Question

The sum of two numbers is 28/25 times the first number. The second number is _% of the first:
(A). 12%
(B). 16%
(C). 14%
(D). None of these

Answer 1

Hint: Start by assuming or taking two numbers A and B . Follow the statements given in the question to form a numerical relation between x and y and try to find out the ratio i.e. y/x in percentage by using all the information and relations formed.

Complete step-by-step answer: Let the first number be ‘x’
 Let the second number be ‘y’.
Then according to the statement given in question
$x + y = \dfrac{{28}}{{25}} \times x$
Shifting x to the other side of equation, we get
$
  y = \dfrac{{28}}{{25}}x - x \\
  y = x\left( {\dfrac{{28}}{{25}} - 1} \right) \\
  y = x\left( {\dfrac{{28 - 25}}{{25}}} \right) \\
  y = x\left( {\dfrac{3}{{25}}} \right) \to eqn(1) \\
$
Now ,According to the second statement we need to find y/x in percentage.
$\dfrac{y}{x} \times 100$
Substituting value of y from equation(1), we get
$
  \dfrac{{x\left( {\dfrac{3}{{25}}} \right)}}{x} \times 100 \\
   \Rightarrow \dfrac{3}{{25}} \times 100 \\
   \Rightarrow 3 \times 4 \\
   = 12\% \\
$
Therefore , the second number is 12 % of the first number.
So, Option A is the correct answer.

Note:Attention must be given while forming or solving the linear or quadratic equation found, Also we must choose the correct ratio or proportion asked i.e. y/x or x/y as per the question. Try to keep the ratio in the simplest form and not complex them.