Question

A stationary shop had three types of pens costing $Rs.\;10$,$Rs.\;25$ and $Rs.\;50$.
There were twice as many 25- rupees pens as there were 10- rupees pens. The 50-rupees pens
added up to a value of $Rs.\;350$. If the total value of pens was $Rs.\;1550$, how many pens of
What type were there?

Answer 1

Hint: In this question, since the number of 10- rupees pen is not given so first we have to assume
the number of 10- rupees pen, suppose$x$. It is given that the number of 25- rupees pen is twice
the number of 10- rupees pen. So we can calculate the number of 25- rupees pen by multiplying
2 with$x$. After that we can calculate the total value of 10- rupees and 25- rupees pen together.
Since the total value of pens and the values of 50- rupees pen are given, so by subtracting we get
the values of 10- rupees and 25- rupees pen together. By comparing the calculated value 10-
rupees and 25- rupees pen together with the given, we get the number of 10- rupees pen and 25-
rupees pen. After that by dividing the total values of 50- rupees pen with 50, we get the total
number of 50- rupees pen.
Let total number of 10- rupees pen $ = x$
It is given that the number of 25- rupees pen is twice the number of 10- rupees pen.
Thus, the total number of 25- rupees pen $ = 2x$
Total value of 10- rupees and 25- rupees pens together $ = 10 \times x + 25 \times 2x$

$\begin{array}{l} = 10x + 50x\\ =
60x\end{array}$ (1)
Given that the total value of pens $ = Rs.1550$
Total value of the 50- rupees pen $ = Rs.\;350$
Thus, Total value of 10- rupees and 25- rupees pens together $ = Rs.1550 - Rs.350$
$ = Rs.1200$
(2)
Now, Comparing (1) and (2) and solving for $x$.
$\begin{array}{l} \Rightarrow 60x = 1200\\ \Rightarrow x = \dfrac{{1200}}{{60}}\\
\Rightarrow x = \dfrac{{120}}{6}\\ \Rightarrow x = 20\end{array}$
Total number of 10- rupees pen = 20
Thus, the total number of 25- rupees pen $ = 2 \times 20$
= 40
Now, we need to find the total number of 50- rupees pen. Dividing the total value of 50- rupees
pen $Rs.\;350$ by 50- rupees.
Total number of 50- rupees pen $ = \dfrac{{Rs.350}}{{Rs.50}}$
Total number of 50- rupees pen $ = 7$
Hence, the total number of 10- rupees pen is 20, total number of 25- rupees pen is 40 and the
total number of 50- rupees pen is 7.
Note: Here we have to find the number of each type of pen. Since the total price of the pen and
The price of a 50- rupees pen is given, so from that we get a price of 10- rupees and 25- rupees pen.
By assuming the price of the 10- rupees pen we can calculate the total values of 10- rupees and
25- rupees pen. By comparing the calculated value with the given value we get the number of 10-
rupees pen and 25- rupees pen. From total price of the pen and the price of 50- rupees pen we get
the number of 50- rupees pen.