Problems on Numbers Questions Answers

15. Sum of two numbers is 25 and their difference is 13. Find their product.
 104
 108
 114
 124
Answer And Explanation
Answer: Option C
Explanation:
Friends, this sort of question is quite important in competitive exams, whenever any question come which have relation between sum, product and difference, this formula do the magic:
\begin{aligned}
=> (x+y)^2 = (xy)^2 + 4xy
\end{aligned}
\begin{aligned}
<=> (25)^2 = (13)^2 + 4xy
\end{aligned}
\begin{aligned}
<=> 4xy = (25)^2  (13)^2
\end{aligned}
\begin{aligned}
<=> xy = \frac{456}{4} = 114
\end{aligned} 
16. Sum of two numbers is 40 and their difference is 4. The ratio of the numbers is
 10:3
 5:9
 11:9
 13:9
Answer And Explanation
Answer: Option C
Explanation:
\begin{aligned}
=> \frac{(x+y)}{(xy)} = \frac{40}{4}
\end{aligned}
\begin{aligned}
=> (x+y)= 10(xy)
\end{aligned}
\begin{aligned}
=> 9x = 11y => \frac{x}{y} = \frac{11}{9}
\end{aligned} 
17. Two numbers differ by 5. If their product is 336, then sum of two number is
 33
 34
 36
 37
Answer And Explanation
Answer: Option D
Explanation:
Friends you remember,
\begin{aligned}
=> (x+y)^2 = (xy)^2 + 4xy
\end{aligned}
\begin{aligned}
=> (x+y)^2 = (5)^2 + 4(336)
\end{aligned}
\begin{aligned}
=> (x+y) = \sqrt{1369} = 37
\end{aligned} 
18. Difference between a twodigit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers
 2
 4
 8
 12
Answer And Explanation
Answer: Option B
Explanation:
Let the ten digit be x, unit digit is y.
Then (10x + y)  (10y + x) = 36
=> 9x  9y = 36
=> x  y = 4. 
19. A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is
 11
 22
 44
 33
Answer And Explanation
Answer: Option C
Explanation:
Let sons age = x. Then, fathers age = 2x.
12(x—2O) = (2x  20) so x = 22
Fathers present age = 44 years 
20. Which among following is not a prime number ?
 97
 33
 45
 72
Answer And Explanation
Answer: Option A
Explanation: