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.
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.
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. 
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.
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.
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.
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. 
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.
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