( {\dfrac{{{\text{108}}}}{{{\text{100}}}} \times {\text{8000}}} \right){\text{  =  Rs}}{\text{.8640}}$

Thus, Total S.P. = 7680 + 8640 = Rs. 16320

And Total C.P. = 8000 + 8000 = Rs. 16000

Since total S.P.> total C.P.,

There was some profit generated. 

Profit = Rs 16320 - Rs 16000 = Rs 320

$ \;\because \;{\text{Profit}}\% \; = \dfrac{{{\text{Profit}}}}{{{\text{C}}{\text{.P}}}} \times 100\;\;{\text{ }} \\ \Rightarrow \dfrac{{32}}{{16000}} \times 100 = 2\% \;{\text{.}} \\$

Thus, the Shopkeeper had a profit of 2%.

6. During a sale, a shop offered a discount of 10% on the marked prices of all the
items. What would a customer have to pay for a pair of jeans marked at Rs 1450 and two shirts marked at Rs 850 each?

Ans: From the given data, 

Total marked price = \[\text{Rs}(1,450\text{ }+\text{ }2850)\text{ }=\text{ Rs}\left( 1,450\text{ }+\text{ }1,700 \right)\text{ }=~\text{ Rs }3,150\]

Also, given that, Discount = 10%

Therefore, Discount
${\text{ = Rs}}{\text{.}}\left( {\dfrac{{{\text{10}}}}{{{\text{100}}}} \times {\text{3150}}} \right){\text{  =  Rs}}{\text{. 315}}$

Discount = Marked price - Sale price

Therefore, Sale price = Marked price – Discount 

∴ Sale price= Rs(3150 - 315) = Rs 2835

∴ Customer have to pay Rs. 2835.

7. A milkman sold two of his buffaloes for Rs 20,000 each. On one he made a gain of
5% and on the other a loss of 10%. Find his overall gain or loss. (Hint. Find CP of each)

Ans: Given.

S.P. = Rs. 20,000

Profit by selling each buffalo = 5%

This implies if C.P. is 100 then, S.P. is Rs. 105

Therefore, C.P. of first buffalo =${\text{Rs}}{\text{.}}\left( {{\text{20000}} \times \dfrac{{{\text{100}}}}{{{\text{105}}}}} \right){\text{ = }}\,{\text{Rs}}{\text{.19,047}}{\text{.62}}$ 

Also, given that, loss after selling second buffalo = 10%

This implies if C.P. is 100 then, S.P. is Rs. 90

Therefore, C.P. of second buffalo = ${\text{Rs}}{\text{.}}\left( {{\text{20000}} \times \dfrac{{{\text{100}}}}{{{\text{90}}}}} \right){\text{ = Rs}}{\text{. 22222}}{\text{.22}}$

Total C.P = ${\text{Rs 19047}}{\text{.62  +  Rs 22222}}{\text{.22  =  Rs 41269}}{\text{.84}}$

Total S.P. $ = {\text{Rs 20000  +  Rs 20000  =  Rs 40000}}$
Loss $ = {\text{Rs}}{\text{. 41269}}{\text{.84  -  Rs}}{\text{.40000  =  Rs}}{\text{. 1269}}{\text{.84}}$ 

Therefore, Total loss = Rs. 1269.84

8. The price of a TV is Rs. 13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.

Ans: For Rs. 100, tax = Rs. 12

${\text{For Rs}}{\text{.13,000; tax  =  Rs}}\left( {\dfrac{{{\text{12}}}}{{{\text{100}}}} \times {\text{13000}}} \right){\text{ =  Rs}}{\text{.1560}}$

Total amount = Cost + Sales Tax = Rs 13000 + Rs 1560 = Rs. 14560

Therefore, Vinod has to pay Rs. 14,560.

9. Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is Rs 1,600, find the marked price.

Ans:

Let $x$ be the marked price.

Discount percent = $\dfrac{{{\text{Discount}}}}{{{\text{Marked}}{\mkern 1mu} {\text{price}}}} \times {\text{100}}$ 

$\Rightarrow 20 = \dfrac{{{\text{Discount}}}}{x} \times 100{\text{ }}\;{\text{ }}$

$\text{Discount}=\dfrac{20}{100}\times x=\dfrac{1}{5}x\text{ }\!\!~\!\!\text{ }$

Also, Discount = Marked price - Sale price

$\text{ }\!\!~\!\!\text{ }\Rightarrow \dfrac{1}{5}x=x-\text{Rs}.1600$

$\Rightarrow x-\dfrac{1}{5}x=\text{Rs}.1600\text{ }\!\!~\!\!\text{ }$

$\Rightarrow \dfrac{4}{5}x=\text{Rs}.1600\text{ }\!\!~\!\!\text{  }\!\!~\!\!\text{ }$

$\begin{align} & x=\text{Rs}\left( 1600\times \dfrac{5}{4} \right) \\ & =\text{Rs}.\text{ }2000 \end{align}$

Therefore, the marked price is Rs 2000.

10. I purchased a hair-dryer for Rs 5,400 including 8% VAT. Find the price before VAT was added.

Ans:

Given, VAT = 8%

This implies, if the price without VAT is Rs 100, then price including VAT will be Rs 108.

Price including VAT = Rs. 108, original price = Rs. 100

When price including VAT = Rs. 5400, 

original price = ${\text{ =  Rs}}{\text{.}}\left( {\dfrac{{{\text{100}}}}{{{\text{108}}}} \times {\text{5400}}} \right){\text{ =  Rs}}{\text{.}}\,{\text{5000}}$

Therefore, price before VAT was added is Rs. 5000.

NCERT Class 8 Exercise 8.2 Solutions - Brief Overview

Question 1

The very first question of class 8 Maths Ch 8 Ex 8.2 PDF requires you to find out the original salary a man. The given data are his new salary and the percentage of the hike he received.

Question 2

In the second question of Maths Class 8 Chapter 8 Exercise 8.2 you need to find out the decreased percentage of people visiting a zoo on Monday as compared to Sunday.

Question 3

This question in NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.2 demands the concept of profit and selling price. If a shopkeeper sells 80 articles at a profit of 16% and the original price is 2400, what will be the selling price? Go through the worked-out solutions to answer these types of questions precisely.

Question 4

Question 4 of NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.2 is also similar to the previous one as you are required to find out the selling price.

Question 5

Here, you need to evaluate both profit and loss percentages on the entire transaction of buying a VCR and a TV.

Question 6

This question in NCERT Class 8 Maths Chapter 8 Exercise 8.2 is a bit more tricky. Given the discount percentage of two shirts and jeans which are of Rs.850 and Rs.1450, respectively, you need to find the amount required to be paid by the customer.

Question 7

Question 7 of NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.2 again deals with both gain and loss percentage. Note that this type of problem gets repeated during exams, so make sure to get familiar with the solution steps.

Question 8

in this question of NCERT Solutions for Class 8 Maths Chapter 8 Exercise 8.2, students are required to find out the total value of a TV inclusive of 12% sales tax.

Question 9

This problem in NCERT Maths Class 8 Chapter 8 Exercise 8.2 is about calculating the MRP of a pair of skates as after putting a discount of 20%, the selling price is Rs.1600.

Question 10

The last question in class 8 Maths Chapter 8.2 talks about a man/woman purchasing a hairdryer at Rs.5400, inclusive of VAT (8%). You need to calculate the only price of the item.

This Maths NCERT Solutions Class 8 Chapter 8 Exercise 8.2 is prepared by maintaining all the guidelines of CBSE, and all the problems are solved in a simple and step by step manner. So, without wasting much time, please go ahead to download NCERT Solutions Class 8 Maths Chapter 8 Exercise 8.2 for a clear comprehension of the topics as well as better grades in exams.

We Cover Other Exercises given in the Chapter 8 Comparing Quantities of Class 8:-