Question Detail

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

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:
$\begin{aligned} => (x+y)^2 = (x-y)^2 + 4xy \end{aligned}$

$\begin{aligned} <=> (25)^2 = (13)^2 + 4xy \end{aligned}$

$\begin{aligned} <=> 4xy = (25)^2 - (13)^2 \end{aligned}$
$\begin{aligned} <=> xy = \frac{456}{4} = 114 \end{aligned}$

1. 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

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

$\begin{aligned} => (a + b + c) = \sqrt{400} = 20. \end{aligned}$

2. 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 is

Answer: Option C

Explanation:

Let the second number is x, then first is 2x, and third is 1/3(2x)
$\begin{aligned} =>2x + x + \frac{2x}{3} = 264 <=> \frac{11x}{3} = 264 \end{aligned}$

$\begin{aligned} => x = 72 \end{aligned}$

3. If one third of one fourth of number is 15, then three tenth of number is

Answer: Option C

Explanation:

Let the number is x,
$\begin{aligned} \frac{1}{3} of\frac{1}{4} * x = 15 \end{aligned}$

$\begin{aligned} => x = 15\times 12 = 180 \end{aligned}$

$\begin{aligned} => so \frac{3}{10} \times x = \frac{3}{10} \times 180 = 54 \end{aligned}$