Exercise 8B
Question 1
If 45% people in a city like football, 40% like cricket and the remaining like other games, then what per cent of the people like other games? If the city has a population of 4,00,000 people, then find the number of people who like one of these games.
Sol :
Population of city=400000
Peoples like football$=400000\times \frac{45}{100}$
=180000
Peoples like cricket$=400000\times \frac{40}{100}$
=160000
Remaining peoples who like other games=400000-(180000+160000)
=400000-340000
=60000
Remaining peoples who like other games(in %) $=\frac{60000\times 45}{180000}$
=15%
Question 2
In an examination, 96% of the students passed and 500 failed. How many students appeared at the examination?
Sol :
If total students be x
Failed student =500 in % (100-96)=4%
So, 4% of total student =500
$\frac{4}{100}\times x=500$
$x=\frac{500\times 100}{4}$
x=12500
Total students appeared 12500
Question 3
Two numbers are respectively $12\frac{1}{2}$% and 25% more than a third number. Find what percent is first number of the second number?
Sol :
Let the 3rd number be 100
The 1st number be $=100+12\frac{1}{2}\%$
$=100+\frac{25}{100}=\frac{225}{200}=\frac{9}{8}$
The 2nd number be $=100+\frac{25}{100}\%$
$=\frac{100+25}{100}=\frac{125}{100}=\frac{5}{4}$
Percent$=\frac{\text{1st number }}{2nd number}\times 100$
Question 4
A person invests Rs. 89856 in mutual funds, which is 26% of his annual income. What is the monthly income.
Sol :
Let, Annual income be x
Amount invested in mutual fund$=x\times \frac{26}{100}$
ATQ,
$\frac{26x}{100}=89856$
$x=\frac{89856\times 100}{26}$
=345600
∴Annual income=345600
∴Monthly income$=\frac{345600}{12}$
=28800
Question 5
The difference between 54% of a number and 26% of the same number is 22526. What is 66% of that number.
Sol :
Let , the number be x
ATQ,
$\frac{54x}{100}-\frac{26x}{100}=22526$
$\frac{54x-26x}{100}=22526$
28x=22526×100
$x=\frac{22526\times 100}{28}$=80450
∴The number=80450
∴66% of the number(80450) $=\frac{80450\times 66}{100}$
=53097
Question 6
When 125 is subtracted from a number, it reduces to its 37.5 per cent. What is 25 per cent of this number.
Sol :
Let the number be x
ATQ,
x-125$=\frac{37.5x}{100}$
$x-\frac{375x}{1000}=125$
1000x-375x=125×1000
$x=\frac{125\times 1000}{625}=200$
∴25% of 200$=200\times \frac{25}{100}$
=50
Question 7
A person spends 75% of his income, if his income increases by 20% and expenses increase by 15% then find the per cent increase in his savings.
Sol :
Let income of the person=100
∴Spending=75%
New income=120
Expenses$=75+75\times \frac{20}{100}$
=90
New saving=(120-90)=30
Difference=(30-25)=5
∴Increase %$=\frac{5}{25}\times 100$
=20%
Question 8
A shopkeeper first increased the price of an article by 25% and then by 20%. What is the total percent increase.
Sol :
Price of article=100
First increased the price of an article$=100\times \frac{25}{100}$
=25
∴Increased price of article=100+25=125
∴Second increased the price of an article$=125 \times \frac{20}{100}$=25
∴Increased price of article=125+25=150
Total price increase=150-100=50
(In %)$=\frac{50}{100}\times 100$
=50
Question 9
A sum of Rs. 2236 is divided among A, B and C in such a way that A receives 25% more than C and C receives 25% less than B. What is A’s sharer in the amount?
Sol :
Let, C's share=x
A's share$=x+\frac{25x}{100}=x+\frac{x}{4}$
B's share$=x+\frac{25x}{100}=x+\frac{x}{4}$
ATQ,
$x+x+\frac{x}{4}+x+\frac{x}{4}=2226$
$3x+\frac{2x}{4}=2226$
$\frac{12x+2x}{4}=2226$
$x=\frac{2226}{14}\times 4$
∴A's share$=610+\frac{610}{4}=770$
Question 10
In a company, there are 75% skilled workers and the remaining are unskilled. 80% of skilled workers and 20% of unskilled workers are permanent. If the number of temporary workers is 126, then what is the number of workers?
Sol :
Let total workers be x
∴Skilled workers$=x\times \frac{75}{100}=\frac{3x}{4}$
∴Unskilled workers$=x-\frac{3x}{4}=\frac{4x-3x}{4}=\frac{x}{4}$
∴Skilled permanent workers$=\frac{3x}{4}\times \frac{80}{100}=\frac{3x}{5}$
∴Unskilled permanent workers$=\frac{x}{4}\times \frac{20}{100}=\frac{x}{20}$
∴Temporary workers$=x-\left(\frac{3x}{5}+\frac{x}{20}\right)=\frac{7x}{20}$
ATQ,
$\frac{7x}{20}=126$
$x=\frac{126\times 20}{7}$
=360
∴Total workers=360
Question 11
Ravi scored 30% marks and failed by 15 marks. Deepak scored 40% marks and obtained 35 marks more than those required to pass. Find the minimum per cent pass marks.
Sol :
Let, Ravi get$=x\times \frac{30}{100}=\frac{3x}{10}$
Deepak get$=x\times \frac{40}{100}=\frac{4x}{10}$
ATQ,
$\frac{4x}{10}-35=\frac{3x}{10}+15$
$\frac{4x}{10}-\frac{3x}{10}=35+15=50$
$\frac{4x-3x}{10}=50$
x=50×10=500
∴Total number of marks=500
∴Ravi get$=\frac{3}{10}\times 500$=150
Deepak get$=\frac{4}{10}\times 500$=200
∴Min pass marks=150+15=165=200-35
∴Percentage of passing marks$=\frac{165\times 100}{500}$
=33%
Question 12
Two candidates fought an election. One of them got 62% of the total votes and won by 432 votes. What is the total number of votes polled?
Sol :
Let, total number of votes polled=x
Won person get$=x\times \frac{62}{100}=\frac{62x}{100}$
Other person get$=x-\frac{62x}{100}=\frac{38x}{100}$
ATQ,
$\frac{62x}{100}-\frac{38x}{100}=432$
$\frac{24x}{100}=432$
$x=\frac{432\times 100}{24}=1800$
Question 13
In an election between two persons, 68 votes were declared invalid. The winning persons for 52% and won 98 votes. Find the total number of votes polled.
Sol :
Let, total number of votes=x
winner get 52%
∴Losing team=(100-52)%
=48%
Winner won by 98 votes
ATQ,
(52%-48%)of x=98
4% of x=98
$x=\frac{98\times 100}{4}=2450$
∴68 votes were invalid
∴Total=(2450+68)=2518
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