# Problems on Numbers Questions Answers

Problems on Numbers Questions Answers (MCQ) listings with explanations which includes questions on simplification of numbers, simplify questions, evaluation questions and other important types which are useful in competitive exams.

11) if the sum of \begin{aligned} \frac{1}{2} \end{aligned} and \begin{aligned} \frac{1}{5} \end{aligned} of a number exceeds \begin{aligned} \frac{1}{3} \end{aligned} of the number by \begin{aligned} 7\frac {1}{3} \end{aligned}, then number

• 1) 15
• 2) 20
• 3) 25
• 4) 30
Ans.   B
Explanation :
Seems a bit complicated, isnt'it, but trust me if we think on this question with a cool mind then it is quite simple... Let the number is x, then, \begin{aligned} (\frac{1}{2}x + \frac{1}{5}x) - \frac{1}{3}x = \frac{22}{3} \end{aligned} \begin{aligned} => \frac{11x}{30} = \frac{22}{3} \end{aligned} \begin{aligned} => x = 20 \end{aligned}

12) find the number, If 50 is subtracted from two-third of number, the result is equal to sum of 40 and one-fourth of that numbe

• 1) 214
• 2) 216
• 3) 114
• 4) 116
Ans.   B
Explanation :
Let the number is x, \begin{aligned} => \frac{2}{3}x-50 = \frac{1}{4}x + 40 \end{aligned} \begin{aligned} <=> \frac{2}{3}x-\frac{1}{4}x = 90 \end{aligned} \begin{aligned} <=> \frac{5x}{12} = 90 \end{aligned} \begin{aligned} <=> x = 216 \end{aligned}

13) Product of two natural numbers is 17. Then, the sum of reciprocals of their squares

• 1) \begin{aligned} \frac{290}{289} \end{aligned}
• 2) \begin{aligned} \frac{1}{289} \end{aligned}
• 3) \begin{aligned} \frac{290}{90} \end{aligned}
• 4) \begin{aligned} \frac{290}{19} \end{aligned}
Ans.   A
Explanation :
If the numbers are a, b, then ab = 17, as 17 is a prime number, so a = 1, b = 17. \begin{aligned} \frac{1}{a^2} + \frac{1}{b^2} = \frac{1}{1^2} + \frac{1}{17^2} \end{aligned} \begin{aligned} = \frac{290}{289} \end{aligned}

14) Sum of three numbers 264, If the first number be twice then second and third number be one third of the first, then the second number

• 1) 70
• 2) 71
• 3) 72
• 4) 73