(Test Bank) Bba Commerce Accountancy Mathematics

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UNIT I 1 COMMISSION, BROKERAGE , DISCOUNT AND PARTNERSHIP OBJECTIVES Money pla ys an important role in any transaction. We are g oing to study some Technical ter ms involved in business transaction s. 1.1 COMMISSION A producer or manufacturer of good s generally does not sell his goods directly to the ultimate consumer. There are agents who purchase the goods from the manufacturer and sell them to the consumer. In a sense, such agents bring the manufacturers and the consumers together f or transaction. The remuneration which an agent gets for his services in the transaction is called commission. Most of the business transactions are made through intermediate persons. 1.2 RATE OF COMMISSION The amount of commission that an agent gets in the transact ion depends on the volume of work done or the services rendered by him. His commission is based on the value of the goods bought or sold and is generally fixed on a percentage basis. In some cases, he is paid a commission on the total sales brought by the agent or on different slabs. For example, it may be 5% on the first Rs. 10,000/ -, 6% on the next Rs. 5,000/ - and so on. 1.3 TYPES OF COMMISSION AGENTS On account of the different fields of specialization in business activities agents can be differenti ated as such as commission agents, brokers, del credere agents, factors, insurance agents, export agents, auctioneers, etc. Agents particularly salesmen are also paid regular salary in addition to commission they earn. Commission Agent : A commission agent is that middle -man who buys or sells goods on behalf of some other person called a s principal. He is usually employed by his principal and gets commission as some percentage of the sale value. Broker : A b roker is that middle -man who brings together a p rospective seller and a prospective buyer and negotiates the sale between them . The Maths_stats_fybcom 2 commission that he gets is called brokerage, which may be charged from both the parties. Accordingly, there are stock -brokers, producer, brokers, bullion -brokers, bill -brokers, insurance -brokers depending upon the field of business in which they work. Factor : A factor is an agent who takes possession of the goods and then sells them in his own name. A factor does the transaction without disclosing the name or identity of hi s principal. He receives payment in his own name and passes receipt for the same. Del Credere Agent : A del credere agent sells goods and at the same time gives a guarantee of the collection of dues from the consumers. In return for this guarantee, he get s an additional commission known as del creders. This commission may be at a flat rate on all the sales or at a higher rate on credit sale s only. Auctioneer : A person who wants to sell his goods or property or machinery approache s such an agent. The agent then gives an advertisement in which he give s some description of the goods and the date of sale . The agent s ells goods to the highest bidder, i.e. the person who o ffers to pay the highest amount in the auction . Such an agent is called an auctioneer. Ge nerally, the auctioneer does not disclose the name of the principal. Solved Examples: Example 1 An agent sold Rs. 3,000 worth of articles on 4½ % commission basis. Find the commission of the agent. Solution : The agent sold Rs. 3,000 worth of articles on 4½ % commission basis Agent‘s commission = 4½ of Rs. 3,000 = Rs 29 × 1001 ×3000 = Rs. 135 Example 2 An agent was paid Rs. 1596 as commission at rate 12% on the sale of bicycles. The selling price of each bicycle was Rs. 950. Find the number of bicycles sold by the agents. Solution : Let be the number of bicycle sold by the agent. Price of one bicycle = Rs. 950 Selling price of Bicycle s = 950 x Maths_stats_fybcom 3 @12% commission on 950 x = 10012 × 950 x =114 x Agent‘s commission = 1596 114 x = 1596 x = 1141596 = 14 Number of Bicycle s sold = 14 Example 3 An insurance agent gets commission of 20% on first year p remium, 6% on second and third year ‘s premium and 4% on subsequent years premium on an insurance policy of R s. 40,000 . Annual rate of premium being Rs. 30 per thousand. Find the total earning of the agent for which 5 annual premiums have been paid. Solu tion: The rate of annual premium is Rs. 30 per thousand. Annual premium = 1200 40000100030 Commission for first year = 240 120010020 Commission for second and third year = 2 144 72 72 12001006 = 2 (72) = 144 Commission for fo urth and fifth year = 2 96 48 48 12001004 2 (48) = 96 Total Earnings = 240 + 144 + 96 = 480 = Rs. 480 Example 4 At 7% rate of commission, a sales girl, got Rs. 210 on the sale of combs . Find the value of the sale if the price of each com b is Rs. 15 per container. Find the number of containers sold by the sales girl. Solution : Since the rate of commission is 7% and she received Rs. 210, total value of her sales = Rs. = Rs. 210 x 7 100 = Rs. 3,000. The price of each container is Rs. 15. Total number of containers sold = 153000 = 200 Maths_stats_fybcom 4 Example 5 Find the commission on total sales worth Rs. 25,000, if the rate of commission is 3% on first Rs. 10,000 a nd 4½ on sales over Rs. 10,000. Solution : Total sales are worth Rs. 25,000. Commission at 3% on first Rs. 10000 = Rs. 10,000 × 3 = Rs. 300 Commission at 4½ % on sales over Rs. 10,000 = Commission at rate 4½% on Rs.15000(25000 -10000). = Rs. 29 × 1001 × 15,000 = Rs. 675 Total commission = Rs. (300 + 675) = Rs .975 Example 6 A salesman is allowed 5% commission on the total sales mad e by him plus a bonus of 1% on the excess of his sale over Rs. 20,000/ -. If the total earning are Rs. 1, 450/- on commission alone, find his total earning s? Solution : Let the total sales be Rs. x. Then commission at 5% on Rs. x = 1005x = 20x . This is given to be Rs. 1 450/- 20x =1450 x = 1450 × 20 x = 29,000 the amount of total sales is = Rs. 2 9,000/ - excess of sales over Rs. 20,000 = Rs. (2 9,000-20,000) = Rs. 9,000/ - Bonus at 1% on Rs. 9,000 = Rs. 1001 ×9000 = Rs. 90/- Example 7 A piece of land was sold for Rs. 19,00,000 through a broker who received 1.25% commission from the seller and 1.75% from the buyer. Find the amount paid by the buyer. Also find the amounts receiv ed by the seller and the broker. Solution : Brokerage paid by the buyer at 1.75% =1.75% of Rs. 19,00,000 = Rs. 10075.1 × 19,00,000 = Rs. 33,250/ - Total amount paid by the buyer = Cost of the land + Brokerage = Rs. 19,00,000 + 33,250 = Rs. 19,33,250/ - Brokerage paid by the seller at 1.25% 1.25% of Rs. 19,00,000= Rs. 10025.1 × 19,00,000 = Rs. 23,750/ - Total amount received by the seller = Cost of the land - Brokerage = 19,00,000 - 23,750 Maths_stats_fybcom 5 = Rs. 18,76,250/ - Total amount received by the broker = Brokerage from the buyer + Brokerage from the seller = Rs. (33,250 + 23,750) = Rs. 57,000/ - Example 8 A merchant instructs his agen t to buy 1,000 micro tip pens and sell them at 15% above the purchase price. The agent charges 1% commission on the purchase and 3% commission on sales and earns Rs. 534/ - as commission. Find the price at which the agent buys the pen. Solution : Suppose t he agent buys each pen for Rs. x. Then cost price of 1000 pens = Rs. 1000 x selling price of 1000 pens at 15% profit. =Rs. 100115 × 1000 x = Rs. 1150 x commission at 1% on the purchase. =1% of Rs. 1000 x = Rs. 1001 ×1000 x = Rs. 10 x (i) commission at 3% on the sales. =3% of Rs. 1150 x = Rs. 1003 ×1150 x = Rs. 269 x (ii) From (i) & (ii) Total commission of the agent =Rs. 10 x + 269 x = 289 x This is given to be Rs. 534/ - 289 x = 534 x = 892 532 =12 The agent buys each pen for R s. 12/- Example 9 A del credere agent charges 3% commission on cash sales and 6% commission on credit sales. If his average commission is 4.3% , find the ratio of cash sales to credit sales. Maths_stats_fybcom 6 Solution : Suppose the cash sales are Rs. x and the credit sales are Rs. y. Then commission at 3% on cash sales of Rs. x is = Rs. 1003x and Commission at 6% on credit sales of Rs. y is = Rs. 1006y Total commission of the agent = Rs. 1006 3 y x (i) Average comm ission at 4.3% on total sales of Rs. ( x + y) = Rs. 100) (3.4 yx = Rs. 1000) (43 yx (ii) From (i) & (ii) 1006 3 100043 43 y x y x After simplification, 43 x – 30 x = 60y – 43y 13 x = 17y 1317 yx The ratio of cash sales to credit sales is 17:13 Example1 0 A salesman is appointed on a fixed monthly salary of Rs. 1,500/ - together with a commission at 5% on the sales over Rs. 10,000/ - during a month. If his monthly income is Rs. 2,050/ -, find his sales during that month. Solution : Commission at 5% o n the sales over Rs. 10,000/ - = month ly income - monthly salary =Rs. 2050 -1500 = Rs. 550/ - the sales over Rs. 10,000/ - = Rs. 550 × 5100 = Rs. 11,000/ - total sales during the month = Rs. (10, 000 + 11,000) = Rs. 21,000/ - Example 11 A salesman is paid a monthly salary plus a commission based as a percentage on sale. If on the sales of Rs. 20,000/ - and R s.25,000/ - in two successive months he received Rs. 1600/ - and Rs. 1750/ - respectively, find his monthly salary and the rate of commission paid on sales. Solution : Let the monthly salary of the salesman be Rs. x and y % be the rate of commission. Maths_stats_fybcom 7 commission in first month at y % on Rs. 20,000/ - =Rs. 100y × 20000 = Rs. 2 00y For the first month total earnings =salary + commission in the first month 1600 = Rs. ( x + 200 y) ……. (1) Also commission in the second month at y % on Rs. 25,000/ - = Rs. 100y ×25000 = Rs. 250 y For the second month total earn ings =salary + commission in the second month 1,750 = Rs. ( x + 250 y) ..…. (2) Subtracting (1) from (2), we get, 50y = 150 y=3 Substituting this value of y in (1), we get, x + 200 × 3 = 1600 x = 1000 The monthly salary of the salesman is Rs. 1000/ - and the rate of commission is 3% . Example 12 At what price should goods costing Rs. 1 8,000 be sold through an agent so that after paying her a commission at 4% on sales, a net profit of 20% on cost can be made? Solution: Let the selling price be Rs. x. After deducting 4% commission, the net receipt =96% of x = x10096 Now, profit at 20% of Rs. 1 8,000/ - = 10020 18,000 = Rs. 3, 600/- Net receipt = Cost + P rofit = Rs. (1 8,000 + 3,600) = Rs. 21,600/- Thus x10096 = 21,600 x = 1009621600 = Rs. 22,500/- Hence, the goods shou ld be sold for Rs. 22,500/ - Example 13 A salesman gets 4% commission on the first Rs. 2 0,000, 7% on the next Rs. 20,000 and 12% on the excess. He also receives an incentive at the Maths_stats_fybcom 8 rate of 3% on total sales, if it exceeds Rs. 50,000. Find the total earning of two salesmen with total sales worth of Rs. 44,000 and Rs. 58,000. Solution : (i) For the first salesman Sales is Rs. 44,000 = 20,000 + 20,000 + 4,000 So, commission = 4% of 20,000 + 7% of 20,000 + 12% of 4,000 = 800 + 14 00 + 480 = Rs. 2680 As his sales of Rs. 44,000 is less than Rs. 50,000, he will not get any incentive amount. So, total earning of the first salesman = Rs. 2680 (ii) For the second salesman Sales is Rs. 58,000 = 20,000 + 20,000 + 18,000 So, commission = 4% of Rs. 20,000 + 7% of Rs. 20,000 + 12% of Rs. 18,000 = 800 + 1,4 00 + 2,160 = 4360 His sales is Rs. 58,000, which exceeds Rs. 50,000 So, incentive amount = 3% of 58,000 = 1,740 So, total earnings of second salesman = commission + incentive = 4360 + 1740 = 6,100 Example 14 A merchant gained a net gain of 18.75% on his cost of Rs. 20,000 after giving the agent a co mmission at 5% on the sale price. Find the sale price. Solution: Let x be the sale price Commission = 5% on sale = x x 05.01005 Gross Profit = Sale Price – Cost Price = x – 20,000 Net Profit = Gross Profit – Commission = (x – 20,000) – 0.05x = 0.95 x – 20,000 But Net Profit = 18.75% on Cost Price = 000,2010075.18 = 3,750 0.95x – 20,000 = 3,750 0.95x = 23,750 x = 000,2595.0750,23 The sale price is Rs. 20,000 Maths_stats_fybcom 9 Example 1 5 A merchant employed an agent to buy and sell some article. The agent charged 3% on the purchase value and 2% on the sale value as commission. The purchased value was Rs. 40,000. The merchant after deducting the commission still receive d a net profit of 19.5% on cost. Find the sale price. Solution: Let x be the sale price. Commission on purchase = 3% on purchased price = 000,401003 = 1,200 Commission on sale s = 2% on sale price = 0.02 x Total Com mission = Commission on purchase + Commission on Sale = x1002200,1 Net Profit = 19.5% on Purchased Price = 19.5% on 40,000 = Rs. 7,800 But Net Profit = Sale Price – Purch ase Price – Total Commission 7,800 = x – 40,000 – (1,200 + 0.02 x) 7,800 = x – 40,000 – (1,200 – 0.02 x) 7,800 = x – 0.98x – 41,200 49,000 = 0.98 x 98.049000 = x 50,0000 = x The sale price was Rs. 50,000 Example 1 6 At what price should goods costing Rs.16,000 be sold through an agent so that after paying her a commission at 4% on sales, a net profit of 20% on cost can be made? Solution: Let gross Receipts be Rs. x After deducting 4% commission, the net receipt = 96% of x x10096 Now, profit at 20% of Rs. 16,000 = 000,1610020 Rs. 3,200 Net receipt = Cost + Profit = Rs. (16,000 + 3,200) = Rs. 19,200 Maths_stats_fybcom 10 Thus 200,1910096 x x = 19,200 96100 Rs. 20,000 Hence, the goods should be sold for Rs. 20,000 Check your progress 1) An agent earns 6 32 % commission on his total sales which are of Rs. 11,520 . Find the amount of his commission. Ans. Rs. 768 2) An insurance agent gets commission of 25% on first year premium, 7% on second and third years premium and 5% on subsequent years prem ium on an insurance policy of Rs . 30,000, annual rate of premium being Rs. 40 per thousand. Find the total earning of the agent for which 5 annual premiums have been paid. Ans. Rs.588 3) An insurance agency pays 20% of annual premium as commission to its agent in the first years, 9% in the secon d and the third year and 7.5% in each subsequent year. A customer insured her car for Rs. 90,000 through an agent and her annul premium was fixed at Rs. 5,600. Find the agent‘ total commission amount if the customer has paid annul premium for six year up to now. Ans. Rs. 3,388 4) An insurance company pays its agent a commission at 20% on the first year‘s premium amount. The rate of commission reduces to 6% for the subsequent years. A customer purchased a policy premium at 5% of the policy amount. Find the agent‘s total earning for the premium for the period of seven years. Ans. Rs. 3,200 5) A merchant pays 10% commission on total sales and pays del credere at a rate of 3% on credit sales. If cash sales were Rs. 4,500 and credit sales were Rs . 7,000 find the total commission earned by the agent. Ans. 1,360 6) A merchant instructs his agent to buy 500 Raincoats and to sell them 20% above the purchase price. The agent charges 1% commission on purchase and 2% commission on the sales and earns Rs . 1,360. Find the price at which the agent buys a Raincoat . Ans. 80 7) An agent was instructed to sell 5000 cotto n shirts on 2% commission and invest the balance after dedcuting commission in purchasing kurtas. The commission paid on purchase is 34 % If the agent earns together Rs. 3550.50 in two transaction s, find the price at which a shir t was sold Ans. Rs. 26 Maths_stats_fybcom 11 8) A del credere agent charges 3% on cash sales and 6% on credit sales. If the agent earns at an average rate of 4.7% on total sales, find the ratio of cash sales to the credit sales. Ans. 13 : 17 9) A salesman is paid a fixed monthly salary plus commission at a certain rate on sales. The salesman received Rs. 1,130 and Rs. 1,360 as remuneration for two successive months and his sales were Rs. 17,100 and 21,700 respective ly. Find the fixed monthly salary and the rate of commission. Ans. 275; 5% 10) A del credere agent charges 4% commission on cash sales and 7% commission on credit sales. If the ag ent earns at an over all rate of 5.4% of total sales, find the ratio of cash sales to credit sales. Ans. 8 : 7 11) A salesman is paid fixed monthly salary together with commission at a certain rate on his total sales during the month. The salesman receive d Rs. 1,256 and Rs. 1,372 as remuneration for two successive months during which his total sales were Rs. 21,400 and Rs. 24,300 respectively. Find the fixed monthly salary and the rate of commission. Ans. Rs. 400 and 4% 12) An agent was paid Rs. 21,708 as commission at a rate 9% on the sale of Refrigerators . The selling price of each Refrigerator was 13,400. Find the number of Refrigerators sold by agent. Ans. 18 Refrigerators 13) A piece of land was sold for Rs. 19,00,000 through a broker who received 1¼ % commission from the seller and 1¾ % commission from the buyer. Find the amount paid the buyer. Find also the amount received by the seller and the broker Ans. 19,33,250, Rs. 18,76,250, Rs. 57,000 14) A merchant instructs his agent to buy 600 pieces of an article and sell at 25% above the purchase price. The agent charges ½ % commission on the purchase and 3% commission on the sale and earns Rs. 1,020. Find the price at which the agent buy s an article. Ans. Rs. 40 15) A del credere agent charges 4% on cash sales and 7% on credit sales. If the consolidated rate at which the agent earns is 5% of total sales find the ratio of cash sales to the credit sales. Ans. 2 : 1 16) A salesman is paid a fixed monthly salary together with commission at a certain rate on the sales. The salesman received Rs. 1,240 and Rs. 1,184 as remuneration for two successive months in which his total sales were Rs. 18,500 and Rs. 17,100 respectively. Find the rate of commission and the fixed monthly salary. Ans. 4% Rs. 500 Maths_stats_fybcom 12 17) A company fixed the rate of commis sion to its salesman as follows : 4% on the first Rs. 5,000, 5% on the next Rs. 8,000, 7% on the next Rs. 10,000 and 11% on the balance. Company has agreed to pay ¼ % of the total sales as bonus if the sales crossed Rs. 30,000. A salesman of the company secured sales worth Rs. 29,000. Calculate total earning of the salesman. Ans. Rs. 1,960 18) A merchant asked his agent to sell 250 hats at 2% commission and to invest the balance in purchas ing ties. The agent charged 1 21 % commissions on both the trans actions. Find the price for which a hat was sold. Ans. Rs. 60 19) A merchant asked his agent to sell 200 caps at Rs. 15 per cap and to purchase 400 towels at Rs . 10 per towel. The agent charged 2%on the sales and 1% on the purchase. How much extra money did the merchant have to pay to the agent? Ans. Rs. 1,110 20) A merchant asked his agent to sell 40 music records at Rs. 25 each and use the money to buy s ome toys at Rs. 10 each. The agent quoted 15% commission on the sale and 6.25% on the purchase. The merchant instructed the agent to adjust the number of toys such that the merchant would not need to give him any extra money. How many toys would the agent buy? Ans. 800 21) The income of a salesman remains unchanged through the rate of commission is increased from 4% to 5%. Find the percentage reduction in his sales. Ans. 20% 22) At what price should goods costing Rs.48,250 be sold through an agent so that after paying him a commission at 3 21 %, a net gain of 20% on the cost may be made? Ans. Rs. 60,000 1.5 DISCOUNT During a festival season you must have seen advertisement banner s displa yed in front of each shops offering discount on the purchase s made by the customer. Such advertisements are published in the newspaper s also. Each shop owner proclaims to sell his goods at 20%, 15%, 30% discount etc. Discount means reduction in price or less than marked price. Marked price /printed price/ Catalogue price/List price is the price quoted on the article for sale. Maths_stats_fybcom 13 Trade Discount is allowed on the list price (L.P) List Price - Trade Discount = Invoice Price Invoice Price - Cash Discount = Net s elling price Net selling price – Profit = cost Example 17 Sachin buys a kurta in a Khadi Bhandar marked at Rs. 400. If a discount of 18% is allowed, find the discount. Solution: Marked price = List price (L.P.) = Rs. 400 Rate of Discount = 18% on L. P. Discount = 18% on L.P. Discount = 18% on 400 = 40010018 = Rs.72 Example 18 Priya purchased a table whose marked price is Rs.7,000. The dealer allowed 6% discount on it. Find (i) discount on Rs.7,000 (ii) amount paid by Priya for the table. Solution: (i) Discount = 6% on L.P. = 6% on Rs. 7000 = 70001006 = Rs. 420 (ii) Amount paid by Priya for the table (or) S.P. = L.P. – Discount = 7,000 – 420 = Rs. 6,580 Example 19 A furniture maker sells a wooden tab le listed Rs.2,500 for Rs.2,200. Find the rate of discount. Solution: Listed price = Rs. 2,500 S.P = Rs.2,200 Discount = L.P. – S.P. = 2,500 – 2,200 = Rs. 300 Rate of discount = ..100 PLDiscount = 500,2100 300 = 12% Maths_stats_fybcom 14 1.6 T RADE DISCOUNT and CASH DISCOUNT When a manufacture or a trade offers a discount to another trader, the discount offered is usually termed as the trade discount. For example, when a wholesaler sells goods in bulk to a r etailer, he / she gives a trade discount. It is also sometimes called as the bulk discount. We shall refers to this as the trade discount and write it as T.D. The rate of Trade Discount is express ed as percentage of the list price. After deducting the trade discount, the remaining amount is what is put down in the invoice or the bill. Hence this is referred to as the invoice price or the reduced list price or the amount of the bill. We will refer to it as the invoice price and denote it as I .P. Thus I.P. = L.P. – T.D. Amount. Even after giving the above trade discount, the seller may offer an extra discount to those buyers who pay immediately by cash and do not ask for credit. This discount is called cash discount and we will denote it as C.D. The rate of cash discount is express ed as a percentage of the invoice price. Note that the rate of cash discount is not express ed as a percentage of the list price. After deducting the cash discount from the invoice price, we get t he Net Selling Price (N.S .P) = I.P. - C.D. This can be remembered in the following way: L.P. One discount is given Two discounts given T.D, C.D. L.P. = Rs ( ) L.P. = Rs. ( ) Discount = ( ) % on L.P. T.D. = ( ) % L.P. SP = L.P. – discount I.P. = L.P. – T.D. C.D. = ( ) % ON L.P. S.P. = I.P. – C.D. Example 20 A firm allows 20% discount on list price and a further 5% discount for cash payment. What is the net selling price of an article which is marked at Rs. 240 Solution : Give n TD% = 20, CD% = 5 and L.P. = Rs. 240. I.P. = L.P. – Trade Discount Amount = L.P. – 20% of L.P. Maths_stats_fybcom 15 = 240 – 20% of 240 = 24010020240 = 240 – 48 I.P = Rs. 192. N.S.P = I.P. – Cash Discount Amount = I.P. – 5% of I.P = 192 – 5% of 192 = 1921005192 = 192 – 9.60 N.S.P = Rs 182.40 Hence the net selling price is Rs. 182.40. Example 21 A firm allows 25% of trade discount and a further discount for cash payment at 10% rate. Find the list price of an article w ith a net selling price of Rs.270. Solution: Given that T.D. % = 25, CD% = 10 and N.S.P. = Rs 270. N.S.P. = I.P. – Cash Discount Amount 270 = I.P. – 10% of I.P = 90% of I.P. = ..10090PI 27090100 = I.P. Rs. 300 = I.P. Now, I.P. = L.P. – Trade Discount Amount 300 = L.P. – 25% of L.P. = 75% of L.P. = ..10075PL 30075100 = L.P. Rs. 400 = L.P. Hence the list price is Rs. 400. Example 22 An articl e was listed at Rs. 5,000. It was sold by the shop owner at a 30% discount and thus a profit of 75% on cost was earned. Find the cost price of the shop owner. Solution: Given that Discount% = 30, Profit% = 75 and L.P. = Rs. 5000 N.S.P. = L.P. – Discoun t Amount = L.P. – 30% of L.P = 70% of L.P. = .000,510070 = Rs. 3,500. Now, N.S.P = C.P. + Profit