Exercise 6.1
1
A shop keeper bought a TV for ₹9000 and sold it for ₹10,000. Find the profit and loss? calculate its percentage.
Cost Price (CP) = ₹
Selling Price (SP) = ₹10,000
Profit = SP - CP = ₹10,000 - ₹9000 = ₹
Profit Percentage = (Profit/CP) × 100
= (
= (
=
2
A person buys an article for ₹650 and gains 6% on selling it. Find the selling price?
Cost Price (CP) = ₹
Profit =
When CP = ₹
Gain = ₹6
SP = ₹100 + ₹6 = ₹
Using proportion:
100 : 650 = 106 : x 100x = 106 × 650
x =
x =
3
Ramesh sold a DVD player for ₹2800 at a gain of 12%. For how much did he buy it?
Given:
Selling Price (SP) = ₹
Gain =
When CP = ₹
SP = ₹100 + 12% of 100
SP = ₹
Using proportion:
x : 100 = 2800 : 112
112x = 100 × 2800
x =
x = ₹
1. What is the ratio of ₹100 and ₹10? Express your answer in the simplest form.
Solution:
Given amounts: ₹
Let's write the ratio:
₹100 : ₹10
To simplify, divide both numbers by
₹100 ÷ 10 =
₹10 ÷ 10 =
Therefore, the ratio in simplest form is:
2. Sudha has ₹5. Money with Radha is 3 times the money with Sudha. How much money does Radha have?
(i) What is the ratio of Radha's money and Sudha's money?
(ii) What is the ratio of Sudha's money and Radha's money?
Solution:
Given: Sudha's money = ₹
Radha's money = 3 × Sudha's money = 3 × ₹5 = ₹
(i) What is the ratio of Radha's money and Sudha's money?
Ratio = ₹15 : ₹5
Simplifying by dividing both by 5:
Ratio =
(ii) What is the ratio of Sudha's money and Radha's money?
Ratio = ₹5 : ₹15
Simplifying by dividing both by 5:
Ratio =
3. A rectangle measures 40 cm at its length and 20 cm at its width. Find the ratio of the length to the width.
Solution:
Given: Length =
Ratio of length to width = 40 : 20
Simplifying by dividing both by 20:
Ratio =
4. The speed of a Garden-Snail is 50 meters per hour and that of the Cheetah is 120 kilometres per hour. Find the ratio of the speeds.
Solution:
Given that:
The speed of a Garden-Snail =
The speed of a Cheetah =
First, convert both speeds to meters per hour:
120 kilometers = 120 × 1000 =
The ratio of the speed of a Garden-Snail to Cheetah =
We divide
Simplifying: 50/120000 =
The ratio of the speed of a Garden-Snail to Cheetah is
5. Divide 96 chocolates between Raju and Ravi in the ratio 5 : 7
Solution:
Given: Total chocolates =
Total parts = 5 + 7 =
One part = 96 ÷ 12 =
Therefore: Raju's share = 5 × 8 =
Ravi's share = 7 × 8 =
6. The length of a line segment AB is 38 cm. A point X on it divides it in the ratio 9 : 10. Find the lengths of the line segments AX and XB.
Solution:
Given: Total length =
Total parts = 9 + 10 =
One part = 38 ÷ 19 =
Therefore: Length of AX = 9 × 2 =
Length of XB = 10 × 2 =
7. A sum of ₹1,60,000 is divided in the ratio of 3 : 5. What is the smaller share?
Solution:
Given: Total amount = ₹
Total parts = 3 + 5 =
One part = ₹1,60,000 ÷ 8 = ₹
Smaller share = 3 × ₹20,000 = ₹
8. To make green paint, a painter mixes yellow paint and blue paint in the ratio of 3 : 2. If he used twelve liters of yellow paint, how much blue paint did he use?
Solution:
Given: Ratio of yellow : blue = 3 : 2 Yellow paint =
If 3 parts = 12 liters
Then 1 part = 12 ÷ 3 =
Blue paint = 2 parts = 2 × 4 =
9. Find the following ratios:
(i)
(i) The ratio of boys and girls in your class.
Solution:
There are total
The ratio of boys and girls in my classroom =
We divide
=
The ratio of boys and girls in my classroom is
(ii)
(ii) The ratio of number of doors and number of windows of your classroom.
Solution:
In my classroom, there are
The ratio of number of doors and number of windows of my classroom =
We divide
=
The ratio of number of doors and number of windows of my classroom is
(iii)
(iii) The ratio of number of text books and number of note books with you
Solution:
I have
The ratio of number of text books and number of note books =
We divide
=
The ratio of number of text books and number of note books is