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
 5
 15
 7.5
 4
Answer And Explanation
Answer: Option 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 number
 2
 3/2
 4/2
 5/2
Answer And Explanation
Answer: Option 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^213x+6 = 0 \end{aligned}
\begin{aligned} => 6x^29x4x+6 = 0 \end{aligned}
\begin{aligned} => (3x2)(2x3) \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.
 120
 123
 124
 125
Answer And Explanation
Answer: Option 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 is
 15
 20
 25
 35
Answer And Explanation
Answer: Option 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 is
 34
 44
 54
 64
Answer And Explanation
Answer: Option 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 number
 8
 10
 12
 14
Answer And Explanation
Answer: Option 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 number
 17
 15
 8
 3
Answer And Explanation
Answer: Option 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)