PARTNERSHIP : IMPORTANT FACTS AND FORMULAE with Examples and Explanations

1. Partnership: When two or more than two persons run a business jointly, they are

    called partners and the deal is known as partnership.

2. Ratio of Division of Gains:

          i) When investments of all the partners are for the same time, the gain or loss is distributed     a  among the partners in the ratio of their investments.

Suppose A and B invest Rs. x and Rs. y respectively for a year in a business, then at the end of the year:

(A’s share of profit) : (B's share of profit) = x : y.

       ii) 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). Now, gain or loss is divided in the ratio of  these capitals.

Suppose A invests Rs. x for p months and B invests Rs. y for q months, then

 (A’s share of profit) : (B's share of profit) = xp : yq.

3. Working and Sleeping Partners: A partner who manages the business is known . as a working partner and the one who simply invests the money is a sleeping partner.

 SOLVED EXAMPLES

Ex. 1. A, B and C started a business by investing Rs. 1,20,000, Rs. 1,35,000 and ,Rs.1,50,000 respectively. Find the share of each, out of an annual profit of Rs. 56,700.

Sol. Ratio of shares of A, Band C = Ratio of their investments

= 120000 : 135000 : 150000 = 8 : 9 : 10.

A’s share = Rs. (56700 x (8/27))= Rs. 16800.

B's share = Rs. ( 56700 x (9/27)) = Rs. 18900.

C's share = Rs. ( 56700 x (10/27))=Rs. 21000.

Ex. 2. Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the lire of each.

 Sol. Clearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald

         for 3 months.

         So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3)

                                             = 540000 : 540000 : 270000 = 2 : 2 : 1.

         Alfred's share = Rs. (16500 x (2/5)) = Rs. 6600

         Peter's share = Rs. (16500 x (2/5)) = Rs. 6600

         Ronald's share = Rs. (16500 x (1/5)) = Rs. 3300.

Ex. 3. A, Band C start a business each investing Rs. 20,000. After 5 months A  withdrew Rs.6000  B withdrew Rs. 4000 and C invests Rs. 6000 more. At the end of the year, a total profit of Rs. 69,900 was recorded. Find the share of each.

Sol. Ratio of the capitals of A, Band C

                     = 20000 x 5 + 15000 x 7 : 20000 x 5 + 16000 x 7 : 20000 x 5 + 26000 x 7

                      = 205000:212000 : 282000 = 205 : 212 : 282.

         A’s share = Rs. 69900 x (205/699) = Rs. 20500                        I

                                                                                                            

        B's share = Rs. 69900 x (212/699) = Rs. 21200;

        C's share = Rs. 69900 x (282/699) = Rs. 28200.

                                                    

Ex. 4. A, Band C enter into partnership. A invests 3 times as much as B

and B invests two-third of what C invests. At the end of the year, the profit earned is Rs. 6600. What is the share of B ?

Sol. Let C's capital = Rs. x. Then, B's capital = Rs. (2/3)x

        A’s capital = Rs. (3 x (2/3).x) = Rs. 2x.

      Ratio of their capitals = 2x : (2/3)x :x = 6 : 2 : 3.

     Hence, B's share = Rs. ( 6600 x (2/11))= Rs. 1200.

Ex. 5. Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for  5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 720, find the total rent of the field.

Sol. Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3)   = 72 : 50 : 140 : 63.

                                                                                      

               Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325

                      (72x)/325=720 ó x=(720 x 325)/72 = 3250   

              

              Hence, total rent of the field is Rs. 3250.

              

Ex.6. A invested Rs. 76,000 in a business. After few months, B joined him Rs. 57,000. At the end of the year, the total profit was divided between them in ratio  2 : 1. After bow many months did B join?

Sol. Suppose B joined after x months. Then, B's money was invested for (12 - x)

                     (76000 x 12)/(57000 x (12-x) =2/1 ó 912000=114000(12-x)

                                               

 114 (12 - x) = 912ó12-x=8óx=4

 Hence, B joined after 4 months.

Ex.7. A, Band C enter into a partnership by investing in the ratio of 3 : 2: 4. After 1 year, B invests another Rs. 2,70,000 and C, at the end of 2 years, also invests Rs.2,70,000. At the end of three years, profits are shared in the ratio of 3 : 4 : 5. Find initial investment of each.

Sol. Let the initial investments of A, Band C be Rs. 3x, Rs. 2x and Rs. 4x respectively. Then,

(3x x 36) : [(2x x 12) + (2x + 270000) x 24] : [(4x x 24) + (4x +270000) x 12]=3:4:5

                     

1O8x : (72x + 6480000) : (144x + 3240000) = 3 : 4 : 5

          108x /(72x+6480000)=3/4  ó 432x = 216x + 19440000

                              ó216x = 19440000       

                                       x=90000

                             

Hence, A’s initial investment = 3x = Rs. 2,70,000;

   B's initial investment = 2x = Rs. 1,80,000;

   C's initial investment = 4x = Rs. 3,60,000.

Download Free eBook- Bank PO Examination - Previous year Questions with Explanatory Answers

 

 Dear Bank Exam Aspirants,

Bank Exam Books extends a great help in preparation for the Bank Exams and also helps in securing a good rank position. The details of the book is as mentioned below.

Book Name : Probationary Officer’s Examination
Book Author : V.V.K. Subburaj
Book Content : Previous Years Question Papers with Explanatory Answers.

Don't forget to leave your valuable comments below

PNB Specialist Officers Exam, 2011 : English Solved Paper

Punjab National Bank (Specialist Officers) Exam., 2011
English Language : Solved Paper(Held on 28-8-2011)

Directions–(Q. 1-15) Read the following passage to answer the given questions based on it. Some words / phrases are printed in bold to help you locate them while answering some of the questions.

The advent of technology has fundamentally changed our lives, but one thing is for sure: The velocity of technological change will accelerate in an exponential manner with significant ramifications for all of us. Just imagine: over half of the scientists and engineers who have ever lived are alive today. China adds about 6.5 million graduates every year, half of them engineers and scientists. It is not only the sheer number of "innovators" who will push the boundaries of science, technology and ultimately life-change, but also the greater degree of interconnectivity which accelerates the generation of knowledge and creates a much more entrepreneurial environment for innovation and change.

Read more »

Prathama Gramin Bank Officers Exam, 2011 : English Solved Paper

Prathama Gramin Bank Officers Exam., 2011
(Held on 25-9-2011)
English Language : Solved Paper

Directions–Read the following passage carefully and answer the questions given below them. Certain words/expressions are given in bold to help you locate them while answering some of the questions.

The Battle of Gettysburg was fought during the first three days of July, 1863. During the night of July 4, Lee began to retreat southward while storm clouds' deluged the country with rain. When Lee reached the Potomac river with his defeated army, he found a swollen, impassable river in front of him, and a victorious Union army behind him. Lee was in a trap. He couldn't escape. US President, Abraham Lincoln saw that. Here was a golden, heaven-sent opportunity - the opportunity to capture Lee's army and end the war immediately. So, with a surge of high hope, Lincoln ordered General Meade not to call a council of war but to attack Lee immediately. Lincoln telegraphed his orders and then sent a special messenger to Meade demanding immediate action.

Read more »

Quantitative Aptitude Model Practice paper for Bank Clerk Exam 2012

This set of 100 questions on Quantitative Aptitude. The questions are framed to allow you to judge for yourself how prepared you are for the upcoming Bank Exam in 2012. Take the test now to further enhance your preparation. Don't forget to leave your comments below.

Quantitative Aptitude

Directions (Q. 1-9): What should come in place of question mark (?) in the following questions?

1. -84 x 29 + 365 = ?
   
(1) 2436    
(2) 2801    
(3) 2801
(4) 2071    
(5) None of these

2. (21.69)² - √324 =?
(1) 440.4615    
(2) 425.4561    
(3) 452.4561
(4) 442.4651    
(5) None ofthese

Read more »

General Awareness Model Practice Paper for IBPS Exam 2012

This set of 100 questions on General Awareness. The questions are framed to allow you to judge for yourself that how prepared you are for the upcoming IBPS CWE Exams in 2012. Take the test now to further enhance your preparation. Don't forget to leave your comments below.

General Awareness Practice Set Solved

1. The Govt of India has decided to declare which of the following rivers a National River?
a) Brahmaputra
b) Yamuna
c) Ganga 
d) Kaveri    
e) None of these

2. Who amongst the folIowing economists gave the concept of "economies of scale", which says "many goods and services can be produced more cheaply in long series"?
a) Edward C Prescott
b) Amartya Sen
c) Gary S Becker
d) Edmund S Phelps
e) Paul Krugman

Read more »

Marketing Aptitude & Computer Knowledge for IBPS CWE 2012

This set of 100 questions on Marketing Aptitude and Computer Knowledge. The questions are framed to allow you to judge for yourself how prepared you are for the upcoming IBPS Exam.
Take the test now to further enhance your preparation. Don't Forget to leave your comments below.

Marketing Aptitude and Computer Knowledge

1. FDI stands for _
(a) Foreign Direct Investment
(b) Foreign Diverse Investment
(c) Frequent Direct Interest
(d) Follow-up Discreet Intent

2. The following is not a function of the DGFT
(a) DGFT entrusted with the responsibility of implementing various policies regarding trade for example, Foreign Trade Policy.
(b) DGFT is the licensing authority for exporters, importers, and export and import business.
(c) DGFT can prohibit, restrict and regulate exports and imports
(d) DGFT acts as market regulator controlling foreign company stocks

Read more »

General Aptitude & Reasoning Ability Model Practice Paper for IBPS CWE 2012

This is set of 25 Question on aptitude & reasoning section, Try to solve these questions and finally check the answers. keep visiting us for more model papers for upcoming exams. Don't forget to leave your comments below.

1. The greatest number which divides 245 and 1295 and leaves the remainder of 9 and 7 respectively is

a. 118                    b. 148              c. 135                   d. 145

2. The distance between A’s house and his office is 61 km. For reaching his house from office he covers 54 km 860 m by taxi, 5 km 65 m bytongaand the rest by rickshaw. Hoe much distance did he cover by rickshaw?

a. 1.075 km           b. 10.75 km     c. 0.1075 km                d. 0.0107 km

Read more »

Punjab National Bank Agriculture Officers Solved Professional Knowledge Agriculture Exam Paper 2009

Punjab National Bank conducted an exam in 2009 to shortlist prospective candidates for the position of Agriculture Officers. This question paper was for the Professional Knowledge Agriculture and was given in 2009. 

Professional Knowledge (Agriculture) : Solved Paper

1. This ‘Biofertilizer’ is a nitrogen fixing micro-organism, beneficial for non-leguminous as well as for vegetable crops—
(A) Rhizobium (RHZ)
(B) Azotobacter (AZT)
(C) Azospirillum (AZS)
(D) Blue Green Algae (BGA)
(E) Phosphate Solubilising (PSB) mobilizing bacteria

2. What percentage of total area under Banana cultivation in India presently, is cultivated by using Tissue-cultured (GMO) plantlets ?
(A) 10 per cent
(B) 15 per cent
(C) 20 per cent
(D) 25 per cent
(E) 30 per cent

Read more »

RATIO AND PROPORTION IMPORTANT FACTS AND FORMULAE & EXAMPLES WITH EXPLANATIONS

I. RATIO: The ratio of two quantities a and b in the same units, is the fraction a/b and we write it as a:b.

In the ratio a:b, we call a as the first term or antecedent and b, the second  term or consequent.

Ex. The ratio 5: 9 represents 5/9 with antecedent = 5, consequent = 9.

Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.

Ex.  4: 5 = 8: 10 = 12: 15 etc. Also, 4: 6 = 2: 3.

    2. PROPORTION: The equality of two ratios is called proportion.

If a: b = c: d, we write, a: b:: c : d and we say that a, b, c, d are in proportion . Here a and d are called extremes, while b and c are called mean terms.

 Product of means = Product of extremes.

Thus, a: b:: c : d <=> (b x c) = (a x d).

3. (i) Fourth Proportional: If a : b = c: d, then d is called the fourth proportional

        to a, b, c.

   (ii) Third Proportional: If a: b = b: c, then c is called the third proportional to

        a and b.

   (iii) Mean Proportional: Mean proportional between a and b is square root of ab

4. (i) COMPARISON OF RATIOS:

        We say that (a: b) > (c: d) <=>  (a/b)>(c /d).

    (ii) COMPOUNDED RATIO:

        The compounded ratio of the ratios (a: b), (c: d), (e : f) is (ace: bdf)

5. (i) Duplicate ratio of (a : b) is (a² : b²).

      (ii) Sub-duplicate ratio of (a : b) is (√a : √b).

     (iii)Triplicate ratio of (a : b) is (^a3 : ^b3).

     (iv) Sub-triplicate ratio of (a : b) is (a ⅓ : b ⅓ ).

     (v) If (a/b)=(c/d), then  ((a+b)/(a-b))=((c+d)/(c-d))    (Componendo and dividendo)

6. VARIATION:

(i) We say that x is directly proportional to y, if x = ky  for some constant k and

     we write, x µ y.

(ii) We say that x is inversely proportional to y, if xy = k for some constant k and

       we write, x∞(1/y)

 

SOLVED PROBLEMS

Ex. 1. If a : b = 5 : 9 and b : c = 4: 7, find a : b : c.

Sol.  a:b=5:9 and b:c=4:7= (4X9/4): (7x9/4) = 9:63/4

         a:b:c = 5:9:63/4 =20:36:63.

                    

Ex. 2. Find:

      (i) the fourth proportional to 4, 9, 12;

     (ii) the third proportional to 16 and 36;

    iii) the mean proportional between 0.08 and 0.18.

Sol.

    

i) Let the fourth proportional to 4, 9, 12 be x.

       Then, 4 : 9 : : 12 : x  ó4 x x=9x12 ó X=(9 x 12)/14=27;

   Fourth proportional to 4, 9, 12 is 27.

 (ii) Let the third proportional to 16 and 36 be x.

      Then, 16 : 36 : : 36 : x  ó16 x x = 36 x 36 ó x=(36 x 36)/16 =81

      Third proportional to 16 and 36 is 81.

                            

(iii) Mean proportional between 0.08 and 0.18

      Ö0.08 x 0.18 =Ö8/100 x 18/100= Ö144/(100 x 100)=12/100=0.12

       

Ex. 3. If x : y = 3 : 4, find (4x + 5y) : (5x - 2y).

Sol.  X/Y=3/4 ó (4x+5y)/(5x+2y)= (4( x/y)+5)/(5 (x/y)-2) =(4(3/4)+5)/(5(3/4)-2)

              

              =(3+5)/(7/4)=32/7

Ex. 4. Divide Rs. 672 in the ratio 5 : 3.

Sol. Sum of ratio terms = (5 + 3) = 8.

      First part = Rs. (672 x (5/8)) = Rs. 420; Second part = Rs. (672 x (3/8)) = Rs. 252.

Ex. 5. Divide Rs. 1162 among A, B, C in the ratio 35 : 28 : 20.

Sol. Sum of ratio terms = (35 + 28 + 20) = 83.

       A's share = Rs. (1162 x (35/83))= Rs. 490; B's share = Rs. (1162 x(28/83))= Rs. 392;

       C's share = Rs. (1162 x (20/83))= Rs. 280.

Ex. 6. A bag contains 50 p, 25 P and 10 p coins in the ratio 5: 9: 4, amounting to

         Rs. 206. Find the number of coins of each type.

 Sol. Let the number of 50 p, 25 P and 10 p coins be 5x, 9x and 4x respectively.

      (5x/2)+( 9x/ 4)+(4x/10)=206ó 50x + 45x + 8x = 4120ó1O3x = 4120 óx=40.

                              

      Number of 50 p coins = (5 x 40) = 200; Number of 25 p coins = (9 x 40) = 360;

      Number of 10 p coins = (4 x 40) = 160.

 Ex. 7. A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the     mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture

Sol. Let the quantity of alcohol and water be 4x litres and 3x litres respectively

    4x/(3x+5)=4/5 ó20x=4(3x+5)ó8x=20 óx=2.5

       Quantity of alcohol = (4 x 2.5) litres = 10 litres.

Andhrabank PROBATIONARY OFFICERS RECRUITMENT 2012

Recruitment of Probationary Officers – Special Drive to clear  backlog of OBC vacancies – 2011-12
Andhra Bank invites applications for the post of Probationary Officers from Indian citizens who  belongs to
OBC category and who  have taken the Common Written Examination for Probationary Officers/
Management Trainees conducted by IBPS in 2011-12 and have a valid Score card issued by IBPS.


Opening date for Online Registration 23.01.2012

Last Date for Online Registration
(Including for candidates from far-flung areas ) 14.02.2012

Start date for payment of fees 23.01.2012

Last Date for payment of fees
(including for candidates from far-flung areas ) 14.02.201

Visit Bank site : ANDHRABANK

Notification Details : http://andhrabank.in/UserFiles/File/BACKLOG_OBC_CATEGORY.pdf

PROFIT AND LOSS IMPORTANT FACTS

COST PRICE: THE PRICE AT WHICH ARTICLE IS PURCHASED.ABBREVATED AS C.P
SELLING PRICE: THE PRICE AT WHICH ARTICLE IS SOLD.

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]%

SOLVED PROBLEMS

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

sol. cp=rs27.50, sp=rs 28.50

gain=rs(28.50 –27.50)=rs1.10

so gain%={(1.10/27.50)*100}=4%

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

sol. cp=rs490,sp= 465.50.

loss=rs(490-465.50)=rs 24.50.

loss%=[(24.50/490)*100]%=5%

Ex.3.find S.P when

(i)CP=56.25,gain=20%.

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.

 ex.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.

ex.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 ?

sol.  let the new sp be rsx.then

           (100-loss%) : (1^st  sp)=(100+gain%) (2^nd sp)

ð  {(100-5)/1400}={(100+5)/x}=> x={(105*1140)/95} =1260.

ð   

ex.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%

Ex7 .If the cost price is 96% of sp then whqt is the profit %

                     Sol. 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%

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

Sol:

(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%

Ex10 A vendor bought bananas at 6 for Rs.10 and sold them at Rs.4 for Rs.6 .Find his gain or loss percent .

Sol:

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% 

                    

                                               

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

Sol. 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.

Ex. 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%?

Sol .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.

 Ex. 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.

Sol .Gain% =[                 Error       *100    ]% =  [(40/960)*100] % = 4 1 %                      

                          (error value)-(error)                                                              6

 Ex 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?

Sol:

  Let the cost of production of the table be Rs x

 The ,125% of 115% of 110% of x=1265

ð  125/100*115/100*110/100*x=1265=>253/160*x=>1265=>x=(1265*160/253)=Rs.800

Ex16 . Monika purchesed a pressure cooker at 9/10^th of its selling price and sold it at 8% more than its S.P .find her gain percent.

 

Sol:

      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%

Ex .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 ?

sol:

     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%

Ex .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?

Sol:

    Let C.P be Rs x. then (105% of x)-(80 % of x)=100 or 25% of x=100

ð  x/4=100 or x=400

ð  so,C.P =Rs 400

Ex 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.

  Sol:

      Let the C.P be Rs x

      1^st S.P=125% of x =125x/100=5x/4;2^nd S.P=80% of x=80x/100=4x/5

      2^nd 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

Ex 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.

   Sol:

        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

ð  ((100+X)/100*125/100*120/100*P)=(165/100*P)

ð  (100+X)=(165*100*100)/(125*120)=110=>X=10%

Ex21 . A man 2 flats for Rs 675958 each.on one he gains 16% while on the other he losses 16%. How much does he gain/loss in the whole transaction?

 Sol:

     In this case there will be alwalys loss. The selling price is immaterial

  Hence, loss % = (common loss and gain%)² /10=(16/10)%=(64/25)%=2.56%

Ex.22. A dealer sold three-fourth of his article at a gain of 20% and remaining at a cost price. Find the gain earned by him at the two transcation.

 Sol:

     Let the C.P of the whole be Rs x

 C.P of 3/4^th =Rs 3x/4,C.P of 1/4^th =Rs x/4

ð  total S.P=Rs [(120%of 3x/4)+x/4]=Rs(9x/10+x/4)=Rs 23x/20

ð  gain=Rs(23x/20-x)=Rs 3x/20

ð  gain%=3x/20*1/x*100)%=15%

Ex 23 ..A man bought a horse and a car riage for Rs 3000.he sold the horse at a gain of 20% and the carriage at a loss of 10%,thereby gaining 2% on the whole.find the cost of the horse.

Sol:

    Let the C.p of the horse be Rs.x, then C.P of the carriage =Rs(3000-x)

20% of x-10% of(3000-x)=2% of 3000

ð  x/5-(3000-x)/10=60=.2x-3000+x=600=.3x+3600=>x=1200

ð  hence,C.P of the horse =Rs 1200

Ex 24  find the single discount equivalent to a series discount of 20% ,10% and 5%’

sol:

     let the marked price be Rs 100

then ,net S.P=95% of 90% of 80% of Rs 100

                      =Rs(95/100*90/100*80/100*100)=Rs68.40

Ex .25 After getting 2 successive discounts, a shirt with a list price of Rs 150 is available at Rs 105. If the second discount is 12.55,find the first discount.

Sol:

   Let the first discount be x%

  Then,87.5% of (100-x)% of 150= 105

ð  87.5/100*(100-x)/100*450=150=>105=>100-x=(105*100*100)/(150*87.5)=80

ð  x=(100-80)=20

ð  first discount = 20%

Ex .26 An uneducated retailar marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the marked price.what is the actual profit on the sales?

Sol:

    Let C.P =Rs 100.then ,marked price =Rs100

S.P=75% of Rs 150=Rs112.50

Hence,gain%=12.50%

Ex27 .A retailer buys 40 pens at the market price of 36 pens from a wholesaler ,if he sells these pens giving a discount of 1% ,what is the profit % ?

 sol:

      let the market price of each pen be Rs 1

 then,C.P of 40 pens = Rs 36 S.P of 40 pens =99% of Rs 40=Rs 39.60

profit %=((3.60*100)/36) %=10%

Ex 28 . At what % above C.P must an article be marked so as to gain 33% after allowing a customer a discount of 5%?

Sol

      Let C.P be Rs 100.then S.P be Rs 133

Let the market price be Rs x

 Then 90% of x=133=>95x/100=133=>x=(133*100/95)=140

Market price = 40% above C.P

Ex .29 . When a producer allows 36% commission on retail price of his product, he earns a profit of 8.8%. what would be his profit % if the commision is reduced by 24%?

 Sol:

    Let the retail price =Rs 100.then, commission=Rs 36

S.P=Rs(100-36)=Rs 64

But, profit=8.8%

C.P=Rs(100/108.8*64)=Rs 1000/17

New commission =Rs12. New S.P=Rs(100-12)Rs 88

Gain=Rs(88-1000/17)=Rs 496/17

Gain%=(496/17*17/1000*100)%=49.6%