# 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 number

1. 5
2. 15
3. 7.5
4. 4

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 number

1. 2
2. 3/2
3. 4/2
4. 5/2

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 50.

1. 120
2. 123
3. 124
4. 125

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 is

1. 15
2. 20
3. 25
4. 35

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 is

1. 34
2. 44
3. 54
4. 64

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 number

1. 8
2. 10
3. 12
4. 14

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 number

1. 17
2. 15
3. 8
4. 3

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)

thanks :))