Current Affairs 8th Class

Category : 8th Class

 Comparing Quantities

• Compound interest: Amount at compound interest is given by \[A=P{{\left( 1+\frac{R}{100} \right)}^{n}}\], where,

A - Amount,   P - Principal,    R - Rate of interest, n - Time period.

(i) Compound interest = A - P

(ii) In case of depreciation (or) decay,

\[A=P{{\left( 1-\frac{R}{100} \right)}^{n}}\]

• If the rates of increase in population P are p%, q% and r% during 1st, 2nd and 3rd years respectively, then the population after 3 years =

\[=P\left( \frac{P}{100} \right)\left( 1+\frac{q}{100} \right)\left( 1+\frac{r}{100} \right)\].

• If principal = R.s P, rate = R% per annum and time = n years, then

(a) Amount after 'n' years (compounded annually) is

\[A=P{{\left( 1+\frac{R}{100} \right)}^{n}}\]

(b) Amount after 'n' years (compounded half-yearly) is

\[A=P{{\left( 1+\frac{R}{2\times 100} \right)}^{2n}}\]

where \[\frac{R}{2}\] is half-yearly rate and 2n is the number of half - years.

(c) Amount after 'n' years (compounded quarterly) is

where\[\frac{R}{4}\] is the quarterly rate and 4n is the number of quarter years.

When T = 2 years and n = 1, then

            CI.- S.I.= \[\frac{R\times S.I}{2\times 100}=P{{\left( \frac{R}{100} \right)}^{2}}\]

(v) When T = 3 years and n = 1, then

\[C.I.-S.I=\frac{S.I.}{3}\left[ {{\left( \frac{R}{100} \right)}^{2}}+3\left( \frac{R}{100} \right) \right]\]

• If a certain amount becomes N times in T years, then it will be

\[{{N}^{2}}\]times in T x 2 years, \[{{N}^{3}}\]times in T x 3 years and N" times in T x x years.

• Profit and loss:

(i) Cost price (C.P.): The price at which an article is purchased is called its cost price.

(ii) Selling price (S.P.): The price at which an article is sold is called its selling price.

(a) If S.P. > C.P., then there is a gain and Gain = S.P. - C.P.

(b) If S.P. < C.P., then there is a loss and Loss = C.P. - S.P.

• Profit and loss percentage:

(i)\[~Profit%=\frac{~Profit%}{C.P.}\times 100%\]           

(ii) \[Loss%=\left( \frac{loss%}{C.P.} \right)100%\]   

Note: Profit and loss percentage are reckoned on cost price.

• Important formulae:

(a) \[S.P.=\left( \frac{100-gain%}{100}\times C.P. \right)\] 

(b)\[S.P.=\left( \frac{100-loss%}{100}\times C.P. \right)\]

(c)\[C.P.=\left( \frac{100}{100+gain%}\times S.P. \right)\]

(d) \[C.P.=\left( \frac{100}{100+loss%}\times S.P. \right)\]

• Discount: In order to give a boost to the sales of an item or to clear the old stock, articles are sold at reduced prices. This reduction is given on the Marked Price (M.P.) of the article and is known as discount.

(a) S.P.= M.P.- Discount              

(b) Discount = M.P. - S.P.

(c)\[Discount\text{ }%=~\frac{M.P.-S.P.}{M.P.}\times 100\]      

(d) Discount = Discount % of M.P.

(e) Additional expenses made after buying an article are included in the cost price and are known as overhead expenses.

C.P. = Buying price + Overhead expenses

(f) Sales tax is charged on the sale of an item by the government and is added to the bill amount.

Sales tax = Tax % of bill amount