EXERCISE 7.1
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1. Express
(i) Rs. 40 as a percentage of Rs. 80
(i) Rs. 40 as a percentage of Rs. 80
Steps for solving: (Hints)
Step 1: Divide Rs. 40 by Rs. 80Step 2: Multiply the result by 100 and simplify to obtain quantity in percentage. Step 3: Place the sign of percentage after the result.
Step 1: Divide Rs. 40 by Rs. 80
Step 2: Multiply the result by 100 and simplify to obtain quantity in percentage.
Step 3: Place the sign of percentage after the result.
Solution:
Rs. 40 as a percentage of Rs. 80 = `\frac {Rs. 40}{Rs. 80}`ｘ100 = 50%
Rs. 40 as a percentage of Rs. 80 = `\frac {Rs. 40}{Rs. 80}`ｘ100 = 50%
(ii) 20 km as a percentage of 80 km
Solution:
20 km as a percentage of 80 km = `\frac {20 km}{80 km}`ｘ100 = 25%
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2. Which is greater
(i) Rs. 10 out of Rs. 50 or Rs. 20 out of Rs. 80
(i) Rs. 10 out of Rs. 50 or Rs. 20 out of Rs. 80
{Hint: We will convert both the quantities into parentage and after then we will compare}
{Hint: We will convert both the quantities into parentage and after then we will compare}
Solution:
Rs. 10 out of Rs. 50 = `\frac {Rs. 10}{Rs.50}`ｘ100 = 20%
Rs. 20 out of Rs. 80 = `\frac {Rs. 20}{Rs. 80}`ｘ100 = 25%
As 25% > 20%
thus Rs. 20 out of Rs. 80 is greater than Rs. 10 out of Rs. 50
(ii) 70 marks out of 80 marks or 44 marks out of 50 marks
Rs. 10 out of Rs. 50 = `\frac {Rs. 10}{Rs.50}`ｘ100 = 20%
Rs. 20 out of Rs. 80 = `\frac {Rs. 20}{Rs. 80}`ｘ100 = 25%
As 25% > 20%
thus
Rs. 20 out of Rs. 80 is greater than Rs. 10 out of Rs. 50
(ii) 70 marks out of 80 marks or 44 marks out of 50 marks
Solution:
70 marks out of 80 marks = `\frac {70}{80}`ｘ100 = 87.5%
44 marks out of 50 marks = `\frac {44}{50}`ｘ100 = 88%
As 88% > 87.5%
44 marks out of 50 marks is greater than 70 marks out of 80 marks
70 marks out of 80 marks = `\frac {70}{80}`ｘ100 = 87.5%
44 marks out of 50 marks = `\frac {44}{50}`ｘ100 = 88%
As 88% > 87.5%
Solution:
16 m out of 60 m = `\frac {16}{60}`ｘ100 = 26.667%
5 m out of 20 m = `\frac {5}{20}`ｘ100 = 25%
As 26.667% > 25%
thus 16 m out of 60 m is greater than 5 m out of 20 m
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16 m out of 60 m = `\frac {16}{60}`ｘ100 = 26.667%
5 m out of 20 m = `\frac {5}{20}`ｘ100 = 25%
As 26.667% > 25%
thus
16 m out of 60 m is greater than 5 m out of 20 m
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3. Which is smaller
(i) 10 % of 50 or 25% of 100
(i) 10 % of 50 or 25% of 100
{Hint: We will convert both the quantities into numbers and after then we will compare}
{Hint: We will convert both the quantities into numbers and after then we will compare}
Solution:
10% of 50 = `\frac {10}{100}`ｘ50 = 5
25% of 100 = `\frac {25}{100}`ｘ100 = 25
As 5 < 25
thus
10% of 50 = `\frac {10}{100}`ｘ50 = 5
25% of 100 = `\frac {25}{100}`ｘ100 = 25
As 5 < 25
thus
10% of 50 is Smaller than 25% of 100
(ii) 20 % of 80 or 12% of 60
Solution:
20% of 80 = `\frac {20}{100}`ｘ80 = 16
12% of 60 = `\frac {12}{100}`ｘ60 = 7.2
As 7.2 < 16
thus
20% of 80 = `\frac {20}{100}`ｘ80 = 16
12% of 60 = `\frac {12}{100}`ｘ60 = 7.2
As 7.2 < 16
thus
12% of 60 is Smaller than 20% of 80
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4. Increase
(i) Rs. 1500 by 12%
(i) Rs. 1500 by 12%
Solution:
12% of Rs. 1500 = `\frac {12}{100}`ｘRs. 1500 = Rs. 180
thus
Increase in Rs. 1500 by 12% = Rs. 1500 + Rs. 180 = Rs. 1680
(ii) 1000 m by 50%
12% of Rs. 1500 = `\frac {12}{100}`ｘRs. 1500 = Rs. 180
thus
Increase in Rs. 1500 by 12% = Rs. 1500 + Rs. 180 = Rs. 1680
(ii) 1000 m by 50%
Solution:
50% of 1000 m = `\frac {50}{100}`ｘ1000= 500 m
thus
Increase of 1000 m by 50% = 1000 m + 500 m = 1500 m
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50% of 1000 m = `\frac {50}{100}`ｘ1000= 500 m
thus
Increase of 1000 m by 50% = 1000 m + 500 m = 1500 m
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5. Decrease
(i) 700 kg by 18%
(i) 700 kg by 18%
Solution:
18% of 700 kg = `\frac {18}{100}`ｘ700 kg= 126 kg
thus
Decrease of 700 kg by 18% = 700 kg - 126 kg = 574 kg
18% of 700 kg = `\frac {18}{100}`ｘ700 kg= 126 kg
thus
Decrease of 700 kg by 18% = 700 kg - 126 kg = 574 kg
(ii) 120 by 40%
40% of 120 = `\frac {40}{100}`ｘ120= 48
thus
Decrease of 120 by 40% = 120 - 48 = 72
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6. Underground water in Islamabad has fallen from 80 feet to 240 feet in last 10 years. What percentage of water has fallen?
Steps for solving: (Hints)
Step 1: Divide 240 feet to 80 feet ( new to old one)Step 2: Multiply the result by 100 % and simplify to obtain quantity in percentage. Step 3: Place the sign of percentage after the result.
Step 1: Divide 240 feet to 80 feet ( new to old one)
Step 2: Multiply the result by 100 % and simplify to obtain quantity in percentage.
Step 3: Place the sign of percentage after the result.
Solution:
Water level before 10 years = 80 feet
Water level after 10 years = 240 feet
240 feet as a percentage of 80 feet =
`\frac {240}{80}`ｘ100 = 300 %
Thus, water in Islamabad has fallen 300 % in last 10 years.
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7. The height of a mango tree is 20 m and the height of a banana tree is 5 m. Express the height of mango tree as a percentage of height of banana tree.
(See question no. 6 as Hint)
Solution:
Height of a mango tree = 20 m
Height of a banana tree = 5 m
Height of mango tree as a percentage of height of banana tree
= `\frac {20 m}{5 m}`ｘ100 = 400 %
Thus, Height of mango tree as a percentage of height of banana tree is 400%
Height of mango tree as a percentage of height of banana tree
= `\frac {20 m}{5 m}`ｘ100 = 400 %
Thus, Height of mango tree as a percentage of height of banana tree is 400%
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8. In a basket out of 150 oranges, 15 are eaten. What percentage has been eaten? What percentage is left?
(See question no. 6 as Hint)
Solution:
Total oranges = 150
Oranges eaten = 15
Percentage of oranges eaten = ?
Percentage of oranges left = ?
Percentage of oranges eaten = ?
Percentage of oranges left = ?
Percentage of oranges eaten (15 out of 150)
= `\frac {15}{150}`ｘ100 = 10 % ----------Ans. 1
Oranges left = Total oranges - oranges eaten = 150 - 15 = 135
Percentage of oranges left
= `\frac {135}{150}`ｘ100 = 90 % ----------Ans. 2
or (2nd method)
Percentage of oranges left = 100 % - Percentage of oranges eaten = 100 % - 10 % = 90 % ----------Ans. 2
Percentage of oranges eaten (15 out of 150)
= `\frac {15}{150}`ｘ100 = 10 % ----------Ans. 1
Oranges left = Total oranges - oranges eaten = 150 - 15 = 135
Percentage of oranges left
= `\frac {135}{150}`ｘ100 = 90 % ----------Ans. 2
or (2nd method)
Percentage of oranges left = 100 % - Percentage of oranges eaten = 100 % - 10 % = 90 % ----------Ans. 2
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9. Monthly income of Arshad and Asghar is Rs. 9500 and Rs. 10500 respectively. Express Arshad's income as a percentage of Asghar's income.
Solution:
Arshad Income = Rs. 9500
Asghar Income = Rs. 1050
Arshad's income as a percentage of Asghar's income
= `\frac {Rs. 9500}{Rs. 10500}`ｘ100 = 90.48 %
Arshad's income as a percentage of Asghar's income
= `\frac {Rs. 9500}{Rs. 10500}`ｘ100 = 90.48 %
Thus, Arshad's income is 90.48% of Asghar's income
Thus, Arshad's income is 90.48% of Asghar's income
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10. Mr. Farooq used 60 off net minutes out of 180 minutes and 600 on net minutes out of 1200 minutes. (i) What percentage of off-net minutes have been used?(ii) What percentage of on-net minutes have been used?
Solution:
(i) What percentage of off-net minutes have been used?
Total off net minutes = 180
Off net minutes used = 60
Percentage of off net minutes used =
`\frac {60}{180}`ｘ100 = 33.33 % -------An.1
`\frac {60}{180}`ｘ100 = 33.33 % -------An.1
Thus, Farooq used 33.33% of off net minutes.
Thus, Farooq used 33.33% of off net minutes.
(ii) What percentage of on-net minutes have been used?
Total on net minutes = 600
On net minutes used = 1200
Percentage of on net minutes used =
`\frac {600}{1200}`ｘ100 = 50 %
`\frac {600}{1200}`ｘ100 = 50 %
Thus, Farooq used 50% of on net minutes.
Thus, Farooq used 50% of on net minutes.
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11. A piece of elastic 48 cm long is stretched to 64 cm. What percentage of the original length is increased?
Solution:
Elastic original length = 48 cm
Starched length = 64 cm
original length Increased = 64 cm - 48 cm = 16 cm
Percentage of the original length increased =
`\frac {16 cm}{48 cm}`ｘ100 = 33.33 % -----Ans.
`\frac {16 cm}{48 cm}`ｘ100 = 33.33 % -----Ans.
Thus, the original length is increased by 33.33%.
Thus, the original length is increased by 33.33%.
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12. The salary of a factory worker is Rs. 5000. He was given an increment of 12%. Find his new salary.
Solution:
Factory worker salary = Rs. 5000
Increment = 12%
12% 0f Rs. 5000 = `\frac {12}{100}`ｘRs. 5000 = Rs. 600
New salary = Rs. 5000 + increment = Rs. 5000 + Rs. 600 = Rs. 5600 ------Ans.
Thus, the new salary of factory worker is Rs. 5600
Thus, the new salary of factory worker is Rs. 5600
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1. Real Life Word Problems on Financial Mathematics, Property Tax, General Sale Tax (GST), Zakat, Ushr, Profit and Loss, Markup, Percentage, Proportion.
2. 5th class Notes: English, Social Study (S.St.), General Science (G.Sc.), Urdu (اُردو), Islamiat (اسلامیات), Mathematics
3. 6th class Notes: Mathematics
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© 2022-23 Academic Skills and Knowledge (ASK)
Note: Write me in the comments box below for any query and also Share this information with your class-fellows and friends.
1. Website for School and College Level Physics
2. Website for School and College Level Mathematics
3. Website for Single National Curriculum Pakistan - All Subjects Notes
© 2022-23 Academic Skills and Knowledge (ASK)
Note: Write me in the comments box below for any query and also Share this information with your class-fellows and friends.
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