Question Set A

cbse 6th Standard Mathematics Decimals Important Questions And Answers Study Material - QB365

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Questions:

Generic 5

7 x 5 = 35

Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement.

Neha's mom bought 4 kgs 700 g of carrots, 7 kg 45 g of tomatoes, 6 kg 85 g of potatoes. While coming back from market vegetable of weight 2 kg 460 g fall from the packet. What quantity of vegetables are left with her?

Raina pays Rs 7500 as rent for 5 months. How much money does she has to pay for the whole year, if rent per month remains the same?

Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850 g flour. Find the total weight of his purchases.

(a) Take Sarita's present age to be y yr.
(i) What will be her age 5 yr from now?
(ii) What was her age 3 yr back?
(iii) Sarita's grandfather is 6 times her age. What is the age of her grandfather?
(iv) Grandmother is 2 yr younger than grandfather. What is grandmother's age?
(v) Sarita's father's age is 5 yr more than 3 times Sarita's age. What is her father's age?

Avneet buys 9 square paving slabs, each with a side of \(\frac{1}{2}\) m. He lays them in the form of a square.

(a) What is the perimeter of his arrangement in the figure(i)?
(b) Shari does not like his arrangement. She gets him to lay them out like a cross. What is the perimeter of her arrangement in the figure (ii)?
(c) Which has greater perimeter?
(d) Avneet wonders, if there is a way of getting an even greater perimeter. Can you find a way of doing this? (The paving slabs must meet along complete edges i.e. they cannot be broken.)

Ravi and Raju measured the length of their pencils.Ravi's pencil was 7 cm and 5 mm long and Raju'spencil was 8 cm and 3 mm long. Write the lengths of Ravi's and Raju's pencil (in cm) using decimals.

Generic 3

9 x 3 = 27

Draw a line segment \(\bar{AB}\) of length 5 cm. Take a point P on it. Through P, draw a perpendicular to AB. (using ruler and compasses).

The pocket money of A B and C are Rs 600, Rs 500 and Rs 550, respectively. Find the
(a) ratio of pocket money of A to that of B.
(b) ratio of pocket money of A to that of C.

10.

17 bags of cement costs Rs.1675.50. How many bags of cement can be bought for Rs.1182?

11.

A carpet measures 30.75 cm by 80 cm. Find its cost at the rate of Rs. 15 per square metre.

12.

Simplify 53.5 - 34.68 + 64.75 - 28.9.

13.

Three squares are joined together as shown in figure. Their sides are 4 cm, 10 cm and 3 cm. Find the perimeter of the figure.

14.

A floor is 6 m long and 5 m wide. How many tiles whose length and breadth are 10 cm and 6 cm respectively are needed to cover the floor?

15.

Complete the table and by inspection of the table, find the solution to the equation m+ 10 = 16.

m+10

16.

Following pictograph represents some surnames of people listed in the telephone directory of a city.

Observe the pictograph and answer the following questions:
(a) How many people have surname 'Roy'?
(b) Which surname appears the maximum number of times in the telephone directory?
(c) Which surname appears the least number of times in the telephone directory?
(d) Which two surnames appear an equal number of times?

Generic 2

11 x 2 = 22

17.

Mahesh spent Rs.30.55 tor Mathematics book and Rs.20.34 tor Science book. Find the total amount spent by Mahesh

18.

Draw a line segment \(\bar{AB}\) of length 8 cm. Draw its perpendicular bisector. Is it a line of symmetry.

19.

3 dozen pens cost is Rs.72.How much 2 dozen pens cost?

20.

The weight of a cylinder filled with gas is 30 kg. If the weight of the empty cylinder is 14 kg 80 g. Find the weight of the gas contained in it

21.

Express as metre using decimals.
25 m 17 cm

22.

7 times of y is subtracted from 40.

23.

If the area of a square is 36 cm², then find its perimeter.

24.

Find the areas of the following figures by counting square.

25.

A piece of wire is 12 cm long. What will be the length of each side, if the wire is used to form a regular hexagon?

26.

Find the perimeter of the following shapes.
An equilateral triangle of side 9 cm

27.

Find the rule, which gives the number of matchsticks required to make the following matchstick patterns. A pattern of letter B as

Multiple Choice Question

16 x 1 = 16

28.

The fare for 5 tickets from Kosi Kalan to Mathura is Rs. 150. The fare for 3 tickets is

(a)

Rs. 90

(b)

Rs. 60

(c)

Rs. 75

(d)

Rs. 45

29.

The ratio of 25 minutes to 1 hour is

(a)

7:5

(b)

5:12

(c)

12:5

(d)

5:7

30.

In a family, there are 8 males and 4 females. The ratio of the number of females to the number of males is

(a)

1:2

(b)

1:4

(c)

1:8

(d)

2:1

31.

\(12+\cfrac { 2 }{ 10 } +\cfrac { 4 }{ 1000 } =\)

(a)

12.204

(b)

12.024

(c)

12.402

(d)

12.240.

32.

3-tenths =

(a)

0.3

(b)

0.03

(c)

0.003

(d)

0.0003.

33.

If Apala's present age is x years, what will be her age in years after 20 years from now?

(a)

x-20

(b)

x-20

(c)

\(\frac { x }{ 20 } \)

(d)

20x

34.

Which of the following is an expression with numbers only?

(a)

x+1

(b)

(c)

1-x

(d)

35.

The rule, which gives the number of matchsticks required to make the matchstick pattern E, is

(a)

(b)

(c)

(d)

5 n

36.

Which of the following letters has no line of symmetry?

(a)

(b)

(c)

(d)

37.

The area of the figure

(a)

5 sq. unit

(b)

9 sq. unit

(c)

7 sq. unit

(d)

8. sq. unit

38.

Perimeter of a regular pentagon =

(a)

4 x Length of a side

(b)

3 x Length of a side

(c)

6 x Length of a side

(d)

5 x Length of a side.

39.

Margarette works in a factory and earns Rs.955 per month. She saves Rs.185 per month from her earnings. Find the ratio of her income to her expenditure.

(a)

154: 37

(b)

191: 37

(c)

191:154

(d)

37:191

40.

23.564 correct to the tenths place is

(a)

(b)

23.55

(c)

23.6

(d)

23.76

41.

The perimeter of a square, whose each side is 1m 30cm 10 mm, is

(a)

5.4 m

(b)

5.14 m

(c)

5.24 m

(d)

5.04 m

42.

If x takes the value 3, then x + 12 is

(a)

(b)

(c)

(d)

43.

The choices of the fruits of 42 students in a class are as follows.
A, O, B, M, A, G, B, G, A, G, B, M, A, G, M, A, B, G, M, B, A, O, M, O, G, B, O, M, G, A, A, B, M, O, M, G, B, A, M, O, M, O
Where A, B, G, M and O stand for the fruits Apple, Banana, Grapes, Mango and Orange respectively. Which fruit is liked by most of the students?

(a)

(b)

(c)

(d)

Fill up / 1 Marks

6 x 1 = 6

44.

A ratio expressed in lowest form has no common factor other than ______________ in its terms.

45.

The line of symmetry of a line segment is the __________ bisector of the line segment.

46.

The value of 3.64 - 1.28 is ____________

47.

Standard unit of area is ------

48.

m exceeds n by 10 can be expressed as ________

49.

The tally marks represent __________.

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Answers Key:

Generic 5

7 x 5 = 35

Step 1. Draw a line segment \(\bar { AB } \) of length 12.8 cm.
Step 2. With A as centre, using compass, draw two arcs on either side of AB. The radius of this arc should be more than half of the length of \(\bar { AB } \).
Step 3. With the same radius and with B as centre, draw another arc using compass. Let it cut the previous arc at C and D.
Step 4. Join \(\bar { CD } \). It cuts \(\bar { AB } \) at E. Then \(\bar { CD } \) is the perpendicular bisector of the line segment \(\bar { AB } \).
Step 5. With A as centre, using compass, draw a circle. The radius of this circle should be more than half of the length of AE.
Step 6. With the same radius and with E as centre, draw another circle using compass. Let it cut the previous circle at F and G.
Step 7. Join \(\bar {FG} \) . It cuts \(\bar {AE} \) at H. Then \(\bar {FG} \) is the perpendicular bisector of the line segment \(\bar {AE} \).
Step 8. With E as centre, using compass, draw a circle. The radius of this circle should be more than half of the length of EB.
Step 9. With the same radius and with B as centre, draw another circle using compass. Let it cut the previous circle at I and J.
Step 10. Join \(\bar {IJ} \) It cuts \(\bar {EB} \) at K. Then \(\bar {IJ} \) is the perpendicular bisector of the line segment \(\bar {EB} \).
Now, the points H, E and K divide AB into four equal parts, i.e.,
\(\bar { AH } =\bar { HE } =\bar { EK } =\bar { KB } \)
By measurement,
\(\bar { AH } =\bar { HE } =\bar { EK } =\bar { KB } \)=3.2 cm.

15.37 kg

Rs 18000

Weight of rice purchased by Ravi
= 5 kg 400 g = 5 kg + 400 g
\(= 5 kg+ 400\times{1\over 1000}kg\) \(\begin{bmatrix} \because 1\ g={1\over 1000} kg\end{bmatrix}\)
\(=5\ kg+{400\over1000}\)kg = (5+ 0.400) kg = 5.400 kg
Weight of sugar purchased by Ravi
= 2 kg 20 g = 2 kg+ 20 g
\(= 2 kg+ 20\times{1\over1000}kg\) \(\begin{bmatrix} \because 1\ g={1\over 1000} kg\end{bmatrix}\)
\(=2\ kg+{20\over1000}kg\) = (2+ 0.020) kg = 2.020 kg
Weight of flour purchased by Ravi
= 10 kg 850 g = 10 kg + 850 g
\(=10\ kg+850\times{1\over 1000}kg\) \(\begin{bmatrix} \because 1\ g={1\over 1000} kg\end{bmatrix}\)
\(=10\ kg+{850\over1000}kg\) (10 + 0.850) kg = 10.850 kg
\(\therefore\) Total weight of his purchases
\(\quad5.400\\\quad2.020\\+10.850\\\_\_\_\_\_\_\_\_\\\ \ 18.270\\\_\_\_\_\_\_\_\_\)

Hence, the total weight of all his purchases is 18.270 kg.

Let Sarita's present age = y yr
(i) Sarita's age after 5 yr from now = (y + 5) yr
(ii) Sarita's age 3 yr back = (y - 3) yr
(iii) Given, Sarita's grandfather is 6 times of her age So,
Sarita's grandfather age = 6\(\times\)Sarita's present age =6\(\times\)y=6yyr
(iv) Given, grandmother is 2 yr younger than grandfather. Age of grandfather = 6y yr [from (iii)]
∴ Age of grandmother = [Grandfather's age - 2] yr =(6y-2)yr
(v) Given, Sarita's father's age is 5 yr more than 3 times Sarita's age.
Sarita's present age =y yr
3 times of Sarita's age = 3y yr
∴ Sarita's father age = 3\(\times\)Sarita's age + 5 = (3y + 5) yr

(a) Avneet lays 9 squares in the form of a square as shown in the figure, then side of the square
\(=\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) m=\frac { 1+1+1 }{ 2 } =\frac { 3 }{ 2 } m\)
\(=\left( \frac { 1 }{ 2 } +1+1+\frac { 1 }{ 2 } +1+1+\frac { 1 }{ 2 } +1+1+\frac { 1 }{ 2 } +1+1 \right) m\)
∴ Perimeter of Avneet's arrangement
= 4 \(\times\) Length of a side = 4 \(\times\) \(\frac{3}{2}\) = 6 m
Hence, the perimeter of Avneet's arrangement is 6 m.
(b) Shari lays 9 squares in the form of a cross as shown in figure, then
Perimeter of Shari's arrangement = Sum of all sides

= AB + BC + CD + DE + EF + FG + GH + HI + IJ + JK + KL+ LA
\(=\frac { 1 }{ 2 } +\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) +\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) +\frac { 1 }{ 2 } +\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) +\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) +\frac { 1 }{ 2 } +\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) +\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) +\frac { 1 }{ 2 } +\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) +\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) \)
\(=\left( \frac { 1 }{ 2 } +1+1+\frac { 1 }{ 2 } +1+1+\frac { 1 }{ 2 } +1+1+\frac { 1 }{ 2 } +1+1 \right) m\)
\(=\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } +8 \right) m=(1+1+8)m=10m\)
Hence, the perimeter of Shari's arrangement is 10m
(c) From above, it is clear that Shari's arrangement i.e, a cross has greater perimeter.
(d) Yes, there is a way shown alongside in which we get a greater perimeter.
Here, we have arrange the 9 squares in the form of a rectangle

Now, length of rectangle
\(=\left( \frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } +\frac { 1 }{ 2 } \right) m=\frac { 9 }{ 2 } m\)
and breadth of rectangle = 1/ 2 m
∴ Perimeter of this rectangle = 2 \(\times\)(Length + Breadth
\(=2\times \left( \frac { 9 }{ 2 } +\frac { 1 }{ 2 } \right) =2\times \left( \frac { 9+1 }{ 2 } \right) \)
\(=2\times \frac { 10 }{ 2 } =10m\)
It is clear that, it has the perimeter equal to cross. So, we can say that cross has greater perimeter comparison to square.

Given, length of Ravi's pencil = 7 cm 5 mm
and length of Raju's pencil = 8 cm 3 mm
We know that, 10 mm = 1cm
\(\therefore\)1 mm = \(\frac { 1 }{ 10 } \) cm or one-tenth cm = 0.1 cm
Now, length of Ravi's pencil = 7 cm 5 mm
= 7 cm and 5 tenths cm
= 7cm + \(\frac { 5 }{ 10 } \) cm
= 7 crn+ 0.5 cm = 7.5 cm
and length of Raju's pencil = 8 cm 3 mm
= 8 cm and 3 tenths cm
=8 cm + \(\frac { 3 }{ 10 } \)cm=8 cm + 0.3 cm = 8.3 cm

Generic 3

9 x 3 = 27

Steps of construction are as follows:
Step I Draw a line segment \(\bar{AB}\) of length 5 cm.
Step II Take a point P and place the pointer of compasses at P draw an arc such that it intersects \(\bar{AB}\) at X and Y.

Step III With X and Y as centres and radius greater than \(\bar{PX}\), draw two arcs such that they intersect at C.
Step IV Join CP Thus, \(\bar{CP}\bot\bar{AB}\)

(a) 6 : 5
(b) 12 : 11

10.

In Rs.1675.50, number of bag purchased = 17
In Rs.1, number of bag purchased \(=\frac{17}{1675.50}\)
In Rs.1182, number of bags purchased \(=\frac{1182\times17}{1675.50}\)
=12 (approx.)

11.

Rs.369

12.

Converting the given decimals into like decimals
we get
53.5 - 34.68 + 64.75 - 28.9
= (53.50 + 64.75)-(34.68 + 28.90)
= 118.25 - 63.58
= 54.67

13.

Given. sides of three squares are 4 cm, 10 cm and 3 cm, respectively.
Total perimeter of given squares
= Sum of all outer sides of the figure
=4+ 4+ 4+ 6+10+ 1+ 3+ 3+ 3+10
=54cm

14.

5000

15.

The complete table is shown below

m	m+10
1	1+10=11
2	2+10=12
3	3+10=13
4	4+10=14
5	5+10=15
6	6+10=16
7	7+10=17
8	8+10=18
9	9+10=19
10	10+10=20
11	11+10=21
12	12+10=22
13	13+10=23

By inspection of the above table, we see that m=6 satisfies the equation m + 10 = 16.
[∵ at m=6, LHS=RHS]

16.

(a) The number of people having surname 'Roy' are 400. Because in the given pictograph, the picture symbol represents 100 people.
(b) Surname 'Patel' appears maximum number of times. Because in the given pictograph, the picture symbol represents 100 people. According to this, surname Patel appears 500 times.
(c) The surname 'Saikia' appears the least number of times. Because in the given pictograph, the picture symbol represents 100 people. According to this, surname 'Saikia' appears 200 times.
(d) The surname 'Rao' and 'Roy' appears an equal number of times.

Generic 2

11 x 2 = 22

17.

Money spent for Mathematics book = Rs.30.55 and money spent for Science book = Rs.20.54
ஃ Total amount spent = 30.55 + 20.54 = ~ 51.09

18.

Yes.

19.

Cost of 3 dozen pens = Rs.72
Cost of 1 dozen pens \(=\frac{72}{3}=Rs.24\)
\(\therefore\) Cost of 2 dozen pens = 2 x 24 = Rs.48

20.

15.920 kg

21.

25.17 m

22.

40-7y

23.

Given, area = 36 cm
Area = Side \(\times\) Side
36 = Side \(\times\) Side
⇒ side \(\times\) side = 6 \(\times\) 6
Side = 6 cm
∴ Perimeter = 4 \(\times\) Side = 4 \(\times\) 6= 24 cm

24.

Given, figure is covered by 2 full squares and 4 half squares.
∴ Area = \(\left( 2\times 1+4\times \frac { 1 }{ 2 } \right) sq\quad units\)
= (2 + 2) sq units = 4 sq units

25.

2 cm

26.

The perimeter of a triangle is 27 cm

27.

Multiple Choice Question

16 x 1 = 16

28.

\(\frac { 150 }{ 5 } \times 3\) = 90

29.

1 hour = 60 minutes
25:60 = \(\frac { 25 }{ 60 } =\frac { 5 }{ 12 } \) = 5:12

30.

\(\frac { 4 }{ 8 } =\frac { 1 }{ 2 } \)= 1:2

31.

(a)
12.204

32.

(a)
0.3

33.

(a)
x-20

34.

(d)
3

35.

(d)
5 n

36.

(a)
P

37.

Area = 3 x -\(\frac{1}{2}\)+1x2+3x\(\frac{1}{2}\)=5

38.

(d)
5 x Length of a side.

39.

40.

41.

42.

(d)
15

43.

Fill up / 1 Marks

6 x 1 = 6

44.

()
1

45.

()
perpendicular

46.

()
2.36

47.

We know that, standard unit of area is cm²or m².

48.

()
m=n+10

49.

()
13

cbse 6th Standard Mathematics Decimals Important Questions And Answers Study Material - QB365 Set A

QB365 Student Learing Managemnet System

Std: 6th Standard CBSE - Mathematics

chapter: Decimals - Important Questions And Answers

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Questions:

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Answers Key:

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