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ALL IMPORTANT FORMULAS IN COMPARING QUANTITIES!

The Following

SP = CP+Gain 

SP = CP-Loss

CP = SP-Gain

CP = SP+Loss

SP = CP+(Gain%/100*CP)

SP = CP-(Loss%/100 *CP)

CP = SP-(Gain%/100 * SP)

CP = SP+(Loss%/100 * SP)

Decrease% = Decrease/CP * 100

Increase% = Increase/CP * 100

Gain% = Gain/CP * 100

Loss% = Loss/CP * 100

If Compounded Annually

A = P(1+R/100)n

Half Yearly

A = P(1+R/200)2n

Quaterly

A = P(1+R/400)4n

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  • Increase and decrease percent
    Increase percent Increase in the value 100%

    Decrease percent Decrease in the value 100% Original value

    Example: In the year 2007, the number of children in a locality was 1500. In the year 2008, the number of children in the locality rose to 2100. Find the percent increase in the number of children of the locality.

    Solution: Increase in the number of children = 2100 – 1500 = 600 Percent increase 600 100  40%

    1500

    Thus, the required percent increase in the number of children of the locality is

    40%.

  •   Discount is the reduction given on the Marked Price (M.P) of an article.

    Discount = Marked Price – Sale price Discount = Discount % of Marked Price 

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C.P. = Buying price + Overhead expenses Profit% Profit 100

C.P.

Example: A shopkeeper purchased 15 dozen cups for Rs 900. However, 9 cups cracked during transportation. The remaining cups were sold for Rs 9 each. Find the gain or loss percent.

Solution:

Cost price of 15 dozen i.e., 180 cups = Rs 900
9 cups were cracked. Therefore, number of cups left = 180 – 9 = 171 These 171 cups were sold at Rs 9 each.

S.P. of 171 cups = Rs 9 × 171 = Rs 1539
Profit = S.P. – C.P. = Rs (1539 – 900) = Rs 639

Profit% Profit 100  639 100  71% C.P. 900

  •   Sales tax is charged on the sale of an item by the government and is added to the bill amount.

    Sales Tax (or VAT) = Tax % of bill amount
    For example, if the tax charged on an item of Rs 4000 is 10%,

    Then, VAT (value added tax) = 10 4000 Rs 400 100

    Therefore, amount paid on buying the item = Rs 4000 + Rs 400 = Rs 4400

  •   Interest is the extra money paid by institutions such as banks or post offices on

    money deposited with them.
    It is also paid by people when they borrow money from these institutions.

    Simple Interest Principal Rate Time 100

    Amount = Principal + Interest
    The interest calculated on the amount of the previous year (or duration at which interest is compounded) is known as compound interest. Compound interest allows the principal to grow faster than simple interest.

    Amount (A) when interest is compounded annually is A P1 R n 100

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Where, P = Principal, R = Rate of interest, n = Time period Amount when interest is compounded half yearly is given by,

AP1 R 2n 200

 

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Finish Line & Beyond
Comparing Quantities
1. Discount
is a reduction given on marked price.Discount = Marked Price – Sale Price.
2.
Discount can be calculated when discount percentage is given.Discount = Discount % of Marked Price
3.
Additional expenses made after buying an article are included in the cost price andare known as
overhead expenses
.CP = Buying price + Overhead expenses
4.
Sales tax is charged on the sale of an item by the government and is added to theBill Amount.Sales tax = Tax% of Bill Amount
5.
Compound interest is the interest calculated on the previous year’s amount(A = P + I), where A is the amount, P is principal and I is interest.
6.
(i) Amount when interest is compounded annuallyA=P(1+
100
 R
)
t
Where, P is principal, R is rate of interest,
t 
is time period(ii) Amount when interest is compounded half yearlyA=P(1+
200
 R
)
t
Where t is number of half years
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