1. The population of Delhi is 40,00,000 it increases at the rate of 10% per annum. What was its population 2 years ago and also what will be its population after 2 years ?
2. The population of a city is 25,000. If increased by 15% during first year. During second year it decreased by 25% and increased by 40% during the third year. What is the population after 3 years ?
3. The tax on a commodity is diminished by 2.5% and its consumption increases by 5%. Find the effect on revenue ?
Ans :Let A be tax on a commodity and B be the consumption.
Now, new revenue = tax × consumption
(1 - 2.5/100)A . (1+5/100)B
97.5/100 * 105/100 AB
Effect on revenue = x + y + xy/ (100 × 100)
= – 2·5 + 5 – 5 × 2·5/ (100 × 100)
= 2·5 – 5 /4000
= 2·5 – 0·00125
= 2·5
4. In an examination 75% students failed in Economics, 55% failed in Maths and 35% failed in both the subjects and 500 passed in both the subjects. Find the total number of students.
By using formula :
% of students who passed in both subjects = [100 – (x + y – z)] % = [100 – ( 75 + 55 – 35)]%
= (100 – 95 )% = 5%
Since, 5 % students = 500 students
⇒ 100% (5 × 20) students = 500 × 20 = 10,000 students.
5. There are 500 students in an examination 85% students passed in Geography and some of the students passed in Civics while 65% students passed in both the subjects. If 300 students failed in both the subjects. Find the % of students who passed in Civics.
Solution : Let the required % of students who passed in Civics is x.
Now, by using Set Theory formula n (A ∪ B) = n (A) + n (B) – n (A ∩ B)
No. of students passed in one or both the subjects = x% + 85% – 65% = (x + 20)%
No. of students passed one or both the subjects = (x + 20) %
Now, Number of students failed = [100 – (x + 20)]% = (80 – x)%
Since, in 100 students, (80 – x) students is failed
∴ In 500 students, 80 – x 100 × 500 students is failed According to questions— 80 – x 100 × 500 = 300
∴ 80 – x = 60; x = 80 – 60 = 20 Required % of students who passed in Civics = 20.
5. In an examination a candidates scores 35% but fails by 45 marks. If the passing marks is 65%. What is the maximum marks ?
Let the maximum marks = 100
Secured marks = 35
Passing marks = 65
Difference = 65 – 35 = 30
When he fails by 30 marks maximum marks = 100
∴ He fails by 1 marks, maximum marks = 100 30
∴ He fails by 45 marks maximum marks
= 100 /30 × 45 = 150.
6. The maximum marks in Civics is 120. A candidates scores 60 marks but fails by 12 marks. What is the percentage pass marks ?
Since candidates get total (60 + 12) marks
∴ Candidates get 72 marks out of 120 marks i.e., In 120 marks,
candidates get 72 marks
∴ In 100 marks, candidates get 72 120 × 100%
Hence, percentage pass marks = 60%.
7. Gita and Reeta appears for an examination. Gita scores 40% and fails by 24 marks. While Reeta scores 45% which is 16 marks more than the pass marks. What are the maximum marks ?
Let the maximum marks = M Gita gets pass marks = 40 /100 M + 24
While Reeta gets pass marks = 45 /100 M – 16
Since, both are equal, So,
40/ 100 M + 24 = 45 /100 M – 16
or 40 = 5 100 M
∴ M = 800.
8. In a school library, 25% books are in Hindi, 80% of the remaining are in English and the remaining 9,000 are in various languages. What are the total number of books in English ?
Let the total books in Library = 100
Now, books in Hindi = 25
Books in English = 75 × 80/ 100 = 60
Remaining books = 100 – (25 + 60) = 15
When remaining books are 15, then total books = 100
∴ If remaining books are 9,000, then total books
= 100 /15 × 9,000 = 60,000
9. An Army lost 25% of its men in war, 10% of the remaining due to diseases and 5% of the rest declared war disabled. Thus, the strength was reduced to 6,41,250 active men. Find the original strength.
Let the original strength = 100
Due to war lost men = 25
Due to diseaseslost men = 75 × 10 /100 = 7·5
Disabled men = (75 – 7·5) × 5 /100
= 3·375
Reduced strength = 100 – (25 + 7·5 + 3·375) = 64·125
When 64·125 is active then original is 100. 6,41,250 is active men,
then original strength = 10,00,000.
Exercise A
2. If the sum of numbers obtained by taking percentage of 25% and 10% of a certain number is 350. Find the certain number ?
3. The difference between the numbers obtained by increasing a certain number by 2% and that obtained by diminishing it by 1·5% is 350. Find the original number ?
4. P% of a number C is equal to Q% of a number D. Find the per cent of C relative to D ?
5. The sum of two numbers is A. Seven times of greater number exceeds five times of the smaller one by kA. Find what per cent the greater number is more than the smaller one ?
6. A shopkeeper marks prices at 121 2 % higher than the original price. Due to increase inflation he further increases the price by 6 1 2 %. How much % profit will he get ?
7. The price of rice is increased by 40%. Find how much per cent its consumption must be decreased if expenditure remains constant ?
8. The price of wheat decreases by 24·5 %. Find by how much per centits consumption must be increased if expenditure remains constant ?
9. The price of kerosene decreases by 25%. Find how much per cent must its consumption be increased if expenditure remains constant ?
10. The population of Bombay was 15,00,000, 3 years ago. If population increased by 10% during first year, decreased by 5% during the second year and again increased by 15% during the third year. What is its population now ?
11. In a factory, the present price of a machine is Rs. 75,000. What was its price 2 years ago and will be its price 2 year hence. If annual rate of depreciation of the machine is 20%.
12. In an election be two candidates Ram and Rahim, Ram got 40% of the votes polled and is defeated by 1600 votes. Find the number of votes polled for Rahim.
13. An ore contains 35% of mass as impurity, whole the metal extracted from this ore contains 5% impurity. How much metal will 240 tonnes of the ore yield ?
14. In April, a cricket team that played 70 games had won 40% of its games. After a phenomenal arising streak this team raised its average to 60%. How many games the team have won in a row to attain this average ?
15. Sheela’s income increases by Rs. 2,000 but the rate of tax being reduced from 15% to 12%. She pays the same amount of tax as before. What is her increased income, if 10% of her income is exempted from tax in both the cases ?
16. Two numbers are 20% and 25% less than a third number. How much % is the second number less than the first ?
17. A reduction of Rs. 2/kg enables a man to purchases 8 kg. more sugar for Rs. 32. Find the original price of rice.
18. A reduction of 60% in the price of chocolates enables a person to buy 10 kg. more for Rs. 240. Find the original price of chocolates per kg.
19. A two digital number obtained by after interchanging the initial number increases by 9. What is percentage increase in number, if the sum of numbers is 3 ?
20. ‘A’ spends 75% of his income and saves the rest. When the cost of living increased, his expenses increased by 251 2 % and his income also increased by 121 2 %. What percentage of his income does he save now ?
21. If the length of a rectangle is increased by 60% and the breadth is decreased by 40%, then find the % change in area of the rectangle.
22. Nitin’s contributions to charity, religious donation and community welfare are in the ratios of 10 : 20 : 40 respectively. Express the contribution in percentage terms.
23. Which is greatest in 50 2 % 0·3, 2 15 ?
24. Gita’s salary is 20% less than Sita’s salary but 30% more than Rita’s salary. If Rita’s salary is Rs. 75 less than Sita’s salary, find the salary of each.
Next Chapter is on Averages
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