GANIT YADNYA 2020

CODE : 5T07A1E

Contributor: Mrs. Prajakti Gokhale

BODMAS PROBLEMS:

Simplify:

1. 2

3 - (

1

4+

1

5)

2. 4 1

2 +[

1

6+ (

1

4+

1

5)]

3. 5

6 + (

15

18 ×

6

9)

4. (51

2 × 1

1

2 ×

8

9) - (2

1

2 ×

3

4)

5. 21

2[(

3

4+

7

2) + (

11

2−

7

4)]

6. [51

2+ 2

3

4+ 1

3

4] ÷

2

3

7. 2

5÷

1

2 ×

9

15 ÷

1

19

8. (11

13 ÷

2

7) 𝑂𝐹 7

7

12− 1

3

5

9. 3

7 (

5

8+

2

11) −

5

6 (

2

3 −

1

4)

Word problems on fraction:

10. Add 1

7 to the sum of

5

8 and

11

16

11. If 3

4 th of tank is filled by water and capacity of tank is 524 liters

find how much more water can be filled in the tank to make it full.

12. The perimeter of rectangle is 20 c.m. The breadth of rectangle is

53

4 c.m. find the length of rectangle.

13. The length of cloth is 7 5

8 meters. Out of which 3 meters of cloth

was cut. Find the remaining cloth.

14. Find the product of 5 3

13 and 2

3

17 .

15. Divide 6 12

17 by 10

4

11

16. Out of 60 Rs. 5

6 th was spent on vegetables, how much is left?

17. The weight of one parcel was 79

11 Kilograms .Out of which 5

8

9

kilograms was delivered in a shop then how much weight is left?

18. Take the reciprocal of 5

7 and add it to

9

11 .

19. Arrange in descending order 2

11,

5

12,

3

13,

9

14

Direct Proportion

Rule: Product of means is equal to product of extremes

If a: b = c: d then ad = bc

20. Find the unknown number in given problems:

1 12 : 4 :: x : 8

2 64 : 16 :: 4 : x

3 35 : x :: 5 : 7

4 121 : 33 :: 11: x

5 91: 52 :: x : 13

6 x : 7.5 :: 5 : 2.5

7 12.2:6.1 : :x:18.3

8 30 : 70 :: 5 : x

9 1.02 : 1.7 :: 5.1 :x

10 100 : x :: 10 : 500

11 8.5 : 17 :: 5 : x

12 21

3 : 14 :: x :

1

3

13 512

: 24:: 15 : x

14 x : 9

10 :: 5 : 0.02

15 0.32: x:: 5: 8

13

Word Problems based on direct proportions:

21. If 15 k.gm rice can be purchased for 600 Rs. Find the price for 27

k.gm of rice.

22. A train covers 350 km in 4 hours. How many kilometres can be

covered in 12 hours?

23. There are 1200 trees in a park each year 5o new trees are planted.

Find how many total trees will be there in the park after 5 years from

now?

24. There are 50 students in the class,30 girls and 20 boys, girl

contributed 7Rs. Each for charity and boy contributed 8 Rs. Each for

charity find how much total amount they contributed together?

25. An airplane requires 300 litre of fuel to fly 1500 k.ms find how

much fuel is needed to fly 6000 kms.

26. There are average 7 faulty bulbs in every 17 crates of 100 bulbs

each, find total how many faulty bulbs will be there in 289 crates on

an average.

27. A moon’s gravity is 1/6th of earth, a person whose weight is 60

kilograms on earth, find his weight on moon.

28. A ray of light from the sun reaches earth in 8 minutes. If a planet

is 5 times away from sun than earth find how much time is required

for the ray of light from sun to reach that planet.

29. If a car travels at the constant velocity of 55kmph it covers 253km

in a certain period of time. If the constant velocity is increased to

60kmph, how much distance will be covered in the same amount of

time?

30. An alarm rings 4 times every 25 minutes, find how many times

it will ring in 3 hours?

Dividing given quantity in certain ratio

This is the most common application of ratio in everyday life like business,

partnership, geometry, formulating word problems and many more fields.

Steps to perform such problems:

● If a number is divided into a:b, then one part of the number is 𝒂

𝒂+𝒃 and the

other is 𝒃

𝒂+𝒃.

● Example:

Let’s divide 4000 Rs. In the ratio 7:3

• The total is 7 + 3 =10

▪ Hence first part and second part :

7

10 times 4000 =

7

10 × 4000 = 2800Rs.

3

10 times 4000 =

3

10 × 4000 = 1200 Rs.

▪ Thus, we have divided Rs. 4000 in the ratio 7:3 getting contribution as

Rs.2800 and Rs. 1200 respectively.

31. In following problems divide the quantity given in given ratio:

17500 in

ratio

5:9:6

4500 in ratio

5:3:1

52000 in

ratio

8:5:13

68000 in

ratio

4:5:8

2500 in the

ratio 2:3:5

Word problems on dividing quantities in given ratio

32. In a certain business, initially two partners invested RS. 17000

and Rs. 13000 respectively. They wanted to share their total profit

proportional to their investment, if the profit incurred is Rs.90000,

what will be the share of each partner?

33. Distribute 5000 Rs. In the ratio 4:1.

34. A certain map of a rectangular field shows dimensions 5 cm and

3 cm respectively, the actual field is 50m long and 30m wide, find the

scale by which the map is drawn?

35. Three medicines were mixed in the ratio 5:4:16, to prepare 500

liters of solution. Find the quantity of each medicine taken.

36. The average of two numbers is 78. If one of the numbers is 54,

find another number.

37. Distribute 4500 rupees in the ratio 4:2:1.

38. There was a rope 20 meters long. It has to be cut down in 3 parts

with ratio 4:5:1. Find the length of each part.

39. The lengths of triangle are in ratio 4:5:7, if the perimeter of

triangle is

960 cm. find the length of each side.

FRACTION COMPARISON WORKSHEET

42. . Which of the following fraction has numerator 5

a) 5

2

b) (c) (d)

40. Which of the following fraction as denominator8?

a. a) b) (c) (d) 41. What fraction does the shaded portion in the adjoining fig.

represents.

1.

b. a) b) (c) (d) 42. Which one of the following is a proper fraction?

a. a) b) (c) (d) 43. Which one of the following is improper fraction?

a. a) b) (c)

(d)

44. What is the value of +

a. a) b) (c) (d)

45. What is the value of +

a. a) b) (c) (d)

46. What is the value of + +

a. a) b) (c) (d)

47. What is the value of + +

a. a) b) (c)

(d)

48. What is the value of -

a. a) b) (c) (d)

49. What is the value of ̶

a. a) b) (c) (d) none of these

50. Which of the following drawing shows 2

i. a)

ii. b)

iii. c)

iv. d)

51. The value of of 24 is

a. a) 12 b) (c) 48

(d)

52. The product of gives

a. (a) (b) (c) (d)

53. The reciprocal of is

a. (a) (b) (c) (d)

54. The value of ÷7

8

a. (a) 4 (b) (c) (d)

55. The value of 3 is

a. (a) 4 (b) 13 (c) (d)

56. Which of the following is the least form of

a. (a) (b) (c) (d) 57. What is the sum of 5.300 and 3.250

a. (a) 8.550 (b) 85.50 (c) 5.6250 (d) 8550

58. What is the value of 29.35 ̶ 04.56

a. (a) 23.75 (b) 16.35 (c) 16.25 (d) 24.79

59. Which one of the following is greatest

a. (a) 5.0 (b) 0.5 (c) 0.005 (d) 0.05

60. Which one of the following is smallest

a. ( a) 2.031 (b) 2.301 (c) 0.2301 (d) 23.01

61. 7 Rupees 7 paisa can be written in rupees as

a. (a) Rs7.07 (b) Rs7.70 (c) Rs0.707 (d) Rs

770

62. 5 cm in Km can be written as

a. (a) 0.0005 (b) 0.00005 (c) 0.0005 (d) 0.05

63. The place of 2 in 21.38 is

a. (a) Ones (b) Tens (c) Tenth (d)

Hundredth

64.

Which one of the following represent the expansion

1. 2 +0 + 0 +3(-1)

b. (a) 20.03 (b) 2.03 (c) 200.03 (d) 2.034

65. The value of 2.71 is

a. (a) 135.5 (b) 1355 (c) 13.55 (d) 1.355

66. The product of 153.7 and 10 is

a. (a) 1.537 (b) 15.37 (c) 153.7 (d) 1537

67. The value of 43.07 is

a. (a) 4.307 (b) 4307 (c) 43.07 (d) 430.7

68. The value of 0.03 is

a. (a) 0.00003 (b) 3 (c) 0.003 (d)

30

69. The value of 1.3 is

a. (a) 403 (b) 0.403 (c) 4.03 (d)

0.0403

70. The value of 0.80 is

a. (a) 16 (b) 0.16 (c)

(d) 1.6

71. The value of 52.5 is

a. (a) 5.25 (b) 0.525 (c) 525 (d) 5250

72. The value of 0.78 is

a. (a) 7800 (b) 0.0078 (c) 0.78 (d) 7.8

73. The value of 26.3 is

a. (a) 0.0263 (b) 0.2630 (c) 26300 (d)

26.300

74. The value of 7.75 is

a. (a) 31 (b) 0.0031 (c) 0.31 (d)

3.1

Measuring Worksheet

Convert the measurements accordingly:-

75.

1a

. 2.6 kg = ___________ g

1b

. 12,128 g = ___________ kg

2a

. 3.62 cm = ___________ mm

2b

. 497 ml = ___________ L

3a

. 10.3 kg = ___________ g

3b

. 2.02 L = ___________ ml

5a

. 3.75 m = ___________ cm

5b

. 1,826 g = ___________ kg

6a

. 0.7 m = ___________ cm

6b

. 32 cm = ___________ m

7a

. 153 mm = ___________ cm

7b

. 1,970 ml = ___________ L

8a

. 1.4 m = ___________ cm

8b

. 4 mm = ___________ cm

9a

. 1.4 kg = ___________ g

9b

. 270 mm = ___________ cm

10a

. 40 mm = ___________ cm

10b

. 16,662 ml = ___________ L

Integer Worksheet:Addition

76.

1

a.

22 + (-9) =

____

1

b.

(-28) + (-10) =

____

1

c.

18 + (-17) =

____

2

a.

(-22) + 26 =

____

2

b.

(-11) + (-17) =

____

2

c.

(-1) + (-5) = ____

3

a.

12 + (-5) =

____

3

b.

29 + 29 = ____

3

c.

(-3) + (-26) =

____

4

a.

16 + 15 = ____

4

b.

(-18) + 19 = ____

4

c.

(-8) + (-12) =

____

5

a.

23 + 8 = ____

5

b.

2 + 12 = ____

5

c.

22 + 23 = ____

6

a.

25 + (-13) =

____

6

b.

22 + (-18) = ____

6

c.

13 + (-26) =

____

Integer Worksheet -Addition

77.

1

a.

(-19) + (-5) + 4 = ______

1

b.

(-3) + 10 + 5 = ______

2

a.

(-10) + (-10) + 7 = ______

2

b.

8 + 8 + (-7) = ______

3

a.

13 + 6 + 8 = ______

3

b.

(-13) + (-2) + (-4) = ______

4

a.

6 + 6 + 6 = ______

4

b.

(-6) + (-10) + (-1) = ______

5

a.

(-20) + 10 + (-4) = ______

5

b.

13 + (-5) + (-7) = ______

6

a.

6 + (-7) + 5 = ______

6

b.

(-14) + 4 + (-3) = ______

7

a.

18 + (-1) + 5 = ______

7

b.

(-3) + (-2) + (-7) = ______

8

a.

(-8) + (-8) + 7 = ______

8

b.

3 + 7 + 5 = ______

1

a.

___ + 6 = 1

1

b.

(-6) + ___ = (-16)

2

a.

___ + (-10) = (-11)

2

b.

___ + 7 = 1

3

a.

___ + 2 = (-3)

3

b.

___ + 1 = (-6)

4

a.

(-2) + ___ = (-5)

4

b.

0 + ___ = (-2)

5

a.

___ + (-10) = (-19)

5

b.

(-1) + ___ = (-4)

6

a.

___ + (-2) = (-6)

6

b.

___ + (-6) = (-15)

7

a.

___ + (-7) = (-9)

7

b.

___ + (-5) = (-7)

8

a.

(-1) + ___ = 8

8

b.

(-6) + ___ = (-2)

________________________________________________________________

1

a.

____ x 8 = (-

64)

1

b.

____ x 0 =

0

1

c.

____ x (-1) =

3

2

a.

____ x (-7) =

56

2

b.

0 x ____ =

0

2

c.

(-9) x ____ = (-

9)

3

a.

(-10) x ____ =

0

3

b.

____ x (-2) =

10

3

c.

(-9) x ____ =

18

4

a.

____ x 6 = (-

24)

4

b.

____ x (-5) =

25

4

c.

(-7) x ____ =

28

5

a.

8 x ____ =

64

5

b.

____ x (-8) =

56

5

c.

10 x ____ = (-

10)

6

a.

4 x ____ =

28

6

b.

____ x (-4) = (-

24)

6

c.

(-8) x ____ =

80

Division worksheet

78.

1

a.

49 ÷ ____ = (-7)

1

b.

____ ÷ (-7) = 2

2

a.

____ ÷ (-7) = 9

2

b.

____ ÷ 2 = 3

3

a.

____ ÷ 9 = (-8)

3

b.

21 ÷ ____ = 7

4

a.

14 ÷ ____ = (-7)

4

b.

30 ÷ ____ = (-10)

5

a.

6 ÷ ____ = (-1)

5

b.

____ ÷ (-10) = 1

6

a.

36 ÷ ____ = (-9)

6

b.

(-22) ÷ ____ = 2

7

a.

____ ÷ 10 = 3

7

b.

____ ÷ (-2) = (-10)

Contributor: Rashmi Sahastrabuddhe

79. The daily expenses of Suraj out of his weekly pocket-money of Rs.50 are as

under:

Day Mon Tue Wed Thurs Fri Sat Sun

Expense 12.50 7.30 9.00 10.20 8.50 0.50 -

a. Find out the sum of daily expenses

b. Suraj’s weekly savings are how many rupees?

80. A petrol tank of 50 litres is half filled. Jay gets another 1/5 of the tank filled.

What fraction of the tank is still empty?

81. Kamlabai buys vegetables weighing 12kgs. She buys 2kg 750gm of potatoes,

1kg 450gm tomatoes and the rest is onions. Find out the weight of onions?

82. A bicycle wheel has 24 spokes. Find the angle formed between a pair of

adjacent spokes.

83. How much be subtracted from (35×25) to get the value equal to 20000÷25?

Mrs. Purva Dhokte

84. How will you get number 100 using Four fives (5’s) and a one (1)?

85. The day before yesterday I was 13. Next year I will be 16. This is true only

one day in a year, what day is my birthday?

86. Milkman has 3 litre jar and 5 litre jar. How can he get 4 litres of milk using

3 litre and 5 litre jar?

87. For Rs 1 you get 20 bananas. For Rs 3 you get 1 apple and for Rs 5 you get

1 mango. Now you want to get 100 fruits for Rs 100. So how many bananas,

apples and mangoes will you buy?

88. Move any 4 match sticks to get 3 equilateral triangles only.

89. Simran drives 10km towards south from her town and turns left and

drives another 25kms. She again turns left and drives 40kms straight and then

turns right and drives for another 5kms to reach her village. Find the shortest

distance between her town and the village. Also, in which direction is the village

from her town.

90. Sameer decided to give Samosas to his friends on his birthday. If he

gives 3 samosas to each friend, one friend will only get 1 samosa. Also if he gives

2 samosas to each friend, he will be left with 13 samosas. How many samosas

Sameer got for his birthday? How many friends are there?

91. Your parents have six sons including you and each son has one sister.

How many people are in the family?

92. A + B = 76

A – B = 38

A / B = ?

93. Its 3.35. If the clock is rotated 90 degrees counter clockwise. What time

will it be?

Contributor: Swati Dharmadhikari

94. A vessel has 5 litres 500 millilitres of mango juice. In how many glasses each

of 50ml capacity

can it be filled?

95. Find 2 positives integers such as their product is 100000 and none of them

contains 0 as a digit.

96. There are four natural numbers less than 100, which have exactly 3 divisors.

One of them is 9, what are the other three? What can be said about these

numbers?

97. In a class 45% of the students are girls, if there are 36 girls in a class, how

many students are there in the class?

98. If 5 men can do certain work in 14 days, then how long will 7 men take to

do the same work?

99. If the lengths of 2 sides of an isosceles triangle are 3cm and 7cm then what

is the length of the third side?

100. How many envelopes of size 25cm × 15cm can be made from a rectangular

sheet of size 6m × 1.3m?

101. In the adjoining figure, find the area of shaded path which is 2 metre wide

all around.

102. In an examination, a student has to secure 45% marks to pass the exam. If

Sujata got 299 marks and failed by 16 marks, what are the maximum marks?

103. I read 49 of a book on one day and 3

5 of the remaining next day. If 100 pages

of the book were still left unread, how many pages did the book contain?

104. (5

12)8 × (

12

5)−4 = (

125

1728)𝑥. Find x.

105. If the cost of one metre cloth is Rs.125.50. Find the cost of 3.8 metre cloth.

106. Find the values of x, y and z:

107. An angle is 30° more than one-half of its complement. Find the angle in

degrees.

108. Find x:

109. How many times will the wheel of a car rotate in a journey of 88km, given that

the diameter of the wheel is 56 cm?

110. If a piece of wire is bent in the shape of an equilateral triangle of size 4.4cm. If

this wire is rebent to form a circle. Find the radius of the circle.

111. From a square cardboard, a circle of biggest area was cut out. IF the area of the

circle is 154cm². Calculate the original area of the cardboard.

[Hint: Side of a square board is equal to the diameter of the circle]

112. Nagma runs around a rectangular park 180m long and 120m wide at the rate of

7.5km/hr. In how much time will she complete 5 rounds?

113. The perimeter of a rectangular fiend is 214m. If its breadth is 34m, find its

length.

Contributor: Kiran Barve

114. Four bells ring at intervals of 3 ,7,12 & 14 mins respectively. All four bells

rang together at 12 noon. When will they ring together next time? *

a. A) 1:24 pm B) 12:24 min C) 2:24 pm D) 1 pm

115. 15 % of students of a school were absent on a specific day. If there were

1020 students present in the school that day, find the total number of students

in the school? A) 5780 B)1200 C) 1250 D) 1180

116. A man purchased 150 oranges at the rate of 3 oranges for 20 Rupees and

another 160 oranges for 4 oranges for 30 Rupees , and sold all of them , an

orange for 6 Rupee rate, whether he will have profit or loss , by what amount

?

117. A) Profit , Rupees. 120 B) Loss Rupees. 620 C) Profit , Rupees. 320

a. D) Loss, Rupees. 340

118. Three numbers are considered such that the cube of the first number

exceeds the product of all three numbers by 2, the cube of the second

number is smaller than the product by three and the cube of third number

exceeds the product by 3. Find those three numbers.

119. *A shopkeeper buys 11 pencils for Rs.10 and the same number at the rate of

9 for Rs.10. If each pencil is now sold for one rupee, find the gain or loss percent

of the whole transaction.

120. When a shopkeeper sells his vase at Rs.425 he makes profit. When he sells

the same vase for Rs.355 he experiences loss. If the amount of profit and loss in

the two cases is same. What is the cost of the article?

121. If J is 150 % of K, then K is what percent of (J + K)?

122. A gets 25% more wage than B, and B gets 20% more wage than C. The

share of C out of a sum of Rs.1480 is?

123. A shopkeeper gets 8% profit after selling a book at 10% discount on printed

price. If the discount is not given what will be the profit percentage?

124. x is a three-digit member such that x − 14 is divisible by 7, x − 22 is divisible

by 11 and x − 35 is divisible by 5. How many such three-digit numbers are

there?*

125. 48 meters long rope was cut 15 times to have pieces of equal length. What

will be the length of each piece?

126. Sum of two numbers A and B is 1800. If 8

15th of A and B are equal, find A?

127. Using the digits 3, 5, 7, 9 how many numbers divisible by 11 can be written

such that each number is greater than (Repetition of digits is not allowed)

128. Area of a regular hexagon ABCDEF is √123

Sq Cm. What is the area of a ∆

ABE.

129. x256 = (256)32 find x.

Contributor: Vinayak Godbole

131. a. How much is 1/4th of 120?

b. how much is 1/5th of 1/4th of 120?

c. How much is ½ of 1/3rd of 72

d. How much is 1/3rd of ½ of 72?

132. Fill in the blanks:

a. 70% of 300 = ……

b. 15% of 1000 = …..

c. 35% of 600 = ……

d. 614 % of 100 = …..

133. Monthly salary of a person is Rs.48000/-, he spends 15% on the house rent,

5% on entertainment, 8% on education and 62% on household expenses per

month. He deposits the remaining amount in a bank as savings. How much does

he spend on each head? How much does he save monthly? Yearly?

(To find his monthly savings is it necessary to find the expenses on each head)

134. Express the following ratios in the simplest form:

1) 63:28

2) 63:108

3) 8a:10a

4) 24ab:18ac

5) Rs.125: Rs.75

6) 2km:800m

135. Observe the adjacent map showing a house (H), a post office (P), a temple

(T) and a school (S) and the straight roads joining them; drawn to scale 1cm to

300m. The angles at P and T are right angles. Draw the figure on a paper and

find the distance between the house and the school.

136. Write the property of angles in a linear pair.

137. In the figure, lines PQ and RS intersect at point T. How many linear pairs

of angles are formed in the figure? Write all of them.

138.

a. In the figure in question 7 above, if angle mSTQ=85 find the measures of

all the remaining angles.

b. Are the angles in a linear pair always supplementary? Give reason.

c. If two angles from a supplementary pair, are they necessarily in a linear

pair? Give reasons.

139. There are 14 boys and 16 girls in a class going on an excursion. The

contribution per student is Rs.350.

1) Find the total contribution of all boys and all the girls separately.

2) Find the total of the contributions

3) Find the total number of students and then find the contribution from all them

4) Write your observations: There are ‘b’ boys and ‘c’ girls in a class going on an

excursion. The contribution per student is Rs. ‘a’. Follow the steps (1) to (4) in

question 11 above and understand the rule – a (b + c) = a × b + a × c

140. The side of a wooden square board is 80cm. Find its cost at the rate Rs.500

per square metre.

a. The population of a town is 120000 of which 49% are females. 85% of the

males are literate. Find the number of illiterate males on the town.

b. Aanandrao had a farm measuring 400m × 300m. In 7

16𝑡ℎ part of the farm

he cultivated sugarcane. He made 3 equal parts of the remaining land and

cultivated wheat jowar and gram in respectively each part. Find the area of

land he utilized for each crop.

c. The perimeter of a rectangular playground is 448m. if the ratio of its length

and its breadth is 5:3, find the area of the playground.

141. Write the correct sign of and = in the box.

a. 15% of 1000 ___ 30% of 500

b. 17% if 600 _____ 15% of 700

c. 35% of 1320 _____ 30% of 1600

d. 14% of 900 ______ 20% of 600

142. Mr.Gagarani invested Rs.120000 in a business and earned a profit of

Rs.28000. Mr.Ramani invested Rs.100000 in a business and earned a profit of

Rs.24000. Whose business was more profitable?

143. A Halwai prepared 25kg pedha which cost him Rs.240 per kg and 15kg of

barfi which cost him Rs.200 per kg. He sold the pedha at 40% profit but had a

loss of 10% in the sale of barfi. What was the percentage of gain in the whole

business?

144. In the given figure, seg AD, seg BE and seg CF are perpendicular to side

BC, side AC and side AB of ∆𝐴𝐵𝐶. If BC=20, AD=9, FC=12 and AC=18; find

AB and BE.

145. The monthly salary of Mr. Joseph was Rs.39750. The firm increased his

monthly salary by 4% because of his good performance. What was his salary for

the next month?

146. ∆𝐷𝐸𝐹 is an isosceles triangle. If m E=72 what are the measures of the

remaining 2 angles?

147. A 360m long train takes 18 seconds to pass a pole beside a track. What is

the speed of the train?

148. The lengths of train A and train B are 354m and 426m respectively. Their

speeds are 90km/hr and 72km/hr respectively. How long will it take for train A

to pass train B if:

1) They are travelling in opposite directions

2) They are travelling in the same direction

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