# Problems on Numbers Questions Answers

• #### 15. Sum of two numbers is 25 and their difference is 13. Find their product.

1. 104
2. 108
3. 114
4. 124

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 = (x-y)^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

1. 10:3
2. 5:9
3. 11:9
4. 13:9

Explanation:

\begin{aligned}
=> \frac{(x+y)}{(x-y)} = \frac{40}{4}
\end{aligned}

\begin{aligned}
=> (x+y)= 10(x-y)
\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

1. 33
2. 34
3. 36
4. 37

Explanation:

Friends you remember,
\begin{aligned}
=> (x+y)^2 = (x-y)^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 two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers

1. 2
2. 4
3. 8
4. 12

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

1. 11
2. 22
3. 44
4. 33

Explanation:

Let sons age = x. Then, fathers age = 2x.
12(x—2O) = (2x - 20) so x = 22
Fathers present age = 44 years

1. 97
2. 33
3. 45
4. 72