5/27/2016 0 Comments ## Partnership1. Partnership: When two or more than two persons run a business together they are partners and the deal between them is called partnership.When investments of all partners are for the same time, the gain or loss is distributed among the partners in the ratio of their investments.2. When investments are for different time periods, then equivalent capitals are calculated for a unit of time by taking ( capital X Number of units of time). And gain or loss is divided based on the ratios of these calculated capitals.3. A partner who manages the whole business4. Working Partner: A partner who just invests money.5. Sleeping Partner:
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5/23/2016 0 Comments ## Pipes and Cisterns- If a pipe can fill a tank in x hrs, Part of tank filled in 1 hr=1/x
- If a pipe can empty a full tank in y hrs, Part emptied in 1 hr= 1/y
- If a pipe can fill a tank in x hrs and another pipe empties the full tank in y hrs such that y>x, then opening both pipes the net part of tank filled (1/x-1/y)
- If a pipe can fill tank in x hrs and another pipe can empty the full tank in y hrs such that x>y, then opening both the pipes, the net part emptied in 1 hr = (1/y-1/x)
5/23/2016 0 Comments ## Time and Work- If A can do a task in n days, then A's 1 day work=1/n
- If A is twice as good a workman as B, Then:
Ratio of Time Taken by A and B to complete the task= 1:2 5/21/2016 0 Comments ## Profit and LossCost Price: It is the price at which an article is purchased Selling Price: It is the price at which an article is sold. Profit and Gain: If SP > CP, It means seller is said to have a profit or gain Loss: If SP< CP, then seller is said to incurred loss ## Formulae1. Gain=SP-CP
2.Loss=CP-SP 3.Gain %= (GainX100)/CP 4.Loss%= (Loss X100)/CP 5. SP= CP(100+Gain%)/100 6.SP=CP(100-Loss %)/100 7.CP=SPX100/(100+Gain%) 8.CP=SPX100/(100-Loss%) 9.If two similar product is sold, one at a gain of x% and teh other at a loss of x%, then the seller always incurs loss. Loss%= (x/10)X(x/10) 10.If a trader sells at cost price but uses false weight then Gain %= 100 x error/(True Value-Error) 5/21/2016 0 Comments ## Important Formulas on Percentage
1. If the price of the commodity increases by r %, then the reduction in consumption to keep the expenditure unaffected is
2. If the price of the commodity decreases by r% , then the increase in consumption to keep the expenditure unaffected is
3.Problems on Appreciation
P is some metric and it increases at the rate of R % per annum, then Result after n years=
Result n years ago=
4.Problems on Depreciation
P is some metric and it depriciates at the rate of R % per annum, then
Result after n years=P{(1-\frac{R}{100})^{N}}
Result after n years=\frac{P}{(1-\frac{R}{100})^{N}}
5. If A is R% more than B, Then B is less than A by
\frac{R}{100+R}\times 100
6. If A is R% less than B, Then B is more than A by
\frac{R}{100-R}\times 100
5/19/2016 0 Comments ## Average- Average=(Sum of all events/ Count of events)
- If a man covers some distance at a kmph and an equal distance at b kmph. Then average speed is (2ab/a+b) kmph
- Sum of first n natural number = n(n+1)/2
\[(\frac{2ab}{a+b})\]
5/18/2016 0 Comments ## Formulas on Series1.
2.
3.
4.Arithmatic Progression a, a+d, a+2d, a+3d..are in arithmatic progression with a common difference of d
If nth term is and last term is equal to l then 1.nth term= 2.Sum of n terms= 3.Sum of n terms=
5.Geometric Progression: a, ar, are in Geometric progression with a common ratio r then
a. nth term= b.Sum of n terms=, If r<1 , If r>1 5/17/2016 0 Comments ## HCF and LCM of Numbers**HCF:**It stands for Highest Common Factor, HCF of 2 or more than 2 no. is the greatest no. that divides each of them exactly.**Method of finding HCF**
**Factorization Method:**Transform the given numbers as the product of the prime factors. The product of least powers of common prime factors is the HCF.**Division Method:**Divide the larger no. by smaller one, now divide the divisor by remainder and repeat the process till you get 0. The last divisor is HCF
**LCM:**It is known as Least Common Multiple and is the least number which is exactly divisible by each one of the considered numbers**Method of finding HCF**
**Factorization Method:**Transform the no. as the product of prime factors, Product of highest powers of all factors gives the LCM.**Division Method:**Divide the given no.s by a factor which exactly divides atleast two of the given no.s and carry forward the indivisible no.s, repeat the process till no common factor is left. Then the product of all divisors and undivided number is the LCM
**HCF & LCM of Fractions**
- HCF= (HCF of Numerators)/ (LCM of Denominators)
- LCM= (LCM of Numerators)/(HCF of Denominators)
**Product of two numbers**= HCF x LCM
5/17/2016 0 Comments ## Tests of Divisibility1. Divisibility Test by 2If a no. is divisible by 2 then its unit digit will be even (0,2,4,6,8) 2. Divisibility Test by 3A no. is divisible by 3, if the sum of its digits is divisible by 3 3.Divisibility Test by 4A no. is divisible by 4, if its last two digit is divisible by 4 4. Divisibility Test by 5A no. is divisible by 5, if its unit digit is either o or 5 5. Divisibility Test by 6If a no. is divisible by 2 and 3, it is divisible by 66. Divisibility Test by 7For a no. to be divisible by 7, Take off the last digit subtract the square of it with the remaining digit, repeat the process, If the result is evenly divisible by 7, then the no. is multiple of 7. 7. Divisibility Test by 8No. is divisible by 8, if the no. formed by last three digits is divisible by 8 8. Divisibility Test by 9A no. is divisible by 9, if the sum of its digits are divisible by 9 9. Divisibility Test by 10No. is divisible by 10 if its unit digit is 0 10. Divisibility Test by 11A no. is divisible by 11, if the difference between the sum of the digits at odd places and even places is either 0 or 11 |