# Problems on Numbers Questions Answers

1) Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the numb

- 1) 5
- 2) 15
- 3) 7.5
- 4) 4

**Ans.**A

**Explanation :**

Let the number be x. 7x -15 = 2x + 10 => 5x = 25 => x = 5

2) Sum of a rational number and its reciprocal is 13/6. Find the numb

- 1) 2
- 2) 3/2
- 3) 4/2
- 4) 5/2

**Ans.**B

**Explanation :**

\begin{aligned} => x + \frac{1}{x} = \frac{13}{6} \end{aligned} \begin{aligned} => \frac{x^2+1}{x} = \frac{13}{6} \end{aligned} \begin{aligned} => 6x^2-13x+6 = 0 \end{aligned} \begin{aligned} => 6x^2-9x-4x+6 = 0 \end{aligned} \begin{aligned} => (3x-2)(2x-3) \end{aligned} \begin{aligned} => x = 2/3 or 3/2 \end{aligned}

3) find the number, difference between number and its 3/5 is 5

- 1) 120
- 2) 123
- 3) 124
- 4) 125

**Ans.**D

**Explanation :**

Let the number = x, Then, x-(3/5)x = 50, => (2/5)x = 50 => 2x = 50*5, => x = 125

4) 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

- 1) 15
- 2) 20
- 3) 25
- 4) 35

**Ans.**B

**Explanation :**

Let the numbers be a, b and c. Then, \begin{aligned} a^2 + b^2 + c^2 = 138 \end{aligned} and (ab + bc + ca) = 131 \begin{aligned} (a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca) \end{aligned} = 138 + 2 x 131 = 400 \begin{aligned} => (a + b + c) = \sqrt{400} = 20. \end{aligned}

5) If one third of one fourth of number is 15, then three tenth of number

- 1) 34
- 2) 44
- 3) 54
- 4) 64

**Ans.**C

**Explanation :**

Let the number is x, \begin{aligned} \frac{1}{3} of\frac{1}{4} * x = 15 \end{aligned} \begin{aligned} => x = 15\times 12 = 180 \end{aligned} \begin{aligned} => so \frac{3}{10} \times x = \frac{3}{10} \times 180 = 54 \end{aligned}

6) A number is doubled and 9 is added. If resultant is trebled, it becomes 75. What is that numb

- 1) 8
- 2) 10
- 3) 12
- 4) 14

**Ans.**A

**Explanation :**

=> 3(2x+9) = 75 => 2x+9 = 25 => x = 8

7) Find a positive number which when increased by 17 is equal to 60 times the reciprocal of the numb

- 1) 17
- 2) 15
- 3) 8
- 4) 3

**Ans.**D

**Explanation :**

If the number is x, Then, x + 17 = 60/x x2 + 17x - 60 = 0 (x + 20)(x - 3) = 0 x = 3, -20, so x = 3 (as 3 is positive)

8) The product of two numbers is 120 and the sum of their squares is 289. The sum of the number

- 1) 20
- 2) 23
- 3) 27
- 4) 150

**Ans.**B

**Explanation :**

We know \begin{aligned} (x + y)^2 = x^2 + y^2 + 2xy \end{aligned} \begin{aligned} => (x + y)^2 = 289 + 2(120) \end{aligned} \begin{aligned} => (x + y) = \sqrt{529} = 23 \end{aligned}

9) Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer

- 1) 12
- 2) 13
- 3) 15
- 4) 17

**Ans.**C

**Explanation :**

Let the three integers be x, x+2 and x+4. Then, 3x = 2(x+4)+3, x= 11 Therefore, third integer x+4 = 15

10) Find the number which when multiplied by 15 is increased by

- 1) 10
- 2) 12
- 3) 14
- 4) 16

**Ans.**C

**Explanation :**

Let the number be x. Then, 15x = x + 196 =â€º 14 x= 196 =â€º x = 14.