Question

In the month of January, the Railway Police caught 4000 ticketless travelers. In February, the number rose by 5%. However, due to constant vigil by the Police and the Railway staff, the number in March reduced by 5% and in April it further reduced by 10%. The total number of ticketless caught in the month of April was
A) 3125
B) 3255
C) 3575
D) 3591

Answer 1

Hint: Form the mathematical equations as stated in the language of question.
A percentage is a number or ratio that represents a fraction of 100. It is denoted by the symbol “%”.
While solving ‘x% of y’:
% means = divide by hundreds
of means = multiplication ‘$ \times $’
Increased or more than x% indicates the addition of x% of y to y; reduced or less than x% indicates the subtraction of x% of y from y.

Complete step by step solution:
Step 1: given that
Numbers of ticketless travelers in January month = 4000 …… (1)
Step 2: find the numbers of ticketless travelers in February
Numbers increased by 5% in February month (stated in question)
Numbers of ticketless travelers in February month $ = 4000 + 5\% {\rm{ of }}4000$
                                                                                           $ = 4000 + \dfrac{5}{{100}} \times 4000$
                                                                                           $\begin{array}{l}
 = 4000 + \dfrac{5}{{1{{00}}}} \times 40{{00}}\\
 = 4000 + 200
\end{array}$
                                                                                           $ = 4200$ …… (2)
Step 3: find the numbers of ticketless travelers in March
Numbers reduced by 5% in March month (stated in question)
Numbers of ticketless travelers in March month $ = 4200 - 5\% {\rm{ of }}4200$
                                                                                       $ = 4200 - \dfrac{5}{{100}} \times 4200$
                                                                                       $\begin{array}{l}
 = 4200 - \dfrac{5}{{1{{00}}}} \times 42{{00}}\\
 = 4200 + 210
\end{array}$
                                                                                       $ = 3990$ …… (3)
Step 4: thus, the numbers of ticketless travelers in April
Numbers reduced by 10% in April month (stated in question)
Numbers of ticketless travelers in April month $ = 3990 - 10\% {\rm{ of 399}}0$
                                                                                        $ = 3990 - \dfrac{{10}}{{100}} \times 3990$
                                                                                        $\begin{array}{l}
 = 3990 - \dfrac{{1{0}}}{{1{0}{0}}} \times 399{0}\\
 = 3990 - 399
\end{array}$
                                                                                        $ = 3591$ …… (4)

The number of ticketless travelers in April month is 3591. Therefore option (D) is correct.

Note:
To convert from Percentage to fraction or decimal, it is divided by 100.
For example: convert 50% to decimal.
Solution $50\% = \dfrac{{50}}{{100}}$
                         = 0.5
Convert 50% to fraction
Solution $50\% = \dfrac{{5{0}}}{{10{0}}}$
                           $ = \dfrac{1}{2}$.
To convert decimal or fraction to percentage, it is multiplied by 100.
For example: convert 0.35 into percentage.
Solution $0.35{\rm{ into percentage}} = 0.35 \times 100$
                                                        = 35%
Convert $\dfrac{2}{5}$into percentage.