# Solved Example

Example-1
A man buys an article for Rs. 27.50 and sells it for Rs. 28.60. Find the gain percent?
Solution
C.P = Rs. 27.50; S.P = Rs. 28.60
Then Gain = S.P - C.P = 28.60 - 27.50 = Rs. 1.10;
Since, Gain% = (gain*100)/C.P%
= >(1.10*100)/27.50%=4%

Example-2

If a radio is purchased for Rs. 490 and sold for Rs. 465.50. Find the loss%?

Solution

C.P = Rs. 490; S.P = Rs.  465.50
Loss = C.P - S.P = 490 - 465.50 = Rs. 24.50
Loss% = (loss*100)/C.P%
= (24.50*100)/490% = 5%

Example-3
Find S.P when C.P = Rs. 56.25 and Gain = 20%
Solution
S.P = [(100 + gain%)/100]*C.P
= >S.P = [(100 + 20)/100] 56.25 = Rs. 67.50

Example-4

Find S.P when C.P = Rs. 80.40, loss = 5%

Solution

S.P = [(100 - loss%)/100]*C.P
= >S.P = [(100 - 5)/100]*80.40 = Rs. 76.38

Example-5
Find C.P when S.P = Rs. 40.60, gain = 16%?
Solution
C.P = (100*S.P)/(100 + gain%)
= > C.P = (100*40.60)/(100 + 16) = Rs 35

Example-6

Find C.P when S.P = Rs. 51.70, loss = 12%?

Solution

C.P = (100*S.P)/(100 - loss%)
C.P = (100*51.70)/(100 - 12) = Rs. 58.75

Example-7
A person incurs 5% loss by selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit?
Solution
Let the new S.P be Rs x then
(100 - loss%): (1st S.P) = (100 + gain%) : (2nd S.P)
(100 - 5)/1140 = (100 + 5)/x
x = (105*1140)/95 = Rs. 1260

Example-8

If the cost price is 96% of the selling price, then what is the profit percent?

Solution

let S.P = Rs. 100 then C.P = Rs. 96
Profit = S.P - C.P = 100 - 96 = Rs. 4
Profit% = (profit/C.P)*100%
= (4/96)*100 = 4.17%

Example-9
A discount dealer professes to sell his goods at cost price but uses a weight of 960 gms for a Kg weight. Find his gain %?
Solution
Gain% = [(error*100)/(true value - error)]% = [(40*100)/1000 - 40)]% = 25/6%

Example-10

A man sold two flats for Rs. 675,958 each. On one he gains 16% while on the other he losses 16%. How much does he gain or lose in the whole transaction?

Solution

Loss% = [common loss or gain%/10]2 = (16/10)2 = 2.56%

Example-11
A man sold two cows at Rs. 1995 each. On one he lost 10% and on the other he gained 10%. What his gain or loss percent?
Solution
Loss of 1%

Example-12

The price of an artic le is reduced by 25% in order to restore the must be increased by ?

Solution

[x/(100-x)]*100 = [25/(100 - 25)]*100 = (25/75)*100 = 100/3%

Example-13
Two discounts of 40% and 20% equal to a single discount of?
Solution
{[(100 - 40)/100]*[(100 - 20)/100]}% = (60*80)/(100*100)% = 48%
Single discount is equal to (100 - 48)% = 52%

Example-14

The cost of an article including the sales tax is Rs. 616. The rate of sales tax is 10%, if the shopkeeper has made a profit of 12%, then the cost price of the article is?

Solution

110% of S.P = 616
S.P = (616*100)/110 = Rs. 560;
C.P = (100*S.P)/(100 + gain%) = >C.P. = (100*560)/(100 + 12) = Rs. 500

Example-15
Sam purchased 20 dozens of toys at the rate of 375 Rs. per dozen. He sold each one of then at the rate of Rs. 33. What was his percentage profit?
Solution
C.P of one toy = Rs. 375/12 = Rs. 31.25; S.P of one toy = Rs. 33
Profit = S.P - C.P = 33 - 31.25 = Rs. 1.75
Profit % = (profit/C.P)*100 = (1.75/31.25)*100; Profit% = 5.6%

Example-16

Two third of consignment was sold at a profit of 5% and the remainder at a loss of 2%. If the total profit was Rs. 400, the value of the consignment was?

Solution

Let the total value be Rs. x then Value of 2/3 = 2x/3, value of 1/3 = x/3
Total S.P value be Rs. x
Total S.P = [(105% of 2x/3) + (98% of x/3)] = (105*2x)/(100*3) + (98/100) + x/3 = > x = (300*400)/8 = Rs. 15000

Example-17
Kunal bought a suitcase with 15% discount on the labelled price. He sold the suitcase for Rs. 2880 with 20% profit on the labelled price. At what price did he buy the suitcase?
Solution
Let the labelled price be Rs. x, Then 120% of x = 2880
x = (2880*100)/120 = Rs. 2400
C.P = 85% of the 2400 = >(85*2400)/100 = Rs. 2040

Example18

A tradesman gives 4% discount on the marked price and gives article free for buying every 15 articles and thus gains 35%. The marked price is above the cost price by?

Solution

Let the C.P of each article be Rs. 100
Then C.P of 16 articles = Rs. (100*16) = Rs. 1600
S.P of 15 articles = 1600*(135/100) = Rs. 2160
S.P of each article = 2160/15 = Rs. 144
If S.P is Rs. 96, marked price = Rs. 100
If S.P is Rs. 144,marked price = (100/96)*144 = Rs. 15000
Therefore marked price = 50% above C.P

Example-19
By selling 33 m of cloth, one gains the selling price of 11m. Find the gain percent?
Solution
Gain = S.P of 33m - C.P of 33m = 11m of S.P
S.P of 22m = C.P of 33m
Let C.P of each meter be Rs. 1, then C.P of 22m = Rs. 22
S.P of 22m = Rs. 33
Gain = S.P - C.P = 33 - 22 = Rs. 11
Gain% = (gain/C.P)*100 = (11/22)*100 = 50%

Example-20

The price of a jewel, passing through three hands, rises on the whole by 65%. If the first and second sellers earned 20% and 25% profit respectively, find the percentage profit earned by the third seller?

Solution

Let the original price of the jewel be Rs. P and
Let the profit earned by the third seller be x%
Then (100 + x)% of 125% of P = 165% of P
[(100 + x)/100]*(125/100)*(120/100)*P = (165/100)*P
100 + x = (165*100*100)/(125*120)
100 + x = 110 thus, x = 10%

Example-21
When a producer allows 36% commission on the retail price of his product, he earns a profit of 8.8%. What would be his profit percent if the commission is reduced by 24%
Solution
Let retail price = Rs. 100 then, Commission = Rs. 36
S.P = retail price-commission = 100 - 36 = Rs. 64
But profit = 8.8%
C.P = (100*C.P)/(gain + 100) = (100*64)/(100 + 8.8) = Rs. 1000/17
New commission = Rs. 12 then, New S.P = 100 - 12 = Rs. 88
Gain = 88 - (1000/17) = Rs. 496/17
Gain% = gain*100/C.P
= (496*17*100)(17*1000)
Gain% = 49.6%

Example-22

Vikas bought paper sheets for Rs. 7200 and spent Rs. 200 on transport. Paying Rs. 600, he had 330 boxes made, which he sold at Rs. 28 each. His profit percentage is?

Solution

Total investments = 7200 + 200 + 600 = Rs. 8000
Total receipt = 330*28 = Rs. 9240
Gain = S.P - C.P = total receipt - total investments
Gain = 9240 - 8000 = Rs. 1240
Gain% = gain*100/C.P = 1240*100/8000 = 15.5%

Example-23
A person earns 15% on investment but loses 10% on another investment. If the ratio of the two investments be 3:5, what is the gain or loss on the two investments taken together?
Solution
Let the investments be 3x and 5x, Then total investment = 8x
Total receipt = 115% of 3x + 90% of 5x = 115*3x/100 + 90*5x/100 = 7.95x
Loss = C.P - S.P = 8x - 7.95x = 0.05x = >loss% = .05x*100/8x = 0.625%

Example-24

The profit earned by selling an arti cle for Rs. 900 is double the loss incurred when the same article is sold for Rs. 490. At what price should the article be sold to make 25% profit?

Solution

Let C.P be Rs x then, 900 - x = 2(x - 450)
3x = 1800 & x = Rs. 600
C.P = Rs. 600, gain required = 25%
S.P = (100 + gain%)*C.P/100 = > S.P = (100 + 25)*600/100 = Rs. 750

Example-25
If an article is sold at 5% gain instead of 5% loss, the seller gets Rs. 6.72 more. The C.P of the article is?
Solution
Let C.P be Rs x = 105% of x - 95% of x = 6.72
(105/100)* x - (95/100)*x = 6.72
x/10 = 6.72 Thus, x = Rs 67.21.