# Ratio and Proportion Questions for SSC

Ratio and Proportion Questions for SSC CGL BANK POO SO and other government exam.

Ratio : The ratio of a to b is a fraction a/b and is written as a:b

Note: the value of ratio remains same if we multiply or divide  the numerator and denominator of a fraction by the same number.

a : b = a/b = am/bm = a : b  or

A : b = a/b = a/mb/m = a/m

Compounded ratio : If two or more ratios are multiplied term by term i.e the numerator to numerator and denominator to denominator, the ratio thus obtained is called their compounded ratio

Example the compounded ratio of a : b and c : d is ac : bd

Duplicate ratio : the duplicate ratio of a : b is a^2 :  b^2

Example the duplicate ratio of 2 : 3 = 4 : 9

Triplicate ratio : the triplicate ratio of a : b is a^3 : b^3

Sub-duplicate ratio : the sub-duplicate ratio of a : b is a^½ : b^½

Sub triplicate ratio : the sub triplicate ratio of a : b is a^⅓ : b^⅓

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Reciprocal or inverse ratio : the inverse ratio of a : b is 1/a : 1/b which is same as     b : a

Proportion : if two ratios are equal, then they are said to be in proportion

Example : consider 2 : 5 and 4 : 10 , since  2/5  = 4/10 , hence 2,5,4 and 10

are in proportion and can be  written as 2 : 5 : : 4 : 10

In the proportion 2 : 5 : : 4 : 10, the end terms 2 and 10 are called extremes and the middle terms  5 and 4 are called means.

Product of extremes = product of means

Continued proportion and third proportion : If a/b = b/c , then  a, b, and c are said to be in continued proportion  and c is called the third proportion. The third proportion of a and b is b^2 / a.

Fourth proportion : if a, b, c and d are in proportion then d is called the fourth proportion. The fourth proportion of a, b and c is bc / a .

Mean proportion : mean proportion of two numbers a and b is √ab

 Short tricks 1. If A : B : C = a : b : c Then A/B : B/C : C/A = a2 c : b2 a : c2 a 2. If A : B = a : b, B : C = b : c, C : D = c :d Then A : C = a : c, A : D = a : d and B : D = b : d 3. If a sum of money R is divided in A and B in the ratio  m : n, then Share of A = R/m  + n × m Share of B = R/m  + n × n Difference between the share of A and B = R/m  + n × (m – n) Following Question Prepared by Best Bank Coaching in Noida 4. If a bag contain the coins of Rs. x, Rs. y and Rs. z in the ratio of m : n : r and the total value of the coins is Rs. R, then Numbers of coin x = m/xm + yn + zr × R Numbers of coin y = n/xm + yn + zr × R Numbers of coin z = r/xm + yn + zr × R
 5. In a glass, the ratio of the mixture of milk and water is m : n and in another glass of same quantity of mixture is p : q. If the mixture of these two glasses mix up in a third glass, then the ratio of milk and water  will be                                        = (m/m + n  + p/p + q) : (n/m + n + q/p + q)
 6. In X lite mixture, the ratio of water and milk is p : q. How many liters of water should be added to this mixture so that the ratio will become r : s.                  = X(ps – qr)r/(p + q)

Allegation and mixture

Allegation rule : The two ingredients should be mixed in the inverse ratio of the differences of the two given prices and the mean price i.e.

(Quantity of cheaper product / quantity of dearer product ) = (Cost price of dearer – mean price) /

(mean price – cost price of cheaper)

Note : C.P. of unit quantity of the mixture is called the mean price.

We represent it as

Cheaper quantity  : dearer quantity = (d – m) : (m – c)

Short tricks on allegation and mixture

 If in a X liter mixture of milk and water, the quantity of milk is m%, then how many liters of milk should be added to the mixture such that the quantity of milk increase to n % = X(n – m)/100 – n If in a X liter mixture of milk and water, the quantity of milk is m%, then how many liters of water should be decreased or vaporized from the mixture such that the quantity of milk increase to n % = X(m – n)/100 – n A container contains X liters of water. If m liters of water is replaced by m liters of milk and this process is repeated n times , then the quantity of water in the new mixture is                   X (1 – m/x)n If by selling mixture of milk and water on the cost price of milk there is a profit of m%, then the ratio of milk and water = 100 : r

Partnership

Partnership : To solve the problems involving partnership , use this trick

(A’s capital × A’s time in partnership)/(B’s capital ×  B’s time in partnership) = A’s profit/B’s profit

For three persons A, B and C

(A’s capital × A’s time) : (B’s capital × B’s time ) : (C’s capital × C’s time ) =

A’s profit : B’s profit : C’s profit

# Practice Question on Geometry for SSC Exam

Practice Question on Geometry for SSC Exam, SSC CGL, BANK, RBI and other government exams.

1. ABCD is a cyclic parallelogram. The angle B is equal to

a. 30°            b. 60°          c. 45°               d. 90°

2. A quadrilateral ABCD circumscribes a circle and AB = 6 cm, CD = 5 cm and AD = 7 cm. The length of side BC is

a. 4 cm         b. 5 cm      c. 3 cm          d. 6 cm

3. The three successive angles of a cyclic quadrilateral are in the ratio 1 : 3 : 4, find the measure of the fourth angle

a. 72             b. 108       c. 36                d.30

4. Two chords of length a unit and b unit of a circle make angles 60 degree and 90 degree at the centre of a circle respectively, then the correct relation is

a. b = 3/2 a           b. b = √2a                c. b = 2a                   d. b = √3a

5. ABC is a cyclic triangle and the bisectors of angle BAC, angle ABC and angle BCA meet the circle at P, Q  and R respectively. Then the angle RQP is

a. 90 – B/2            b. 90 + B/2              c. 90 +            d. 90  – A/2

## Practice Question on Geometry for SSC Exam

6. Ashok has drawn an angle of measure 4527’ when he was asked to draw an angle of 45. the percentage error in his drawing is

a. 0.5                       b. 1.0                         c.1.5                  d. 2.0

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7. The angle between the external bisectors of two angles of a triangle is 60. Then the third angle of the triangle is

a. 40                       b. 50                          c. 60                 d. 80

8. The measure of an angle whose supplement is three times as large as its complement, is

a. 75                       b. 30                         c. 45                   d. 60

9. If the complement of an angle is one- fourth of its supplementary angle, then the angle is

a. 60                      b. 30                         c. 90                   d. 120

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10. If D, E and F are the mid_ points of  BC, CA and AB respectively of the triangle ABC then the ratio of area of the parallelogram DEFB and area of the trapezium CAFD is

a. 2:3                    b. 3:4                         c. 1:2                   d. 1:3

11. If the ratio of the angles of a quadrilateral is 2 : 7 : 2 : 7, then it is a

a. Trapezium      b. Parallelogram    c. square              d. Rhombus

12. In the given figure angle ONY = 50° and OMY = 15°. then the value of the angle MON is

a.30          b. 40              c. 20               d. 70

13. Two circles intersect at A and B. P is a point on produced BA. PT and PQ are tangents to  the circle. The relation of PT and PQ is

a. PT = 2PQ                   b. PT < PQ                 c. PT > PQ                   d. PT = PQ

14. AB is a chord of a circle with center O. DC is a line passing through O starting from D (on a circle) end on ( C is a point on the produced line AB). If angle BCO = 30, then angle AOD is

a. 90                              b. 120                              c. 100                         d. 80

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15. If the ratio of the angles of a quadrilateral is 2 : 2 : 2 : 2 , then it is a

a. Trapezium               b.rectangle                     c. square                    d. Rhombus

16. If O is the cir-cum center of a triangle ABC lying inside the triangle, then angle OBC – angle BAC is equal to

a.90                             b. 60                                  c. 110                           d. 120

17. Two circles of radii 5 cm and 3 cm touch externally, then the ratio in which the direct common tangent to the circles divides externally the line joining the centers of the circles is :

a. 5 : 3                        b. 3 : 5                                c. 2.5 : 1.5                   d. 1.5 : 2.5

18. The distance between the centers of two circles having radii 8 cm and 3 cm, is 13 cm. The length (in cm ) of the direct common tangent of the two circles is

a. 15                            b. 16                                   c. 18                              d. 12

19. For a triangle cir-cum center lies on one of its sides. The triangle is

a. Right angled          b. Obtused angled          c. isosceles                  d. Equilateral

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20. ABCD is a rhombus whose side AB = 4 cm and angle ABC = 120, then the length of diagonal BD is equal to

a. 1 cm                         b. 2 cm                              c. 3 cm                           d. 4 cm

21. A square ABCD is inscribed in a circle of unit radius. Semi circles are described on each sides as a diameter. The area of the region bounded by the four semicircles and the circle is

a. 1 sq. unit                b. 2 sq. unit                      c. 1.5 sq. unit                d. 2.5 sq. unit

22. A, B, C, D are four points on a circle . AC and BD intersect at a point E such that angle BEC = 130 and angle ECD = 20, angle BAC is

a. 120                         b. 90                                 c. 100                           d. 110

23. Three circles of radius 6 cm each touches each other externally. Then the distance of the center of one circle from the line joining the centers of other two circles is equal to

a. 6√5 cm                    b. 6√3 cm                          c. 6√2 cm                        d. 6√7 cm

24. The sides of a triangle are in the ratio 3 : 4 : 6. The triangle is

a. Acute angled              b. Right angled                         c. Obtuse angled                         d. Either acute angled or right angled

25. AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD (in cm ) is

a. 4                      b. 5                   c. 6                    d. 8

 1. d 7. c 13. d 19. a 25. b 2. a 8. c 14. a 20. d 26. 3. a 9. a 15. b 21. 27. 4. b 10. a 16. b 22. d 28. 5. a 11. b 17. 23. b 29. 6. b 12. d 18. d 24. a 30.

# Geometry for SSC CGL Exam

Geometry for SSC Exam, IBPS SO, RRB and government exam preparation.

Angles  An angle is a measurement of rotation of a line about a fixed point

The fixed point is called the vertex of an angle.

Angle is generally measured in degree

We read it as angle AOB

Types of angles

Acute angle If an angle is less than 90°, then it is called an acute angle

Right angle if an angle is equal to 90°, then it is called right angle

Obtuse angle If an angle is greater than 90° but smaller than 180°, then it is called an obtuse angle

Straight angle If an angle is equal to 180°, then it is called a straight angle

Reflexive angle If an angle is greater than 180° and smaller than 360°, then it is called reflexive angle

Complete angle If an angle is equal to 360°, then it is called complete angle

Complementary angles  Two angles are called complementary if their sum is equal to 90°

Supplementary angles Two angles are called supplementary if their sum is equal to 180° or equal to two right angles.

Transverse lines when two lines intersected by a third line then the third line is called transverse line

Corresponding angles If the lines are parallel then their corresponding angles are equal and if the corresponding angles are equal then the lines are parallel

Corresponding angles is in the form of F

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Alternate angle if the lines are parallel then their alternate angles are equal and its converse is also true

Alternate angle is in the form of Z

Vertically opposite angles when two lines intersect each other then the angles made at their intersection point are called vertically opposite angles.

These angles are in the form of X

Triangle A plane figure bounded by three straight lines is called a triangle

• A triangle has 3 angles
• The sum of angles of a triangle is 180°

Scalene triangle A triangle whose all sides are of different length

## Geometry for SSC Exam

Isosceles triangle A triangle whose at least two sides are equal

Equilateral triangle a triangle whose all sides are equal

In equilateral triangle all angles are 60°

Right angled triangle A triangle in which an angle is equal to 90°

Pythagoras theorem In a right angled triangle AB2 + BC2 = AC2

Its converse is also true i.e. AB2 + BC2 = AC2, then the triangle is right angled triangle.

Acute angled triangle If all the angles of a triangle are acute angle, Then there is acute angled triangle.

Obtuse angled triangle If one angle of a triangle is obtuse, then there is obtuse angled triangle.

Median The median is a line segment joining a vertex to the mid_point of opposite sides.

Centroid The intersection point of medians is called centroid.

All the medians are concurrent i.e. they intersect each other at same point

Centroid divides the median into 2:1.

Orthocentre the intersection of  altitudes drawn from vertex to its opposite sides is called orthocentre.

All the altitudes are concurrent.

Incentre The intersection point of angle bisector is called the incentre.

All the angle bisectors are concurrent.

Incircle is the centre of largest circle that can be inscribed in a triangle.

Circumcenter The intersection point of perpendicular bisector of any two sides of a triangle is called the circumcentre.

• All the perpendiculars bisectors are concurrent
• Circumcenter is the radius of largest circle that is outside the triangle and touch the vertices of triangle

Some important results on triangle

• If a side of a triangle is produced then the angle so formed is called  exterior angle and is equal to the sum of opposite interior angles

• The sum of exterior angles of a triangle is equal to 360
• The sum of two sides of a triangle is always greater than the third side
• The angle opposite to greater side of a triangle is greater i.e. if AB > BC > CA, then angle C > angle A > angle B and conversely
• If any two sides of a triangle are equal, then the angles opposite to them are also equal and conversely
• Centroid divides the median of a triangle in 2:1
• In equilateral triangle centroid, orthocentre, incentre and circumcentre coincides i.e. they lie on the same point
• The line joining the mid_ points of two sides of a triangle is parallel to the third side
• Let ABC is a right angled triangle, right angle at B and D is the mid_ point of AC . then BD = ½ AC

• Let the bisector of angle B and angle C intersect each other at a point O.

Then angle BOC = 90 + ½ A

If ABC is a triangle and line BC is produced to D and AL is the bisector of angle A, then Angle ABC + angle ACD = 2 ( angle ALC)

Congruent triangles Two triangles are said to be congruent if they are the same triangle with different rotation i.e. they are of same size (all angles and all sides are equal)

If ABC is congruent to DEF  we written this as  ABCDEF

Every triangle is congruent to itself

Some important triangle

# Geometry Question for SSC CGL

Sufficient condition for congruence of two triangles

• SAS (side angle side) If two sides and angle between them of one triangle is equal to the corresponding sides and angle between them of the other triangle
• ASA (angle side angle) If two angles and included side of one triangle is equal to the corresponding angle and included side of the other triangle
• SSS (side side side) If three sides of one triangle is equal to the corresponding sides of the other triangle
• RHS (right angle – hypotenuse side ) If the hypotenuse and other side of one triangle is equal to hypotenuse and the corresponding side of the other triangle

Similar triangles Two triangles are said to be similar if they have same shape but their size can be different i.e. their corresponding sides are in proportion and their corresponding angles are equal

If ΔABC is similar to ΔDEF  we written this as  ΔABC∼ΔDEF

A/B D/E = B/C E/F = AC/DF

• Every triangle is similar to itself
• If ΔABC∼ΔDEF then area ΔABC/area ΔDEF = (AB/DE)2= (BC/EF)2 = (AC/DF)2

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Quadrilaterals A plane figure bounded by 4 line segments is called quadrilateral

Sum of all the angles of a quadrilateral is 360°

AC and BD are the diagonals of a quadrilateral

Parallelogram  A quadrilateral whose opposite sides are parallel  is called a parallelogram

• Opposite sides of a parallelogram are equal
• Opposite angles of a parallelogram are equal
• Diagonals of a parallelogram bisect each other
• Sum of consecutive angles of a parallelogram is 180°

Rectangle A quadrilateral whose opposite sides are parallel and interior angles is equal to 90°

• Opposite sides of a rectangle are equal
• All the angles of a rectangle are equal to 90°
• Diagonals of a rectangle are equal and bisect each other

Rhombus A parallelogram whose all sides are equal is called a rhombus

• Diagonals bisects each other at  90°
• Sum of the squares of the side is equal to the squares of the diagonals

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Square A parallelogram whose all sides are equal and interior angles are equal to 90°

• Diagonals of a square bisect each other at 90°
• Diagonals of a square are equal

Polygons A polygon is a plane figure bounded by n straight lines

Number of sides                                          polygon

3                                                                    triangle

5                                                                    pentagon

6                                                                    hexagon

7                                                                    heptagon

8                                                                    octagon

9                                                                    nonagon

10                                                                 decagon

Regular polygons If all sides and all angles of a polygon are equal, then it is called a regular polygon

Properties of a polygon

• Sum of all interior angles of a polygon of sides n is (n – 2) × 180°
• Each exterior angle of a regular polygon of n sides is (360/n)°
• Each interior angle of a regular polygon is (n – 2) × 180°/n
• number of diagonals of a polygon of n sides is n × (n – 3)/2
• Sum of all exterior angle of a regular polygon is 360°

Circle A circle is the set of all points in a plane which are equidistant from the fixed point

This fixed point is called the center of the circle and the distance of the centre to the circle is called radius

In the above figure O is the center of circle

OD is the radius of a circle

Chord The line segment joining the two points on a circle is called a chord. In the above figure AB is the chord and CD is also a chord

Diameter the chord passing through the center is called a diameter. CD is a diameter

Tangent A line segment which touch the circle at only one point is called a tangent. EF is a tangent in the above figure

Secant A line which intersect the circle at two points is called a secant. GH is a secant in the above figure

Some important results on circle

• The perpendicular from the center of a circle to a chord bisects the chord.
• The line joining the center of circle to the mid_ point of the chord is perpendicular to the chord.
• The perpendicular bisectors of two chords of a circle intersect at the center of a circle.
• The angle subtended by an arc of the circle at the center is double the angle subtended by it at the circle.
• Chords which are equidistant from the center of a circle are equal.
• Equal chords are equidistant from the center of a circle.
• Angle in a same segment of the circle are equal.
• Tangent is perpendicular to the line joining the center of the circle to the point of contact.
• Angle in a semi_circle is 90°.
• Through a single point, an infinite number of circle can be drawn.
• Through two points , an infinite number of circles can be drawn.
• Through three-col-linear points, a unique circle can be drawn.

Practice Question on Geometry for SSC Exam

## SSC CGL Tier 1 Aptitude questions answer 31st August 3rd Shift

Below are questions from SSC CGL Tier 1 Aptitude  questions answer 31st August 3rd Shift which have been taken from few best SSC coaching students of Noida. These questions are memory based.

1. If x + 1/x 0,  x2 + 1/x2 = 1  and x3 + 1/x3 = 0 , then the value of ( x + 1/x) ^4 is equal to

Solution (x + 1/x )^4 = (x + 1/x)^3 (x + 1/x)

= (x^3 + 1/ x^3 + 3(x + 1/x ) ) (x + 1/x)

= 3 (x + 1/x)^2

= 3 ( x2 + 1/x2 + 2 )

= 3( 1 + 2 ) = 9

1. If principal of Rs. 3000 amounts to 6000 in 2 years on C.I. , then how much it will amount in 4 years ?

Solution  6000 = 3000(1 + r/100)^2

(1 + r/100)^2 = 2

Amount = 3000(1+ r/100)^4

= 3000((1+ r/100)^2)^2

= 3000*2^2 = 3000*4 = 12000

1. If the marked price of an article is 900 and two successive discounts of 10% and 20% are given, then the selling price of the article is

Solution selling price = 9008010090100

= 9*9*8 = 648

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1. If 5 man can make 5 mats in 10 days then how many mats can be made by 10 men in 10 days ?

Solution M1 =5, W1 = 5, D1 = 10 days

M2 = 10, W2 = ?, D2 = 10 days

M1 W2 D1  = M2 W1 D2

5*W2*10 = 10*5*10

W2 = 10

1. If 3rd day of a month is TUESDAY , then the 25th day of that month is

Solution since 3 + 7*3 = 24

So 24th day is TUESDAY

Hence 25th day is WEDNESDAY

Directions (6 _ 10) read the pie chart carefully and answer the question below

Marks scored by A,B,C and D in an exam is given by the sector angle and total marks of A,B,C and D are 150

1. Find the average marks of A, B, C and D
2. What is the marks of A
3. What is the ratio of D to the average marks of A,B and C
4. Find the difference between the marks of D and B
5. How much more marks A got than B

Solution complete angle of pie chart = 360

Marks of A = 108360150 = 45

Marks of B = 72360150 = 30

Marks of C = 60360150 = 25

Marks of D = 120360150  = 50

Answer 6 average marks = total marks / no. of  students

= 150 / 4 = 37.5

Answer 7 marks of A = 45

Answer 8  marks of D = 50

Marks of A + B + C = 100

Ratio  = 50 / 100 = 1 : 2

Answer 9 difference between the marks of B and D = 50 – 30 = 20

Answer 10  A – B =  45 – 30 = 15

1. If orthocentre of a triangle lies on one of its side, then the circumcentre of  this triangle lies
1. Inside the triangle
2. Outside the triangle
3. on the other side
4. On the same side

Solution when the orthocentre of a triangle lies on its side, then there is a right angled triangle

In right angled triangle circumcentre lies on the hypotenuse.

All above questions have been taken from students who appeared for SSC CGL Tier 1 exam on 31st August 3 rd shift.  Students of coaching like Plutus academy , Vidyaguru etc took part in this activity.

# Ssc cgl aptitude questions solution Evening shift held on 29th August Tier 1

Below we have tried to give questions which were asked in Ssc cgl aptitude questions solution with Solution Evening shift. These questions have been taken on memory base. As exams are computer based, students forget few numbers and then those numbers are verified with other students. We have tried to bring out maximum number of questions of aptitude from best ssc coaching students. Few questions came in exam from notes of ssc coaching. Although these questions are considered to be very easy for students preparing for Bank PO exam but then even students from best bank PO coaching prefer solving these questions

1. The sum of a number and it’s reciprocal is 2. Find the number

Options : 1,0,-1, none

Solution let the number be x

Its reciprocal = 1/x

X + 1/x = 2

x2+1 – 2x = 0

(x – 1)2 = 0

x= 1

1. A train crosses a 50 m long platform in 14 seconds and a pole in 10 seconds find speed of train in Kmph

Solution the train covers 50 m in 4 seconds

Speed = 501560/1000 kmph

= 45 kmph

1. Two ships are sailing in a river on opposite side of a tower having height of 100 m. The angle of elevations for both the shifts are 30° and 60°. Find the distance between the ship.

Solution One ship is B and another ship is C

100 / BD = 3

BD= 100/ 3

Similarly

100/CD = 1/3

CD = 100*3

BD + CD = 100/3 + 100*3

= 400/3

4) 9x^2+16^y2=60

3x+4y=10

Find xy

Solution 3x + 4y = 10

Squaring on both sides

9x^2 + 16y^2 + 24xy = 100

60 + 24xy = 100

24xy = 40

Xy = 40/24 = 5/3

5) Rs. 2000 amounts to Rs. 4000 in two years on CI. In how much time will it be Rs. 8000?.

6 years

8 years

4 years

None

Solution 4000 = 2000(1 + r/100)^2

(1 + r/100)^2 = 2

8000 = 2000(1+ r/100)^t

(1+ r/100)^t = 4

(1+ r/100)^2)^t/2 = 4

2*t/2 = 4

T = 4

6) x^2+1/x^2=2 find x-1/x

Solution (x – 1/x )^2 =  x^2+1/x^2 – 2

= 2-2 = 0

X – 1/x = 0

7) A completes work in 15 days and B In 20 days. They agree to do the work together for Rs. 450. Find share of A

Solution efficiency ratio of A and B = 20 : 15

= 4:3

Share of A = (450/4+3)*4

= 1800/7

8) In triangle ABC, AD is the median. O is a point on AD which is the centroid. Ratio AO:OD is?

1. Cos@/(1+sin@)+sin@/(1-sin@)=4

Find @

Ans 60°

1. Avg salary of 19 employees is 40,000. If one more employee joins them the avg salary becomes 44000. Find that newly joined employee’s salary

Solution average salary of 19 employees increased by 4000

It means that newly joined employees salary is 76,000 more than the new average salary

His salary = 76,000+ 44,000 = 1,20,000

1. If the CP of an article is decreased by 10%. How much should new CP be increased so that the profit remains same

Solution new cp increased = 10*100/ 100-10

= 1000/90 = 11.11%

1. Cost of a piece of cloth is Rs. 32 per metre. A shopkeeper announces 25% discount. If any customer wants to have benefit of Rs. 40 then what length of the cloth he should purchase?

Solution discount on 1m = 32*25/100 = 8m

Discount on 5 m = 8*5 = 40m

1. Ratio of investments made by A and B is 1/3:1/5. They together invested Rs. 960. Find the share of each.

Answer A share = 600    and     B Share = 360

Solution A:B = 1/3 : 1/5

= 5:3

Share of A = (960/8)*5 = 600

Share of B = 960-600 = 360

1. Area of rectangle is 60 sq m and its perimeter is 34. Find the length of its diagonal

Solution area = xy = 60

Perimeter = 2(x + y) = 34

X + y = 17

Squaring on both sides

x^2 + y^2 + 2xy = 289

x^2 + y^2 + 120 = 289

x^2 + y^2 = 169

Diagonal = 169^½

= 13

1. In a circle a chord AB is drawn O is the center of the circle. Radius of circle is 10 cm Length of Chord AB is 16 cm. Find length of OD, where OD is a perpendicular on the chord AB

Solution OD^2 + BD^2 = OB^2

OD^2 = 100 – 64 = 36

OD^2 = 6

29 august _ shift 1

1. If you divide Rs. 960 among A and B in the ratio 1/2:1/3 then what is the difference in their share?

Solution A:B = 1/3 : 1/5

= 5:3

Share of A = (960/8)*5 = 600

Share of B = 960-600 = 360

Their difference = 600 – 360 = 240

1. Average marks of 20 students in a class is 35. If one student’s marks were misread as 85 instead of 45, what is the original average of the class?

Solution If one student’s marks were misread as 85 instead of 45 it means that the sum of total marks of all students increased by 40

So average increased by 40/20 = 2

Original average = 35- 2 = 33

1. If tan (x – 15 ) = 3, then x = ?