S.chand publication New Learning Composite mathematics solution of class 8 Chapter 4 Playing with Numbers Exercise 4C

 Exercise 4C

Question 1

Replace each letter with correct numeral

Sol :

Question 2

What should come in place of the question mark (?) in the following number series?

(a) 563  582  620  677  753  848  ?

(b) 17  17  51  255 1785  16065  ?

Sol 

Question 3

What is the value of x in figure III?

(a) 4 

(b) 16

(c) 25

(d) 36

Sol :

Question 4

In

the values f a and b are :

(a) 1 , 2

(b) 2 , 3

(c) 1 , 3

(d) None of these

Sol :

Question 5

The missing number is 

(a) 17

(b) 30

(c) 71

(d) 16

Sol :

Question 6

In a digital display which digit can display all 10 digits from 0 to 9

(a) nine 

(b) six

(c) zero

(d) eight

Sol :

Question 7

Complete the magic square so that the sum of the numbers in each row, each column and along the diagonals may be 15 .

Sol :

Question 8

Write the nine, non-repetitive digits in the circles of this triangle in such a way as to have a total of 20 on each side.

Sol :

Question 9

The magic hexagon has a total of 19 hexagons within it. All sets of 3,4 and 5 hexagons in a row add to 38 . Fill in the missing figures. No number should be repeated.

Sol :

Question 10

Rumours: Rumours spread very fast. Sometimes an incident witnessed by just a few person becomes becomes the talk of the town within less than two hours. Suppose a man comes at about 8 a.m. to a town with a population of about 50,000 and conveys an interesting news to just three persons. This takes up say 15 minutes. Within 2 hours it becomes a talk of the town. Show, how is it possible.

Sol :

At 8.15a m the news is come to know 4 persons. The news comer and 3 local peoples. Each of three peoples pass news to three other peoples and it takes 15min.

In half of an hour, the news is the common knowledge of 4+(3×3)=13 person

In their turn each of the person who have learn't the news last pass it to three other. By 8:45 am the news is know by =13+(3×9)=40 peoples

If it continues to spread. i.e if everyone who hers it passes it on to three others within the next 15min the result will be

By 9am ,the news will be known by=40+(3×27)=121

By 9:15am ,the news will be known by=121+(3×81)=121+183=364

By 9:30am ,the news will be known by=364+(3×243)=1093

By 9:45am ,the news will be known by=1093+(3×729)=3280

By 10am ,the news will be known by=3280+(3×2187)=9841

By 10:15am ,the news will be known by=9841+(3×6561)=29529

By 10:30am ,the news will be known by=29529+(3×19683)=88573

Question 11

Number patterns

0 x 9 = 1

1 x 9 + 2 = 11

12 x 9 + 3 = 111

123 x 9 + 4 = 1111

1234 x 9 + 5 = 11111

12345 x 9 + 6 = 111111

123456 x 9 + 7 = 1111111

1234567 x 9 + 8 = 11111111

12345678 x 9 + 9 = 111111111

123456789 x 9 + 10 = 1111111111

Investigate a similar number pattern where the first two line are:

1 x 8 = 9

12 x 8 + 2 = 98

Sol :

1×8+1=9

12×8+2=98

123×8+3=987

1234×8+4=9876

12345×8+5=98765

123456×8+6=987654

1234567×8+7=9876543

12345678×8+8=98765432

123456789×9+9=987654321

Question 12

Question 13

Do it yourself

Question 14

Blaise Pascal (1623 – 62) was a famous French mathematician and philosopher. One of his most important discoveries is known as Pascal’s Triangle. See if you can discover the secret of this pattern of numbers.

Solve.

(a) Write Row 8 of Pascal’s Triangle

Sol :

1, 7, 21 ,35 ,21 ,7 ,1

(b) Write Row 9 of Pascal’s Triangle.

Sol :

1, 8, 28 , 56 ,70 , 56 , 28 , 8 , 1

(c) Write Row 10 of Pascal’s Triangle.

Sol :

1, 9, 36 ,84 ,126 ,126 ,84 ,36 ,9 ,1

(d) What is the sum of the numbers in Row 1 of Pascal’s Triangle?

Sol :

1

(e) What is the sum of the numbers in Row 3 of Pascal’s Triangle?

Sol :

4=2²

(f) Find the sum of the numbers in Row 8 of Pascal’s Triangle without adding.

Sol :

2⁷=128

Question 15

Sudoku: Fill in the grid so that every horizontal row, every vertical column and every 3 x 3 box contains the digits 1 – 9, without repeating the numbers in the same row, column or box. You can’t change the digits already given in the grid.

			9	3
	7		5		8
9	2	4	1
	8					2	6
6			2		3			4
	3	5					7
					2	6	5	8
			6		1		2
				4	7

Sol :

8	5	6	9	3	4	7	1	2
1	7	3	5	2	8	9	4	6
9	2	4	1	7	6	3	8	5
4	8	9	7	1	5	2	6	3
6	1	7	2	8	3	5	9	4
2	3	5	4	6	9	6	7	1
7	4	1	3	9	2	6	5	8
3	9	8	6	5	1	4	2	7
5	6	2	8	4	7	1	3	9

Question 16

One way of expressing 10 as a combination of five 9’s is 9 + 99/99 = 10. Find the further ways of doing so.

Sol :

(i) $9+\frac{9}{9}=10$

(ii) $\left(99+\frac{99}{99}\right)-90=10$

(iii) $9+\frac{9\times 9}{9\times 9}=10$

(iv) $9+\left(\frac{9+9}{9+9}\right)=10$

(v) $\left(9+\frac{9}{9}\right)\times \frac{9}{9}=10$

Question 17

A clock takes three seconds to strike 3 O’clock. How long does it take to strike 6 O’clock?

Sol : 7.5 sec

Question 18

What is the smallest integer that can be written with two digits?

Sol :

$\frac{1}{1} ,\frac{2}{2} , \frac{3}{3} , \frac{4}{4}$ etc .......$\frac{9}{9}$

Question 19

Write 1 by using all the ten digits.

Sol :

$\frac{148}{296}+\frac{35}{70}=1$

other way

123456789⁰ , 234567^9-8-1 etc

Question 20

Write 10 with five 9s. Do it in at least two ways?

Sol :
$9\frac{99}{99}=10$ , $\frac{99}{9}-\frac{9}{9}=10$

Question 21

Write 100 by using all the ten digits.

Sol :

$=70+24\frac{9}{18}+5\frac{3}{6}=10$

$=50\frac{1}{2}+49\frac{38}{76}=100$

$87+9\frac{4}{5}+3\frac{12}{60}=100$

$80\frac{27}{54}+19\frac{3}{6}=100$

Question 22

Show four different ways of writing 100 with five identical digits.

Sol :
(i) (5+5+5+5)5=100
(ii) (5×5)+(5×5)+(5×5)+(5×5)=100

(iii) 111-11=100
(iv) $33\times 3+\frac{3}{3}=100$

Question 23

What is the biggest number that can be written with four 1s?

Sol :

11¹¹>1111

Question 24

Calculate the length of the strip of all the millimetre squares in one square metre, if placed one along side the other.

Sol :
1sqm=10000 thousand sqm

=(1000×1000)m²

It is placed one alongside the other will stretch out 1 meter .1000 thousand squares will therefore be 1000 meters long , i.e. 1 kilometre long 

Question 25

Calculate the height of a pole made of all the millimetre cubes in one cubic metre,  if placed one a top another​

Sol :

Number of cubes$=\frac{1000\times 1000\times 1000}{1}$

Height of 1 cube=1mm

Height of 1000000000 cubes=1000000000mm or 1000km