Profit, Loss, Discounts, Successive Discount, True Discount, Banker's Discount Tricks and Formulas

Profit & Loss

  • If the value of a machine is ‘P’ in a year, then its value after ‘N’ years at a depreciation of ‘R’ p.c.p.a is P(1R/100)N

  • If the value of a machine is ‘P’ in a year, then its value ‘N’ years ago at a depreciation of ‘R’ p.c.p.a is P/[(1R/100)N]

  • Selling Price =[(100+Gain%)×CostPrice]/100=[(100Loss%)×CostPrice]/100

  • Profit=SPCP

  • Loss=CPSP

  • PercentageProfit=ProfitCP×100=SPCPCP×100

  • PercentageLoss=LossCP×100=CPSPCP×100


  • Discount=MarkedPriceSellingPrice

  • DiscountPercentage=DiscountMarkedPrice×100

Buy x and Get y Free

  • If articles worth Rs. x are bought and articles worth Rs. y are obtained free along with x articles, then the discount is equal to y and discount percentage is given by

    • Percentagediscount=yx+y×100

Successive Discounts

When a discount of a% is followed by another discount of b%, then Totaldiscount=(a+bab100)%

False Weights

  • If an item is claimed to be sold at cost price, using false weights, then the overall percentage profit is given by

    • PercentageProfit=(ClaimedWeightofitemActualWeightofitem1)×100

True Discount

Suppose a man has to pay Rs. 156 after 4 years and the rate of interest is 14% per Annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment ofRs. 100 now will clear off the debt of Rs. 156 due 4 years hence. We say that: Sum due =Rs.156 due 4 years hence;

  • Present Worth (P.W.) =Rs.100;

  • True Discount (T.D.) =Rs.(156100)=(Sumdue)(P.W.)

  • T.D.=InterestonP.W .

  • Amount =(P.W.)+(T.D.)

  • Interest is reckoned on R.W. and true discount is reckoned on the amount

  • Let rate =R% per annum & time =Tyears. then,

  • P.W.=(100×Amount)/(100+[R×T]) =(100×T.D.)/(R×T)

  • T.D.=(P.W.)×R×T/100 =([Amount]×R×T)/(100+[R×T])

  • Sum=([S.I.]×[T.D.])/([S.I.][T.D.])

  • (S.I.)(T.D.)=S.I.onT.D.

  • When the sum is put at compound interest, then P.W. =Amount/(1+R/100)T

Banker’s Discount

  • Banker’s Discount (B.D.) is the S.I. on the face value for the period from the date on which the bill was discounted and the legally due date.

  • Banker’s Gain (B.G.)=(B.D.)(T.D.) for the unexpired time

  • When the date of the bill is not given, grace days are not to be added

  • B.D.=S.I. on bill for unexpired time

  • B.G.=(B.D.)(T.D ).) =S.I.onT.D. =(T.D.)2/P.W.

  • T.D.=P.W.×B.G.

  • B.D.=(Amount×Rate×Time)/100

  • T.D.=(Amount×Rate×Time)/(100+[Rate×Time])

  • Amount=(B.D.×T.D.)/(B.D.T.D.)

  • T.D.=(B.G.×100)/(Rate×Time)