Ayush Agarwal Maths

Percentage -   According to mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted by using the percent sign, "%" .  Percentage formula -  Percentage = (Obtained marks/Total                                marks)×100 Example :-  3/5 ×100 = 0.60×100 = 60% =                                  60percent About Percentage - 1. 10% is equal to 1/10 fraction 2.  20% is equivalent to ⅕ fraction 3.  25% is equivalent to ¼ fraction 4.  50% is equivalent to ½ fraction 5.  75% is equivalent to ¾ fraction 6.  90% is equivalent to 9/10 fraction Points to remember :- 1. A percentage is a dimensionless number, it has no unit of measurement.  Practice Questions - Q1.   Convert as a fraction and as a decimal :   40% Q2. Express the ratio 4:5 as a percentage. Q3. Find 30% of ₹800. Q4. If 10% of a number is 45, then find the number? Thank you for visiting  Keep sharing  Join us now :-  Instagram

Compound Interest - compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest. Applications of Compound Interest  1. In increase or decrease in population.  2. The growth of bacteria when the rate of growth is known.  3. Depreciation in the values of machines.  Important Facts :  1. When time is given in days, we convert it to year by dividing it by 365. 2. When time is given in months, we convert it to year by dividing it by 12. 3. When dates are given, the day on which the sum is borrowed is not included but the day on which money is returned is included, while counting the number of days. Remark - negative sign of rate indicates the depreciation.  Practice Questions  1.Find the compound interest on ₹ 5000 at 8% per annum for 2 years, compounded annually?  2.Find the amount of ₹18000 for 3 years, compounded annually at 10% per annum. Also, find the compound interest.  3.The compound interest on Rs. 30,000 at 7% pe

Simple interest -  Simple interest  is  interest  calculated on the principal portion of a loan  to a savings account.

                   CUBES AND CUBE ROOTS Cube number- A cube number is a number multiplied by itself twice, or we can say the cube of a number m is its third power.  For example- m³ =  m  ×  m 2  =  m  ×  m  ×  m . 8³ = 8 × 8 2  = 8  × 8  × 8 = 512 .  15³ = 15  ×  15 2  =  15  ×  15  ×  15 = 3375 .   Perfect cube - A natural number is said to be a perfect cube if it is the cube of some natural numbers.  Examples-   1 ³ = 1, 2³ = 8, 3³ = 27, 4³ = 64,  etc.            Thus 1, 8, 27, 64 etc.., are perfect cubes.  Facts About cube numbers:- 1. The cube of a number is that number raised to the power 3 .  2. The cube of an even natural number is even.  3. The cube of an odd natural number is odd.  4.  Numbers ending in 1, 2, 3, 4, 6, 7, 8, 9, 000, 125, 375, 625 or 875 may be cube numbers.  Practice Questions 1. Find the cube of 21 .  2. Find the least number by which 750 should be multiplied, so that it becomes a perfect cube. 3. Solve :- (i) ∛4096  (ii) ∛(729/1000 ) 4. By w