Maths of the world

 Contents

    1.Percentage

    2.Algebra Formulas

 

1. Percentage

1.A student has to get 40% marks to pass in the  examination.Suppose he gets 30marks and fails by 30 marks. Then what are the maximum marks in the examination?

 

 

2.In a city 12% households earn less than Rs. 30,000 per year. 6% household earn more than Rs. 2,00,000 per year, 22% households earn more than Rs, 1,00,000 per year and 990 house-holds earn between 36,000 and Rs.1,00,000 per year. How many households earn between Rs. 1,00,000 & 2,00,000 per year.

 

 

 3. If 80% of a number added to gives the result as the number itself the number is ?

 

 

 

1. Reduction o 25% in the price of Rice enables Bhomkesh to buy 2Kg more rice for Rs. 240. The reduce per kg price of rice is?

 

2. When the price of sugar decreased by 10% a man could buy 1 kg more for Rs. 270, then the original price i

 

3. The price of sugar is reduced by 20%. Now a person can buy 500gm more sugar for Rs. 36. Then the original price of sugar/kg is

 

4. As a result of 25% hike in the price o rice per kg, a person is able to purchase 6kg less rice for Rs. 1200, What was the original price of rice per kg.

 

5. As a result of 25% hike in the price of rice per kg a person is able to purchase 6 kg less rice for R. 1200, what was the original price of  rice per kg.

 

6. A reduction of 20% in the price of wheat enables Rakhi to buy 5 kg more whet for Rs 320. The original rate of wheat kg was?

 

1. If 60% of a school are  are boys and girls 972. Then how many students in a school?

2. If income of Deepa is 15000 and Deepa expense 30% Then how much save Deepa.

3. 75gm of sugar solution has 30% sugar in it. Then the quantity of sugar that should be added to the solution to make the quantity of sugar 70% in the solution.

4. A man spends 75% of his income, His income increase by 20%and he increased his expenditure by 15%. His savings will then be increased by 

5. A dozen pairs o Stock quoted at 180 are available at discount of 20%. How many pairs  of stocks can be brought for 48?

6.The population of a village is 25,000. One fifth are females and rest are males.

5% of males and 40% of females are uneducated, What percentage on the whole are educated.

 

 

TIME & WORK 

1. A&B  can complete a work in 8 days and B&C together in 12 days. All of the three together can complete the work in 60 days. A&C together complete the work in.

 

 2.A can do a peace of work in 12 days. When he had worked for 3 days , B joined him. If they completed the work in 3 more days . In how many days can B alone finish the work ?

 

3. A  can do a peace of work in 20 day which B can o in 12 days , B worked at it for 9 days can finish the remaining work in?

4. A alone can complete a peace of work in 12 daysy. A&B  together can complete it in 8 days . How long will B alone tak to it to complete the work.

5.A can finish a peace of work in 24 days , B in 9 days and C in 12 ays. B&C start the work but are forced to leave ater 3 days. The maintaining work done by A in?

 

2. Important Formulas in Algebra

Here is a list of Algebraic formulas –

• a² – b² = (a – b)(a + b)
• (a + b)² = a² + 2ab + b²
• a² + b² = (a + b)² – 2ab
• (a – b)² = a² – 2ab + b²
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
• (a – b – c)² = a² + b² + c² – 2ab + 2bc – 2ca
• (a + b)³ = a³ + 3a²b + 3ab² + b³ ; (a + b)³ = a³ + b³ + 3ab(a + b)
• (a – b)³ = a³ – 3a²b + 3ab² – b³ = a³ – b³ – 3ab(a – b)
• a³ – b³ = (a – b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² – ab + b²)
• (a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴
• (a – b)⁴ = a⁴ – 4a³b + 6a²b² – 4ab³ + b⁴
• a⁴ – b⁴ = (a – b)(a + b)(a² + b²)
• a⁵ – b⁵ = (a – b)(a⁴ + a³b + a²b² + ab³ + b⁴)