## 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.**

## 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.**