Chapter 1 Commission, Brokerage and Discount Miscellaneous Exercise 1 Solutions

(b) Del Credere Agent

(a) Factor

(c) Nominal Due Date

(a) The legal due date

(a) Face value

(b) Present worth

(d) True discount

(c) List price

(b) Invoice price = Net selling price

(b) True discount

Drawee

Auctioneer

Catalogue/List

Commercial Discount

higher

bankers gain

legal due date

broker

Trade, Catalogue/List

Invoice Price

False

False

True

False

True

False

False

True

False

True

Rate of commission = 6.5% on the total sales ∴ Commission on a turnover of ₹ 75,000 = × 75,000 = ₹ 4,875 Rate of bonus = 1% on sales over ₹ 50,000 ∴ Amount of bonus = × (75,000 – 50,000) = ₹ 250 ∴ Total income of the sales man = ₹ 4,875 + ₹ 250 = ₹ 5,125

Rate of brokerage = % Amount of brokerage = ₹ 73,125 Let the selling price of the shop be ₹ 100 then the brokerage = ₹ Thus, if the amount of brokerage is ₹ then the selling price of the shop is ₹ 100 If the amount of brokerage is ₹ 73,125, then the selling price of the shop is = 73125 × × 100 = ₹ 97,50,000 The shop is sold at 30% profit ∴ If the cost of the shop is ₹ 100, then it is sold at ₹ 130 Thus, if the shop is sold at ₹ 130, then its cost price is ₹ 100 If the shop is sold at ₹ 97,50,000 then its cost price is = = ₹ 75,00,000 Then, the cost of the shop is ₹ 75,00,000

Rate of commission = 5% Total sales = ₹ 30,600 Amount of commission = × 30,600 Rate of delcredere = 1.5% = × 30,600 = ₹ 459 Thus, the agents gets 1,530 + 459 = ₹ 1,989 And the merchant receives = 30,600 – 1,989 = ₹ 28,611

Rate of commission = 7% on first ₹ 50,000 = × 50,000 = ₹ 3,750 Let the total sales be ₹ x Rate of commission on the balance sales = 5% Commission on the balance sales = × (x – 50000) = – 2,500 Total commission = 3750 + – 2,500 = + 1,250 Now, the amount to be remitted to the principal = Value of goods sold – Commission of the agent = x – ( + 1250) = – 1250 The agents remits ₹ 93,750 to his principal ∴ – 1,250 = 93,750 ∴ = 95,000 ∴ x = ₹ 1,00,000 Thus, the value of the goods sold by the agent is ₹ 1,00,000

Given, PW = ₹ 11,000, SD = ₹ 11,660 n = year = year We have, ∴ The rate of interest is 8% p.a.

Marked price of the article = ₹ 800 Rate of discount = 2.5% Amount of discount = × 800 = ₹ 20 ∴ Selling price of the article = 800 – 20 = ₹ 780 Now, given, gain = 20% Let cost price of the article be ₹ 100, then The selling price of the article is ₹ 120 Thus if cost price of the articles is ₹ x Then the selling price is ₹ 780 ∴ x = ∴ x = 650 ∴ Cost price of the article is ₹ 650

Let the monthly salary of the salesman be ₹ x And the rate of commission be y% Income = monthly salary + commission on the sales 17600 = x + × 96,000 ∴ 17600 = x + 960y ………(1) and 18800 = x + × 108000 ∴ 18,800 = x + 1080y ………(2) Subtracting equation (1) from equation (2), we get 1,200 = 120y ∴ y = 10 Substituting y = 10 in (1), we get 17,600 = x + 960(10) ∴ x = 17,600 – 9,600 = 8,000 ∴ Salary of the salesman = ₹ 8,000 Rate of commission = 10%

Catalogue price of a mixer = ₹ 5,500 Trade discount = 15% on catalogue price = × 5,500 = ₹ 825 Freight charges = 2% of the catalogue price = = ₹ 137.5 ∴ Cost price of a mixer for the merchant = 5,500 – 825 + 137.5 = 4,812,5 Catalogue price = ₹ 5,500 Rate of discount = 5% ∴ Selling price of one mixer = 5500 – × 5,500 = ₹ 5,225 ∴ Profit on one mixer = 5,225 – 4,812.5 = ₹ 412.5 Now, total profit = ₹ 41,250 ∴ Number of mixers = = 100 Thus the number of mixers is 100.

Face value of the bill = ₹ 7,000 Date of drawing = 3rd May Period = 3 months Normal due date = 3rd August Legal due date = 6th August Rate of interest = 5.5% Date of discounting = 25th May Unexpired period (number of days from date of discounting to legal due date) ∴ Bankers discount = 7,000 × = ₹ 77 Also PW = SD – BD = 7,000 – 77 = ₹ 6,923 ∴ Present worth is ₹ 6,923

Face value of the bill = ₹ 3,500 Date of drawing = 14/04/2005 Date of discount = 06/07/2005 Rate of interest = 5% Cash value = ₹ 3,465 Bankers discount = Face value – Cash value = 3,500 – 3,465 = ₹ 35 Let the unexpired days be n days ∴ BD = ∴ 35 = ∴ n = 73 days Thus, legal due date is 73 days from the date of discounting ∴ Legal due date = 17/09/2005 ∴ Nominal due date = 14/09/2005 ∴ The period of the bill is 5 months

BG = BD – TD ∴ BG = ₹ 80 Also BG = ∴ 80 = ∴ TD = ∴ TD = ₹ 4,000 Now BD = TD + BG = 4,000 + 80 = ₹ 4,080 Also, BD = ∴ 4,080 = ∴ FV = ∴ FV = ₹ 2,04,000 Amount of the bill = ₹ 2,04,000

Rate of discount = 35% Let the list price be ₹ 100. Then discount at 35% = ₹ 35 ∴ Net selling price = 100 – 35 = ₹ 65 ……..(1) The manufacturer makes a clear profit of 30% on the cost after allowing a 35% Discount. Let the cost be ₹ 100. Then selling price at 30% profit is 100 + 30 = ₹ 130. Thus, if the net selling price is ₹ 130, then the cost price is ₹ 100. But, the net selling price is ₹ 130, then the cost price is ₹ 65 ……[from (1)] ∴ The cost price is = ₹ 50 Hence, we have, Now, the cost of production has increased by 20%. Let the old cost price be ₹ 100. ∴ The new cost price is ₹ 120. But, the old cost price is ₹ 50. ∴ The new cost price is = = ₹ 60. The old net price is ₹ 65. Now 20% of ₹ 65 = = ₹ 13 ∴ New net price = 65 + 13 = ₹ 78 Hence, we have Now, 100 – 78 = ₹ 22 Thus, the rate of discount should be reduced by 22%, The original rate of discount is 35%. Hence, the reduction in discount should be (35 – 22)% = 13% so as to make the same rate of profit, keeping the list price unaltered.

Rate of discount = 25% on the catalogue price of a radio. Let the catalogue price of the radio be ₹ 100. Then, the discount on a radio = ₹ 25. Net selling price = 100 – 25 = ₹ 75. He makes a profit of 20%. Let the cost price be ₹ 100. Then, at 20% profit, net selling price = ₹ 120. Thus, if net SP is ₹ 120, then cost price is ₹ 100. But, the net SP is ₹ 75. ∴ The cost price is × 100 = = ₹ 62.50 ∴ Profit on a radio set = 75 – 62.5 = ₹ 12.50 Thus, if the profit on a radio set is ₹ 12.50 then its catalogue price is ₹ 100. But the profit on a radio set is ₹ 160. ∴ The catalogue price of radio = × 100 = 12.80 × 100 = ₹ 1,280 ∴ Thus, the catalogue price of the radio is ₹ 1280

Face value of the bill = ₹ 4.800 Date of drawing = 09/03/2006 Period of the bill = 6 months Normal due date = 09/09/2006 Legal due date = 12/09/2006 Rate of discount = 6% = 6.25% Now, for the unexpired Thus the banker charges ₹ 120 Amount received by the holder = 4,800 – 120 = ₹ 4,680

BD = FV – Cash value = 65,700 – 65,160 = ₹ 540 Let the unexpired days be x days BD = ∴ 540 = ∴ x = 60 days The unexpired days = 60 days Date-of drawing = 10th July Period of the bill = 6 months Nominal due date = 10th January (next year) Legal due date = 13th January (next year) Then the date of discount is 60 days before, the legal due date ∴ The date of discounting is 14th November

Let the sale value of the car be ₹ x Rate of commission of the agent = 3% Since the owner received ₹ 48,500 after agent has charged his commission x – = 48500 ∴ = 48500 ∴ x = ∴ x = ₹ 50,000 ∴ Sale value of the car = ₹ 50,000 Against commission received from the owner = × 50,000 = ₹ 1500 Against commission received from the buyer = × 50,000 = ₹ 1000 ∴ Agents total remuneration = 1,500 + 1,000 = ₹ 2,500

Total sales = ₹ 51,000 Let eash sales be ₹ x ∴ Credit sales = ₹ (51,000 – x) Agent’s commission on cash sales = 4% = × x = Commission on credit sales = 6% = (51,000 – x) Given total commission = ₹ 2,700 ∴ Cash sales = ₹ 18,000 ∴ Credit sales = 51,000 – 18,000 = ₹ 33,000