Exercise 8F
Question 1
55 per cent of the students in a school are girls. What percentage of the students are boys? Find the number of students, if there are 216 boys.
Sol :
∴Percentage of boys=100-55=45%
45% of student=216
1% of student$=\frac{216}{45}$
45% of student$=\frac{216 \times 100}{45}$=480
∴Total number of student=480
Question 2
If 10% is deducted from a bill, Rs. 7200 remains to be paid. How much is the bill?
Sol :
∴Remaining bill=(100-10)=90%
90% bill=7200
1% bill $=\frac{7200}{90}$
100% bill $=\frac{7200 \times 100}{90}$=8000
∴Total bill=8000
Question 3
Calculation gives the length of a line segment as 6.4 cm, while from drawing and measurement it is obtained as 6.6 cm. Find the error per cent.
Sol :
∴Error length=(6.6-6.4)=0.2 cm
In 6.4 cm the error is 0.2 cm
In 1 cm the error is $=\frac{0.2}{6.4}$ cm
In 100 cm the error is $=\frac{0.2\times 100}{6.4}=\frac{25}{8}=3\frac{1}{8}$ cm
Question 4
Atul deposited 30% of his income in a bank. After spending 50% of the remaining, he had Rs. 10,500 left with him. What is his income?
Sol :
Remaining income after depositing in bank=100-30=70%
50% of 70%=35%
35% of income is 10500
1% of income is $\frac{10500}{35}$
100% of income is $=\frac{10500 \times 100}{35}$=30000
∴Atul's income is 30000
Question 5
Manish obtained 498 marks out of 600 marks and Aravind scored 640 marks out of 800 marks. Whose performance is better?
Sol :
∴Percentage of Manish score$=\left(\frac{498}{600} \times 100\right)$=83 %
∴Percentage of Arvind's score$=\left(\frac{640}{800}\times 100\right)$=80%
Ans : Manish's performance is better than Arvind performance
Question 6
In a graduate class of 200, 40% are women and 1/5 becomes lecturers. If the number of men who became lecturers is twice that of women, calculate approximate percentage of men who became lecturers.
Sol :
Number of women$=\frac{40}{100}\times 200$=80
Number of women who become lecturer$=80\times \frac{1}{5}$=16
Number of men who becomes lecturer=16×2=32
Number of men=200-80=120
∴Percentage of men who becomes lecturer$=\left(\frac{32}{120}\times 100\right)$
=26.6%
≃27%
Question 7
The price of an article is reduced by 25%. In order to retain the original price, by what percentage should the present price be increased?
Sol :
Let the price 100
25% reduced new price 75
So the price raised should be $=\left(\frac{25}{75}\times 100\right)$=33.33%
Ans : The present price increased 33.33%
Question 8
In a mixture of milk and water, the proportion of water by weight is 75%. If in the 60 g mixture, 15 g of water is added, what would be the percentage of water?
Sol :
In 60 g mixture , weight of water$=\left(\frac{75}{100}\times 60\right)$=45 gm
15 g water is added , now weight of water=45+15=60gm
Now , Percentage of water $=\left(\frac{60}{75}\times 100\right)$=80%
Question 9
One litre of water is evaporated from a 6 litre solution containing 4% sugar. Find the percentage of sugar in the remaining solution.
Sol :
Quality of sugar in 6 litre solution $=\left(\frac{4}{100}\times 6\right)$=0.24 litre
1 litre of water evaporated from a 6 litre solution
Now, quantity of solution=(6-1)=5 litres
Percentage of sugar in remaining solution$=\left(\frac{0.25}{5}\times 100\right)$=4.8%
Question 10
State Electricity Board gives 15% discount on electricity bills, if it is paid before due date. A person gets Rs. 54 as discount. What was the actual amount of the bill?
Sol :
State Electricity Board gives 15 Rs discount on 100
State Electricity Board gives 1 Rs discount on $=\frac{100}{15}$
State Electricity Board gives 54 Rs discount on $=\frac{100\times 54}{15}$=360
Ans : Actual deposit of bill is 360
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