Question

The cost of 4 pens and 4 pencils is Rs. 100. Three times the cost of a pen is Rs. 15 more than the cost of a pencil box. The cost of a pen and a pencil box respectively are
A.\[Rs.15{\text{ and Rs}}{\text{.8}}\]
B.$Rs.10{\text{ and Rs}}{\text{.15}}$
C.$Rs.12{\text{ and Rs}}{\text{.10}}$
D.$Rs.16{\text{ and Rs}}{\text{.12}}$

Answer 1

Hint- In order to solve this question, we will first assume the cost of a pen and pencil box as a variable then we will form two equations with two variables then by simplifying it we will get the answer.

Complete step-by-step answer:
Let the cost of the pen be Rs. X and the cost of a pencil box is Rs. Y
Given that the cost of 4 pencil boxes and 4 pens \[ = Rs.100\]
$ \Rightarrow 4x + 4y = 100$
Taking 4 as common
$ \Rightarrow x + y = 25...........\left( 1 \right)$
Also given that 3 times the cost of the pen is 15 more than the pencil box
$
   \Rightarrow 3x = y + 15 \\
   \Rightarrow 3x - y = 15................\left( 2 \right) \\
 $
Adding equation (1) and (2)
$
   \Rightarrow x + y + 3x - y = 25 + 15 \\
   \Rightarrow 4x = 40 \\
   \Rightarrow x = 10 \\
$
Substitute the value of x as 10 in equation (2s), we get
$
   \Rightarrow 3 \times 10 - y = 15 \\
   \Rightarrow y = 30 - 15 \\
   \Rightarrow y = 15 \\
$
Hence, the cost of the pen is Rs. 10 and the cost of the pencil box is Rs. 15
Note- In order to solve these types of questions which are statement based, read the statement carefully and gather as much information required to solve the question. Remember a linear equation can be solved when the number of variables is equal to number of equations. Also remember the concept of solving equations using elimination method, substitution method and cross multiplication method.