![number system number system](https://4.bp.blogspot.com/-F4hcmfE6VsQ/VvDhqbDQnTI/AAAAAAAAJNI/0v91QvK8itUIRZJG832uVi0Ug8JRedzjg/s320-rw/number%2Bsystem.jpg)
Ques 1.
The difference between a two- digit number and the number obtained by interchanging the two digit is 63. Which is the smaller of the two numbers ?
(a)29
(b) 70
(c)92
(d) Cannot be determined
Ans 1. Let the ten's digit be x and unit's be y .
Then. ( 10x + y) - ( 10x + x) = 63 ⇔ 9 ( x- y) = 63 ⇔ x - y = 7
Thus, none of the numbers can be determined.
Ques 2.
A certain number of two-digit is three times the sum of its digit and if 45 be added to it, the digit are reversed .The number is :
(a) 23
(b) 27
(c) 32
(d) 72
Ans 2. Let the ten's digit be x and unit's digit be y.
Then, 10x + y = 3 ( x+ y) ⇔ 7x - 2y = 0
10x + y + 45 = 10y + x ⇔ y -x = 5
Solving (i) and ( ii), we get : x = 2 and y = 7.
Required number = 27.
10x + y + 45 = 10y + x ⇔ y -x = 5
Solving (i) and ( ii), we get : x = 2 and y = 7.
Required number = 27.
Ques 3.
The sum of three numbers is 264.If the first number be twice the second and third number be one-third of the first ,then the second number is :
(a) 48
(b) 54
(c) 72
(d) 84
Ans 3.
![](https://4.bp.blogspot.com/-uwDRN1_9gvw/VvDaw7hAgNI/AAAAAAAABHs/dKvsDoAk3yIYterZexvpMFwDCVvFOPbJw/s640-rw/7.jpg)
Ques 4.
The Product of two number is 192 and the sum of these of these two numbers is 28. What is the smaller of these two numbers ?
(a) 12
(b) 14
(c) 16
(d) 18
Ans 4. 12
Ques 5.
The difference between two positive integers is 3.If the sum of their squares is 369, then the sum of the numbers is :
(a) 25
(b) 27
(c) 33
(d) 81
Ans 5.Suppose the required number is x. Then from question,
x2 + ( x + 3)2 = 369 ⇔ x2 + x2 + 9 + 6x = 369
⇔ 2x2 + 6x - 360 = 0 ⇔ x2 + 3x - 180 = 0
⇔ ( x+15) (x -12) = 0 ⇔ x = 12
So, The numbers are 12 and 15.
∴ Required sum = ( 12 + 15) = 27.
Ques 6.
The sum of the digit of a two-digit number is 15 and the difference between the digit is 3. What is the two- digit number ?
(a) 69
(b) 78
(c) 96
(d) Cannot be determined
Ans 6. Cannot be determined
Ques 7.
Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the number.
(a) 3
(b) 10
(c) 17
(d) 20
Ans 7. 3
Ques 8.
One -fifth of a number is equal to 5/8 of another number. If 35 added to the first number,it becomes four times of the second number. The second number is :
(a) 25
(b) 40
(c) 70
(d) 125
Ans 8.
![](https://1.bp.blogspot.com/-BGMxeu5xgs4/VvDfb6W-eNI/AAAAAAAABIA/iLSyaMf-V1EsM77v8HZm1F0Aknm9Yx2vg/s640-rw/18.jpg)
![](https://1.bp.blogspot.com/-BGMxeu5xgs4/VvDfb6W-eNI/AAAAAAAABIA/iLSyaMf-V1EsM77v8HZm1F0Aknm9Yx2vg/s640-rw/18.jpg)
Ques 9.
If the sum of one-half and one-fifth of a number exceeds one-third of that number by 7 1/3, the number is :
(a) 15
(b) 18
(c) 20
(d) 30
Ans 9. Suppose the required number is x.
![](https://3.bp.blogspot.com/-FAxbycHgbiA/VvDfn5isKqI/AAAAAAAABIE/lZf7vj4oFbIj1qX_FYAo_c8tPOa1ff2mw/s640-rw/19.jpg)
![](https://3.bp.blogspot.com/-FAxbycHgbiA/VvDfn5isKqI/AAAAAAAABIE/lZf7vj4oFbIj1qX_FYAo_c8tPOa1ff2mw/s640-rw/19.jpg)
Ques 10.
A number of two digit has 3 for its unit's digit,and the sum of digit is 1/7 of the number itself. The number is
(a) 43
(b) 53
(c) 63
(d) 73
Ans 10.
![](https://4.bp.blogspot.com/-0Auf8p_9Kdc/VvDhSSF8gII/AAAAAAAABIg/UBDblFPvTdcQt50-lfdC-bTnoKdZNGlwA/s640-rw/20..jpg)
![](https://4.bp.blogspot.com/-0Auf8p_9Kdc/VvDhSSF8gII/AAAAAAAABIg/UBDblFPvTdcQt50-lfdC-bTnoKdZNGlwA/s640-rw/20..jpg)
Ques 11.
The sum of three consecutive odd numbers is 20 more than the first of these numbers. What is the middle number ?
(a) 7
(b) 9
(c) 11
(d) Data inadequate
Ans 11. Suppose the three numbers are x, x + 2 and x + 4
The, x + ( x+ 2) + ( x+ 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7.
∴ Middle number = x + 2 = 9.
The, x + ( x+ 2) + ( x+ 4) = x + 20 ⇔ 2x = 14 ⇔ x = 7.
∴ Middle number = x + 2 = 9.
Ques 12.
A two-digit number is such that the product of the digit is 8. When 18 is added to the number , then the digit are reversed. The number is :
(a) 18
(b) 24
(c) 42
(d) 81
Ans 12.
![](https://2.bp.blogspot.com/-719A_14vluA/VvDgFhY91aI/AAAAAAAABIQ/hDOBGQpB8VkcHgVmKrWjlkDUs5W3ntCNw/s640-rw/24.jpg)
![](https://2.bp.blogspot.com/-719A_14vluA/VvDgFhY91aI/AAAAAAAABIQ/hDOBGQpB8VkcHgVmKrWjlkDUs5W3ntCNw/s640-rw/24.jpg)
Ques 13.
The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131.Their sum is :
(a) 20
(b) 30
(c) 40
(d) None of these
Ans 13.
![](https://2.bp.blogspot.com/-2YvVF85IQis/VvDf9RHJL3I/AAAAAAAABIM/MaeuTabuZFUpy6BaQI_Ao37FzOSIbLkdA/s640-rw/29.jpg)
![](https://2.bp.blogspot.com/-2YvVF85IQis/VvDf9RHJL3I/AAAAAAAABIM/MaeuTabuZFUpy6BaQI_Ao37FzOSIbLkdA/s640-rw/29.jpg)