Current Affairs 6th Class

  Introduction     Ratio of two quantities is the comparison of the given quantities. Ratio is widely used tor comparison of two quantity in such a way that one quantity is how much increased or decreased by the other quantity. Proportion is representing the equality of two ratios and it is used where equivalent quantity is required. Map drawing is the appropriate example of use of proportion. The length between two points on the map is taken according to the proportion of the actual length.                 Unitary method is used to calculate the problems with variable quantities. Therefore, the method by which one variable is changed into a single unit is called unitary method.  

   Ratio     Two or more quantities are compared by their difference. Mariam has 24 note books but Hilary has 78, comparison of both the quantities is their difference, Mariam has, 78 - 24 = 54 note books less than those Hilary has. In another words it is said that, Hilary has 54 more books than those Mariam has. Another method which is used to compare the two or more quantities is division method. Peter has 20 litres of milk but John has 5 litres, the comparison of the quantities is said to be, Peter has 15 litres more milk than John, but by division of both the quantity it is said that Peter has, \[\frac{20}{5}=4\] times bigger quantity of milk than John. It can be expressed in the ratio form as \[=\frac{1}{4}\] When Peter has 4 litres milk, John has 1 litre and quantity of milk is increased according to the ratio of y. In the ratio of \[=\frac{4}{1}\] is called antecedent and 1 is consequent. Two numbers x and y whenever, written in the form of  \[x:y\] is called in ratioand read as \[x\]is to y. In the ratio\[~x\text{ }:\text{ }y,\]\[x\] is the first and \[y\]is second term. The terms of the ratio can not be interchanged or \[x\text{ }:\text{ }y\] cannot be written as \[y:x.\]The ratio form of the numbers can be expressed infraction in this way that the antecedent is numerator and consequent is denominator, therefore, the fractional form of \[x:y=\frac{x}{y}.\]         The distance between two points on the map is 4 cm, which represents the distance of 1500 km. Find the ratio of actual as well as mapped or imaginary distance? (a) 2 : 345                                             (b) 375 : 1 (c) 23 :56                                              (d) All of these (e) None of these     Answer: (b)                 Explanation                 Ratio of the actual distance to the given scale \[=\frac{1500}{4}=\frac{375}{1}=375:1.\]       Simplest form of Ratio                 If the common factor of antecedent and consequent is not other than 1 then it is called in its simplest form of ratio. Complex form of ratio can be converted into its simplest form by division with same number to both the antecedent and consequent.                 The simplest form of ratio is also called ratio in its lowest term. The ratio 24 : 30 is not in its simplest form because, it has common factor 6, therefore, the simplest or lowest term of ratio,                 \[24:30=\frac{24}{30}=\frac{4}{5}=4:5,\] In this ratio, the factor of antecedent 4 and consequent 5 is 1 only, therefore, called simplest form of ratio.                     The area of a circular garden inside the rectangular garden is 515 sq. metres. If the area of rectangular garden is 5000 sq. metres. Find the ratio in its simplest form of area of rectangular as well as more...

  Proportion     The equality of two ratios is called proportion. If a tray of cake is distributed among eight boys and each boy gets equal part of the cake then cake is distributed in proportion. The smallest form of ratio, 12 : 96 is 1: 8 and 19 :152 is 1: 8 therefore,12 : 96 = 19 : 152 is in proportion. if\[x:y=m:n\]then \[x,y,m\]and n are said in proportion and written as, \[x:y::m:n.\]In the proportion, \[x:y::m:n,\]\[x\] and n are first and last term and therefore called extreme terms and middle term y and m are called means. Product of extreme terms of a proportion, \[x\times n\]is always equal to the product of middle terms, \[y\times m,\]therefore,\[x\times n=y\times m.\]lf\[x\times n\ne y\times m\]then, they are not in proportion.         The age ratio of Peter and his father is 2 : 5. Find the age of Peter if his fathers age is 40 years? (a) 17                                                     (b) 16            (c) 18                                                     (d) 19 (e) None of these                Answer: (b)                 Explanation 2 : 5 Peter age :\[\text{40}\Rightarrow \frac{\text{2}}{\text{5}}\text{=}\frac{\text{peter}\,\text{age}}{\text{40}}\] Therefore, age of Peter \[\text{=}\frac{\text{40 }\!\!\times\!\!\text{ 2}}{\text{5}}\text{=}\frac{\text{80}}{\text{5}}\text{=16}\,\text{yearas}\]       Continued Proportion Three numbers a, b and c are said to be in continued proportion even if a, b, b, c are in proportion. The continued proportion a, b, b, c is written as, a : b : : b : c. In the continued proportion, a : b : : b : c, a and c is called extreme terms and twice b is called middle or means term. The product of the extreme and middle terms is always equal. Therefore, \[a\times b=b\times b\]or \[a\times c=b\times c\]or\[a\times c={{b}^{2}}\]or\[{{b}^{2}}=ac.\]         The terms a, 5 and 10 are in continued proportion then find the value of a from the options given below? (a) \[\frac{7}{2}\]                                             (b) \[\frac{3}{4}\] (c)  \[\frac{5}{2}\]                                             (d) All of these (e) None of these     Answer: (c) Explanation   \[a:5::5:10\Rightarrow \] Product of extreme terms = Product of middle terms\[\Rightarrow a\times 10=5\times 5\Rightarrow 10a={{5}^{2}}\Rightarrow a=\frac{{{5}^{2}}}{10}=\frac{25}{10}=\frac{5}{2}\]     Mean Proportion The middle term of a continued proportion is called its mean. If a, b and c are in continued proportion then, b is called its mean proportional between a and c, and mean proportion is calculated by \[{{b}^{2}}=ac\]or \[b=\sqrt{ac}.\]         Find the mean proportion between 5 and 125? (a) 35                                                     (b) 25 (c) 45                                                     (d) All of these  (e) None of these                             Answer: (b)                                              Explanation Let us consider the mean proportion between  5 and 125 is x, therefore,   \[x=\sqrt{5\times 125}=\sqrt{625}=25.\]                     The ratio of man and woman in a joint family is 9 : 8, if number of more...

  Introduction     Lines and angles are the main geometrical concept and every geometrical figure is made up of lines and angles. Triangles are constructed by these lines and angles. In this chapter we will learn about the basic shapes of geometrical figures.                

Geometrical Basic Shapes       Point A dot which indicates position but not dimension is called a point. A point does not have length, breadth and height. P and Q are points in the figure below.        In the picture above, P and Q are points In the picture above two points lie on the same line and therefore called collinear points. Points do not lie on the same line are called non collinear points.       Line A set of infinite points which can be extended infinite distance in both sides is called a line.                 \[\] In the picture above, M is a line   Features of the Line (i) The length of a line is infinite. (ii) It has no terminal, therefore, can be extended infinitive in both directions. (iii) It is made up of infinite points.       Line Segment A line of fix length is called line segment. In the picture above, P and Q is a line segment and represented by \[\overline{PQ}.\]       Features of the Line Segment (i) A Line segment has fix length. (ii) It has two end points.       Ray A ray is defined as the line that can be extended infinite in one direction. In the picture above, end point of terminal point Ray AB is represented as AB     Angle Angle is formed between two rays which having common end point. Symbol of angle \[=\angle \]   Vertex or common end point = 0 Arms of angle \[\angle AOB\] = OA and OB the name of the above angle can be \[\angle \text{ }AOB\]or \[\angle BOA\] The unit of measurement of an angle is degree \[{{(}^{o}})\]       Types of Angles There are various types of angles which are the following:     Acute Angle The angle between 0° and 90° is called an acute angle.     In the picture above \[\angle AOB\]or \[\angle BOA\] is an acute angle. The inclined arm OA on the horizontal is less inclined than vertical line. \[{{10}^{o}},{{30}^{o}},{{60}^{o}},{{80}^{o}}\] are acute angles.   Right Angle An angle of \[{{90}^{o}}\] is called right angle.                       Obtuse Angle An angle whose measure is between \[{{90}^{o}}\] and \[{{180}^{o}}\] is called an obtuse angle.                      Straight Angle                                                   An angle whose measure is \[{{180}^{o}}\]is called straight angle.  Or an angle more...

   Operations on Decimals           Addition of Decimals Consider the following decimal numbers 45.56, 23.5. The addition of the decimals is    (Unlike decimal is first converted into like decimal)       Add the following decimals: 34.45, 45.67, 32.1. (a) 113.23                                            (b) 114.24 (c) 112.22                                             (d) None of these (e) All of these     Answer: (c)                 Explanation