EduSahara™ Worksheet

Question 1

1.

40 is divided into two parts such that the sum of their reciprocals is
5
32
.

Find the two parts

(i)

(

32

,

8

)
(ii)

(

34

,

6

)
(iii)

(

33

,

7

)
(iv)

(

30

,

10

)
(v)

(

31

,

9

)

Question 2

2.

A number is of two digits. The digit in unit's place is the square of the digit in ten's place. The number formed by reversing the digits exceeds twice the number by 15 . Find the number

(i)

36
(ii)

42
(iii)

39
(iv)

38
(v)

40

Question 3

3.

In a two digit number, the unit's digit exceeds it ten's digit by 2 and the product of the given number and the sum of its digits is equal to 144 . Find the number

(i)

57
(ii)

46
(iii)

13
(iv)

24
(v)

35

Question 4

4.

The sum of the numerator and denominator of a fraction is
12
.

If
4
is added to both the numerator and denominator,

the fraction is increased by
8
77
. Find the fraction

(i)

3
7
(ii)

7
5
(iii)

5
7
(iv)

1

Question 5

5.

The denominator of a fraction exceeds the numerator by
3
.

The square of the fraction is equal to
1
4
. Find the fraction

(i)

1
2
(ii)

1
6
(iii)

5
6
(iv)

3
4
(v)

3
8

Question 6

6.

The area of a rectangular room is 44.00 sq.m. If the length and breadth are increased by 9 m, the area would become 260.00 sq.m. Find the original dimensions of the room

(i)

21.00 m , 2.10 m
(ii)

4.00 m , 11.00 m
(iii)

22.00 m , 2.00 m

Question 7

7.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 192 . Find the three numbers.

(i)

14, 15, 16
(ii)

15, 16, 17
(iii)

18, 19, 20
(iv)

13, 14, 15
(v)

16, 17, 18

Question 8

8.

A play field is
50.00 m
by
40.00 m
.
It has a road all around it on the outside.

Find the width of the road if its area is
13
5
of the area of the play field

(i)

19.00 m
(ii)

18.00 m
(iii)

22.00 m
(iv)

21.00 m
(v)

20.00 m

Question 9

9.

A stream flows from A to B, a distance of 14.00 km. A man who can row in still water at 9.00 kmph, can row up and down in 5.60 hr . What is the speed of the stream?

(i)

7.00 kmph
(ii)

8.00 kmph
(iii)

6.00 kmph
(iv)

5.00 kmph
(v)

4.00 kmph

Question 10

10.

The sum of the squares of two consecutive odd numbers is 514. Find the numbers

(i)
15

,

17

or

(-15)

,

(-17)
(ii)
16

,

18

or

(-16)

,

(-18)
(iii)
12

,

14

or

(-12)

,

(-14)
(iv)
18

,

19

or

(-18)

,

(-19)
(v)
14

,

16

or

(-14)

,

(-16)

Question 11

11.

Find the number which is less than its square by 30

(i)

5
(ii)

7
(iii)

4
(iv)

8
(v)

6

Question 12

12.

One pipe can fill a cistern in
1
hours less than the other.

The two pipes together can fill it in
6

6
25
hrs.

Find the time that each pipe will take to fill the cistern.

(i)

11 hr , 12 hr
(ii)

12 hr , 13 hr
(iii)

13 hr , 14 hr
(iv)

15 hr , 16 hr
(v)

10 hr , 10 hr

Question 13

13.

Find the number which exceeds its reciprocal by
2

2
3

(i)

4
(ii)

1
(iii)

6
(iv)

2
(v)

3

Question 14

14.

Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 320 . Find the three numbers.

(i)

21, 22, 23
(ii)

19, 20, 21
(iii)

17, 18, 19
(iv)

18, 19, 20
(v)

20, 21, 22

Question 15

15.

The sum of the squares of two consecutive even numbers is 452. Find the numbers

(i)
(-17)

,

(-15)

or

17

,

15
(ii)
(-13)

,

(-11)

or

13

,

11
(iii)
(-18)

,

(-17)

or

18

,

17
(iv)
(-16)

,

(-14)

or

16

,

14
(v)
(-15)

,

(-13)

or

15

,

13

Question 16

16.

The perimeter of a rectangular room is 104.00 m and the length of its diagonal is 38.47 m . Find the dimensions of the room

(i)

32.00 m , 20.00 m
(ii)

35.00 m , 17.00 m
(iii)

33.00 m , 19.00 m
(iv)

36.00 m , 16.00 m
(v)

34.00 m , 18.00 m

Question 17

17.

The perimeter of a rectangular room is 34.00 m and the length of its diagonal is 16.03 m . Find the dimensions of the room

(i)

14.00 m , 3.00 m
(ii)

15.00 m , 2.00 m
(iii)

16.00 m , 1.00 m
(iv)

17.00 m , 0.00 m
(v)

8.00 m , 9.00 m

Question 18

18.

Find two natural numbers which differ by 13 and the sum of whose squares is 3365

(i)

(

34

,

47

)
(ii)

(

37

,

50

)
(iii)

(

35

,

48

)
(iv)

(

33

,

46

)
(v)

(

32

,

44

)

Question 19

19.

A can do a work in
x
days and B can do it in
(

x

+

14

)
days.

Both of them working together can do it in
7

1
17
days. Calculate
x

(i)

11
(ii)

13
(iii)

8
(iv)

10
(v)

9

Question 20

20.

The sum of the ages of a father and his son is 41 years whereas five years ago, the product of their ages was 84. Find the current ages of the son and the father.

(i)

8 years , 33 years
(ii)

6 years , 35 years
(iii)

7 years , 34 years
(iv)

10 years , 31 years
(v)

9 years , 32 years

Question 21

21.

If the difference of two numbers is 9 and their product is 10, find the numbers

(i)
13

,

3

or

(-13)

,

(-3)
(ii)
10

,

1

or

(-10)

,

(-1)
(iii)
11

,

2

or

(-11)

,

(-2)
(iv)
8

,

(-1)

or

(-8)

,

1
(v)
9

,

0

or

(-9)

,

0

Question 22

22.

A two digit number is such that the product of the digits is 9. When 72 is added to the number, the digits are reversed. Find the number

(i)

22
(ii)

20
(iii)

19
(iv)

17
(v)

18

Question 23

23.

Twice the square of a number exceeds 4 times the number by 646. Find the number

(i)

(-18)
(ii)

(-20)
(iii)

(-17)
(iv)

(-14)
(v)

(-16)

Question 24

24.

The product of two consecutive even numbers is 360. Find the numbers

(i)

-21 , -19 or 21 , 19
(ii)

-22 , -21 or 22 , 21
(iii)

-18 , -15 or 18 , 15
(iv)

-20 , -18 or 20,18
(v)

-19 , -17 or 19 , 17

Question 25

25.

In a two digit number, the unit's digit exceeds it ten's digit by 2 and the product of the given number and the sum of its digits is equal to 1264 . Find the number

(i)

90
(ii)

57
(iii)

101
(iv)

68
(v)

79

Assignment Key