EduSahara™ Worksheet

Question 1

1.

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)

16, 17, 18
(ii)

18, 19, 20
(iii)

21, 22, 23
(iv)

20, 21, 22
(v)

19, 20, 21

Question 2

2.

A two digit number is such that the product of the digits is 24. When 18 is subtracted from the number, the digits are reversed. Find the number

(i)

64
(ii)

63
(iii)

62
(iv)

66
(v)

65

Question 3

3.

The sum of the numerator and denominator of a fraction is
13
.

If
6
is added to both the numerator and denominator,

the fraction is increased by
11
36
. Find the fraction

(i)

1
10
(ii)

1
12
(iii)

(
-1
12
)
(iv)

12
1
(v)

1
4

Question 4

4.

Find two natural numbers which differ by 11 and the sum of whose squares is 5365

(i)

(

46

,

57

)
(ii)

(

48

,

59

)
(iii)

(

47

,

58

)
(iv)

(

45

,

56

)
(v)

(

43

,

54

)

Question 5

5.

The sum of the squares of two consecutive even numbers is 340. Find the numbers

(i)
(-15)

,

(-13)

or

15

,

13
(ii)
(-16)

,

(-14)

or

16

,

14
(iii)
(-13)

,

(-11)

or

13

,

11
(iv)
(-11)

,

(-10)

or

11

,

10
(v)
(-14)

,

(-12)

or

14

,

12

Question 6

6.

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

x

−

3

)
days.

Both of them working together can do it in
7

5
29
days. Calculate
x

(i)

15
(ii)

17
(iii)

16
(iv)

13
(v)

19

Question 7

7.

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 (-6) . Find the number

(i)

21
(ii)

24
(iii)

23
(iv)

25
(v)

26

Question 8

8.

The denominator of a fraction exceeds the numerator by
2
.

The square of the fraction is equal to
64
81
. Find the fraction

(i)

1
(ii)

8
9
(iii)

4
5
(iv)

7
9

Question 9

9.

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

The two pipes together can fill it in
4

4
17
hrs.

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

(i)

8 hr , 9 hr
(ii)

7 hr , 8 hr
(iii)

10 hr , 11 hr
(iv)

6 hr , 6 hr
(v)

9 hr , 10 hr

Question 10

10.

The area of a rectangular room is 40.00 sq.m. If the length and breadth are increased by 9 m, the area would become 238.00 sq.m. Find the original dimensions of the room

(i)

8.00 m , 5.00 m
(ii)

10.00 m , 4.00 m
(iii)

9.00 m , 4.44 m
(iv)

4.00 m , 10.00 m
(v)

3.00 m , 13.33 m

Question 11

11.

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

Find the width of the road if its area is
17
7
of the area of the play field

(i)

27.00 m
(ii)

26.00 m
(iii)

25.00 m
(iv)

23.00 m
(v)

24.00 m

Question 12

12.

Find the number which is less than its square by 182

(i)

11
(ii)

14
(iii)

17
(iv)

15
(v)

13

Question 13

13.

Twice the square of a number exceeds 2 times the number by 60. Find the number

(i)

(-3)
(ii)

(-7)
(iii)

(-5)
(iv)

(-4)
(v)

(-6)

Question 14

14.

The sum of the ages of a father and his son is 44 years whereas two years ago, the product of their ages was 279. Find the current ages of the son and the father.

(i)

9 years , 35 years
(ii)

11 years , 33 years
(iii)

13 years , 31 years
(iv)

12 years , 32 years
(v)

10 years , 34 years

Question 15

15.

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)

4.00 kmph
(ii)

7.00 kmph
(iii)

8.00 kmph
(iv)

5.00 kmph
(v)

6.00 kmph

Question 16

16.

The area of a rectangular room is 104.00 sq.m. If the length and breadth are increased by 10 m, the area would become 504.00 sq.m. Find the original dimensions of the room

(i)

8.00 m , 13.00 m
(ii)

13.00 m , 8.00 m
(iii)

12.00 m , 8.67 m
(iv)

4.00 m , 26.00 m
(v)

7.00 m , 14.86 m

Question 17

17.

In a two digit number, the unit's digit exceeds it ten's digit by 1 and the product of the given number and the sum of its digits is equal to 115 . Find the number

(i)

56
(ii)

34
(iii)

23
(iv)

45
(v)

12

Question 18

18.

Find the number which exceeds its reciprocal by
12

12
13

(i)

14
(ii)

13
(iii)

16
(iv)

10
(v)

12

Question 19

19.

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

Find the width of the road if its area is
17
16
of the area of the play field

(i)

17.00 m
(ii)

15.00 m
(iii)

14.00 m
(iv)

13.00 m
(v)

16.00 m

Question 20

20.

66 is divided into two parts such that the sum of their reciprocals is
66
893
.

Find the two parts

(i)

(

47

,

19

)
(ii)

(

46

,

20

)
(iii)

(

45

,

21

)
(iv)

(

48

,

18

)
(v)

(

49

,

17

)

Question 21

21.

The product of two consecutive odd numbers is 323. Find the numbers

(i)

17 , 19 or -17,-19
(ii)

18 , 20 or -18 , -20
(iii)

19 , 21 or -19 , -21
(iv)

16 , 18 or -16 , -18
(v)

14 , 17 or -14 , -17

Question 22

22.

The perimeter of a rectangular room is 104.00 m and the length of its diagonal is 39.92 m . Find the dimensions of the room

(i)

35.00 m , 17.00 m
(ii)

39.00 m , 13.00 m
(iii)

37.00 m , 15.00 m
(iv)

36.00 m , 16.00 m
(v)

38.00 m , 14.00 m

Question 23

23.

The sum of the squares of two consecutive odd numbers is 10. Find the numbers

(i)
(-5)

,

(-4)

or

5

,

4
(ii)
(-4)

,

(-2)

or

4

,

2
(iii)
(-2)

,

0

or

2

,

0
(iv)
(-3)

,

(-1)

or

3

,

1
(v)
0

,

1

or

0

,

(-1)

Question 24

24.

If the difference of two numbers is 8 and their product is 308, find the numbers

(i)
(-17)

,

(-25)

or

17

,

25
(ii)
(-15)

,

(-23)

or

15

,

23
(iii)
(-14)

,

(-22)

or

14

,

22
(iv)
(-13)

,

(-21)

or

13

,

21
(v)
(-11)

,

(-19)

or

11

,

19

Question 25

25.

A stream flows from A to B, a distance of 9.00 km. A man who can row in still water at 10.00 kmph, can row up and down in 2.81 hr . What is the speed of the stream?

(i)

7.00 kmph
(ii)

4.00 kmph
(iii)

5.00 kmph
(iv)

6.00 kmph
(v)

8.00 kmph

Assignment Key