Percentage, Profit and Loss (Stocks and Shares (Rate of Return
1) A buyer…
Percentage, Profit and Loss
1) A shopkeeper uses a weighing balance that shows 1,050 gm for a kg. He sold his product at 10% above the cost price. The net profit percentage is:
Sol: The weighing balance is showing 1,050 gm for 1 kg
=> While he is selling, he is selling 1,050 gm assuming it as a kg
=> We need to calculate selling price not for 1kg, but for 1.050kg
Given, there is a profit of 10%
=> SP = (1.1)CP(1.050)
=> SP = 1.155CP
=> There is a net profit % of 15.5%
Faulty Meter Scale
2) A meter scale reads 100 cm as 90 cm. Shopkeeper promises to sell 1 m of cloth at cost price. Find his profit percentage
Sol: SP of 90 cm = CP of 100 cm = C (say)
=> CP of 90 cm = 0.9C
=> %P = (SP - CP)/CP
=> %P = (C - 0.9)/0.9 = 11.11%
Note: In this kind of problems, determine either CP or SP for a single quantity and then apply formula. In this case, we considered the quantity to be 90 cm.
1) A dishonest milk vendor sells milk at his cost price but he adds 200ml for every 1 lit of milk. Further, he sells 20% less than the quantity that he claims to sell. Find the profit percentage of the vendor?
Sol: Let the cost price of 1 lit milk for vendor = C
(i) He adds 200 ml of water => C = 1.2 lit
(ii) He sells 20% less than what he claims to sell
=> If he sells 1 lit milk i.e., 1.2 lit of milk solution, then he claims to sell x lit i.e., => 1.2 = 4/5(x) => x = 1.5 lit
Hence SP = 1.5 C and CP = C (for 1.2 lit)
Profit % = 50%
1) Three persons A, B and C invested P/-, Q/- and R/- in a firm respectively. Calculate the ration of their returns at the end of year if their periods of investments are x, y and z respectively.
Sol: Returns at the end of the year=> A : B : C = Px : Qy : Rz
=> If the total profit earned is given, then calculate the individual profits for each of A, B and C from the above ratio.
2) A and B invest 20,000 and 30,000 respectively and start a business. Since A manages the business, he gets a salary which is equal to 20% of the balance profit after deducting his salary. If A's total earnings are 4800 at the end of 1 year, calculate the total profit made by the business.
Sol: Ratio of returns A : B = 2 : 3
Let total profit be 'P'
Given A's earnings = 4800 = Profit share of A+ salary(S)
Salary = (1/5)(P-S) => 6S = P
=> Profit share of A = (2/5)(P-S) => 4800 = 2S + S => S = 1600
Therefore, P = 9600
Stocks and Shares
2) Face Value
3) Rate of Return
4) Market Value
5) % Dividend
Note: Unless and until mentioned, Face Value by default must be assumed as 100.
Premium Value of a Stock and Income Earned
2) Calculate the annual income from 32400 invested in 12% stock at 8% Premium
Sol: 12% stock at 8% premium => Each share is bought at a premium price of 8% or 8% above Face Value or 108/-.
=> Therefore, given 12% stock at 108 => 12/- for every 108/- of investment
Given total investment = 32400 => No. of shares bought = 32400/108 = 300
=> Annual income earned = 12(300) = 3600
4) A man invests in a 6% stock @ 5% premium. He gets a dividend of 3600 at the end of the year. Calculate his investment?
Sol: Let his investment be 'P'
He invests 6% stock at 5% premium => 6% stock at 105
=> (6/105)P = 3600 => P = 63000
5) A man invests 1395 in a 3% stock @ 93. After a month, he sells 1000/- worth stock @ 95 and the remaining @ 80/-. Calculate the overall profit/loss of the transaction.
Sol: Investment = 1395 in 3% stock @ 93
=> No. of stocks = 1395/93 = 15
He sells 1000 worth stock @ 95, 1000 worth => 1000 = 10x100 (where 100 is FV)
=> He sells 10 stocks at 95 and the remaining @ 80
=> 5 stocks at 80
Therefore, Amount obtained = 95(10) + 80(5) = 1350 ---- (1)
Net profit/loss = SP - CP = 1350 - 1395 = -45
=> 45/- Loss