Aptitude
PROFIT OR GAIN:IF SP IS GREATER THAN CP,THE SELLING PRICE IS SAID TO HAVE PROFIT OR GAIN.
LOSS: IF SPIS LESS THAN CP,THE SELLER IS SAID TO INCURED A LOSS.
FORMULA :
1.GAIN=(SP)-(CP).          
2.LOSS=(CP)-(SP).
3.LOSS OR GAIN IS ALWAYS RECKONED ON CP
4. GAIN %={GAIN*100}/CP.                                                                             
5.LOSS%={LOSS*100}/CP.
6.SP={(100+GAIN%) /100}*CP.
7.SP={(100-LOSS%)/100}*CP.
8.{100/(100+GAIN%)} *SP
9.CP=100/(100-LOSS%)}*SP
10.IF THE ARTICLE IS SOLD AT A GAIN OF SAY 35%, THEN SP =135% OF CP
11.IF A ARTICLE IS SOLD AT A LOSS OF SAY 35%. THEN SP=65% OF CP.
12.WHEN A PERSON SELLS TWO ITEMS,ONE AT A GAIN OF X% AND OTHER AT A LOSS OF X%.THEN THE SELLER ALWAYS INCURES A LOSS GIVEN:
{LOSS%=(COMON LOSS AND GAIN ) 2}/10.=(X/10) 2
13.IF THE TRADER PROFESSES TO SELL HIS GOODS AT CP BUT USES FALSE WEIGHTS,THEN
GAIN=[ERROR/(TRUE VALUE)-(ERROR)*100]%

1 A man buys an article for rs.27.50 and sells it for rs.28.50. find his gain %.

cp=rs27.50, sp=rs 28.50
gain=rs(28.50 –27.50)=rs1.10
so gain%={(1.10/27.50)*100}=4%

2. If the a radio is sold for rs 490 and sold for rs 465.50.find loss%.

cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%

3.find S.P when (i)CP=56.25,gain=20%. (ii)CP=rs 80.40,loss=5%

sol:
(i)SP =20% of rs 56.25 ,=rs{(120/100)*56.25}=rs67.50.
(ii)CP=rs 80.40,loss=5%
 sol: sp=85% of rs 80.40
=rs {(85/100)*80.40}=rs 68.34.

4 find cp when: (i) sp =rs 40.60 : gain=16% (ii) sp=rs51.70:loss=12%

(i)  cp=rs{(100/116)*40.60}=rs 35.
(ii) cp=rs{(100/88)*51.87}=rs58.75.

5 A person incures loss for by selling a watch for rs1140.at what price should the watch be sold to earn a 5% profit ?

let the new sp be rsx.then
  (100-loss%) : (1st  sp) = (100+gain%) (2ndsp)
   =>  {(100-5)/1400} = {(100+5)/x}
   => x = {(105*1140)/95} = 1260.

6 A book was sold for rs 27.50 with a profit of 10%. if it were sold for rs25.75, then what would be % of profit or loss?

sol. SP=rs 27.50: profit =10%.
sol. CP=rs {(100/110)*27.50}=rs 25.
When sp =Rs25.75 ,profit =Rs(25.75-25)=Rs 0.75                       
Profit% = {(0.75/25)*100}% = 25/6% =3%

7 .If the cost price is 96% of sp then whqt is the profit %

sp=Rs100 : then cp=Rs 96:profit =Rs 4.
Profit={(4/96)*100}%=4.17%

Ex.8. The cp of 21 articles is equal to sp of 18 articles.find gain or loss %

CP of each article be Rs 1
CP of 18 articles =Rs18 ,sp of 18 articles =Rs 21.
Gain%=[(3/18)*100]%=50/3%

9 By selling 33 metres of cloth , one gains the selling price of 11 metres . Find the gain percent .

(SP of 33m)-(CP of 33m)=Gain=SP of 11m
SP of 22m = CP of 33m
Let CP of each metre be Re.1 , Then, CP of 22m= Rs.22,SP of 22m=Rs.33.
Gain%=[(11/22)*100]%=50%

10 A vendor bought bananas at 6 for Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss percent .

Suppose , number of bananas bought = LCM of 6 and 4=12
CP=Rs.[(10/6)*12]=Rs.20  ; SP= Rs[(6/4)*12]=Rs.18
Loss%=[(2/20)*100]%=10% 

11. A man brought toffees at for a rupee. How many for a rupee must he sell to gain 50%?

C.P of 3 toffees=Re 1; S.P of 3 toffees =150% of Re.1=3/2.
    For Rs.3/2, toffees sold =3, for Re.1, toffees sold = [3*(2/3)] = 2.

12.A grocer purchased 80 kg of sugar at Rs.13.50 per kg and mixed it with 120kg sugar at Rs.16per kg. At what rate should he sell the mixer to gain 16%?

C.P of 200 kg of mixture = Rs. (80 * 13.50+120*16) = Rs.3000.
       S.P =116% 0f Rs.3000 =Rs.[(116/200) *3000]=Rs.3480.
\ Rate of S.P of the mixture =Rs.[3480/200] per kg =Rs.17.40 per kg.

13. Pure ghee cost Rs.100 per kg. After adulterating it with vegetable oil costing Rs.50 per kg, A shopkeeper sells the mixture at the rate of Rs.96 per kg, thereby making a profit of 20%.In What ratio does he mix the two?

Mean cost price =Rs. [ (100/120)*96 ]=Rs.80 per kg.

By the rate of allegation :
:========================================:
:    C.P of 1kg ghee   : C.P of 1kg oil  :
:           100        :     50          :
:......................:.................:
:    Mean price     :
:     80      :
:========================================:  
Required ratio = 30 : 20 = 3 : 2

14. A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 gms for a kg weight . Find his gain percent.

Gain% =[ ( Error/(error value)-(error) )* 100 ]% =  [(40/960)*100] % = 4 1/6 %                      

15. If the manufacturer gains 10%,the wholesale dealer 15% and the retailer 25%,then find the cost of production of a ,the retail price of which is Rs.1265?

  Let the cost of production of the table be Rs x
 The ,125% of 115% of 110% of x=1265
=>  125/100*115/100*110/100*x=1265=>253/160*x=>1265=>x=(1265*160/253)=Rs.800

16 . Monika purchesed a pressure cooker at 9/10th of its selling price and sold it at 8% more than its S.P .find her gain percent.

Let the s.p be Rs. X .then C.P = Rs.9x/10,Receipt=108% of rs.x=Rs 27x/25
Gain=Rs (27x/25*9x/10)=Rs(108x-90x/100)=Rs18x/100
Gain%=(18x/100*10/9x*100)%=20%

17 An article is sold at certain price. By selling it at 2/3 of its price one losses 10%,find the gain at original price ?

let the original s.p be Rs x. then now S.P=Rs2x/3,loss=10%
now C.P=Rs20x/27*27/20x*100)%=35%

18. A tradesman sold an article at a loss of 20%.if the selling price has been increased by Rs100,ther would have been a gain of 5%.what was the cost price of the article?

Let C.P be Rs x. then (105% of x)-(80 % of x)=100 or 25% of x=100
=> x/4=100 or x=400
=>  so,C.P =Rs 400

19. A man sells an article at a profit of 25%if he had bought it 20% less and sold it for Rs 10.50 less,he would have gained 30%find the cost price of the article.

 Let the C.P be Rs x
      1st S.P=125% of x =125x/100=5x/4;2nd S.P=80% of x=80x/100=4x/5
      2nd S.P=130% of 4x/5=(130/100*4x/5)=26x/25
      => 5x/4-26x/25=10.50óx=(10.50*100)/21=50
   hence C.P=Rs.50

20.The price of the jewel,passing through three hands,rises on the whole by65%.if the first and the second sellers 20%and25% profit respectively find the percentage profit earned by the third seller.

Let the orginal price of the jewel be Rs p and let the profit earned  by the thrid seller be x%
Then,(100+x)% of 125% OF 120% OF P=165% OF P
=> ((100+X)/100*125/100*120/100*P)=(165/100*P)
=>  (100+X)=(165*100*100)/(125*120)=110=>X=10%

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