Cost Price-The price at which an article is purchased is called its cost price (C.P.)
Selling Price-The price at which the article is sold is called its selling price (S.P.)
If the cost price (C.P.) of the article is equal to the selling price (S.P.), Then there is no loss or gain.
If the selling price (S.P.) > cost price (C.P.), then the seller is said to have a profit or gain, Gain or Profit = S.P. - C.P.
If the cost price (C.P.) > selling price (S.P.), then the seller is said to have a loss, Loss = C.P. - S.P.
Gain% = {Gain*100}/{C.P.}
Loss% = {Loss*100}/{C.P.}
S.P.= {(100+Gain%/100)x C.P}
S.P.= {(100-Loss%/100)x C.P}
C.P.= {(100)/(100+Gain%)x S.P}
C.P.= {(100)/(100-Loss%)x S.P}
If an article is sold at a profit/gain of 30%, then S.P. = 130% of the C.P.
If an article is sold at a loss of 20%, then S.P. = 80% of the C.P.
When there are two successive Profit of x % and y % then the resultant profit per cent is given by [x + y+ (x*y/100)]
If there is a Profit of x% and loss of y % in a transaction, then the resultant profit or loss% is given by [x – y - (x*y/100)]
Note- For profit use sign + in previous formula and for loss use – sign.
if resultant come + then there will be overall profit . if it come – then there will be overall loss.
If a cost price of m articles is equal to the selling Price of n articles, then Profit percentage (m-n)/n×100%
If m part is sold at x% profit , n part is sold at y % profit, and p part is sold at z% profit and Rs. R is earned as overall profit then the value of total consignment R×100 / (mx+ny+pz)
A man purchases a certain no. of article at m a rupee and the same no. at n a rupee. He mixes them together and sold them at p a rupee then his gain or loss % [{2mn/(m+n)p} -1]× 100 Note += profit ,- = loss
When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then in this transaction the seller always incurs a loss given by: = {x^2/100}%
A single discount equivalent to discount series of x% and y% given by the seller is equal to (x +y - xy/100)%
If a seller marks his goods at x% above his cost price and allows purchasers a discount of y % for cash, then overall gain or loss (x – y –xy/100)%
Profit or loss according to sign .+ = gain, - = loss
If a trader professes to sell his goods at cost price, but uses false weights, then Gain% = {(Error)/(True value - Error)x 100] %
Quiz Based on Concepts
1. 1/3 of a commodity is sold at 15% profit, ¼ is sold at 20% profit and the rest at 24% profit. If the Total profit is Rs. 80 is earned then find the value of commodity?
A) 350 B) 410 C) 400 D) 300 E) None of these
1. Part sold at 24% profit = 1-(1/3+1/4) = 5/12 Value of commodity = (80×100) / (1/3*15+1/4*20+5/12*24)= 400
2. A man purchases a certain no. of apple at 5 per rupee and same no. at 4 per rupee. He mixes them together and sells them at 4 per rupee. What is his gain or loss%?
A) Gain 20 % B) Gain 11.11% C) Loss 11.11% D) Loss 20 % E) None of these
2. Gain or loss = [2*5*4/4(5+4) - 1] × 100 % = 11.11% Sign is + ive so gain 11.11%
3. A trader allows a Discount of 5% for cash payment. How much approx % above cost price must he mark his goods to make a profit of 10%?
A) 8.9% B) 10% C) 12.75% D) 15.8% E) None of these
3. 10 = x-5 – 5x/100 19x/20 = 15; x=15.789% = approx 15.8%
4. If selling price is doubled, the profit triples. Find the profit percent?
A) 100% B) 116.67% C) 200% D) 300% E) None of these
4. Let C.P. be Rs. x and S.P. be Rs. y. Then, 3(y - x) = (2y - x) y = 2x. Profit = Rs. (y - x) = Rs. (2x - x) = Rs. x. So profit % =100%
5. The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
A) 2200 B) 2400 C) 2500 D) 2000 E) None of these
5. Let CP is x. Then (1920-x)/x*100= (x-1280)/x*100 On solving x=1600 Selling Price = 1600*125/100= Rs. 2000
What is Number Series?
Number series is a arrangement of numbers in a certain order, where some numbers are wrongly put into the series of numbers and some number is missing in that series, we need to observe and find the accurate number to the series of numbers.
Different types of Number Series
There are some format of series which are given in Exams.
Perfect Square Series:
This Types of Series are based on square of a number which is in same order and one square number is missing in that given series.
Example 1: 441, 484, 529, 576?
Answer: 441 = 21^{2}, 484 = 22^{2}, 529 = 23^{2}, 576 = 24^{2} , 625 = 25^{2}.
Perfect Cube Series:
This Types of Series are based on cube of a number which is in same order and one cube number is missing in that given series
Example 2: 1331, 1728, 2197, ?
Answer : 11^{3} , 12^{3} , 13^{3} , 14^{3}
Geometric Series:
This type of series are based on ascending or descending order of numbers and each successive number is obtain by multiplying or dividing the previous number with a fixed number.
Example 3: 5, 45, 405, 3645,?
Answer: 5 x 9 = 45, 45 x 9 = 405, 405 x 9 = 3645, 3645 x 9 = 32805.
Two stage Type Series:
A two tier Arithmetic series is one in which the differences of successive numbers themselves form an arithmetic series.
Example 4: i. 3, 9, 18, 35, 58,——
ii. 6, 9, 17, 23,———-
Mixed Series:
This type of series are more than one different order are given in a series which arranged in alternatively in a single series or created according to any non-conventional rule. This mixed series Examples are describes in separately.
Examples 5:
11, 24, 50, 102, 206, ?
Answer:
11 x 2 = 22 +2 = 24,
24 x 2 = 48 + 2 = 50,
50 x 2 = 100 + 2 = 102,
102 x 2 = 204 + 2 = 206,
206 x 2 = 412 + 2 = 414.
So the missing number is 414.