Question

A bag contains ${\rm{Rs}}{\rm{.}}\;{\rm{187}}$ in the form of ${\rm{1}}$
rupee, ${\rm{50}}$ paise, and ${\rm{10}}$ paise coin in the ratio ${\rm{3:4:5}}$
respectively. Find the number of each type of coin.

Answer 1

Hint: Apply the formula for ratio. ${\rm{1}}$ rupee contains ${\rm{100}}$ paise, The
amount of ${\rm{50}}$ paise in ${\rm{1}}$ rupee will be $2$. The amount of ${\rm{10}}$
paise in ${\rm{1}}$ rupee will be $10$.
Complete step by step answer:
Given, total amount of money the bag contains $ = {\rm{Rs}}{\rm{.}}\;{\rm{187}}$
Available types of money are ${\rm{1}}$ rupee, ${\rm{50}}$ paise, and ${\rm{10}}$ paise
coins.
The ratio of ${\rm{1}}$ rupee, ${\rm{50}}$ paise and ${\rm{10}}$ paise coins are
${\rm{3:4:5}}$
Step I
Let the number of ${\rm{1}}$ rupee, ${\rm{50}}$ paise, and ${\rm{10}}$ paise coins are
${\rm{3}}x$, ${\rm{4}}x$ and ${\rm{5}}x$ respectively.
We know that, ${\rm{1}}$ rupee contains ${\rm{100}}$ paise
Converting ${\rm{50}}$ paise, and ${\rm{10}}$ paise into ${\rm{1}}$ rupee will be
$\dfrac{{50}}{{100}}$ and $\dfrac{{10}}{{100}}$ respectively.
Step II
According to the question,
$\begin{array}{c}3x + 4x \times \dfrac{{50}}{{100}} + 5x \times \dfrac{{10}}{{100}} =
187\\3x + 2x + \dfrac{x}{2} = 187\\\dfrac{{11x}}{2} = 187\end{array}$
Further solving the above equation to determine the value of $x$,
$\begin{array}{c}11x =
187\, \times 2\\x = \dfrac{{187 \times 2}}{{11}}\\ = 34\end{array}$
Hence the value of $x$ is $34$
Now, number of ${\rm{1}}$ rupee coins $ = 3x = 3 \times 34 = 102$
Number of ${\rm{50}}$ paise coins $ = 4x = 4 \times 34 = 136$
Number of ${\rm{10}}$ paise coins $ = 5x = 5 \times 34 = 170$
Hence, the total amount of ${\rm{1}}$ rupee, ${\rm{50}}$ paise, and ${\rm{10}}$ paise
coins are $102,\;136,\;{\rm{and}}\;{\rm{170}}$ respectively.
Note:
Know the difference between rupees and paise.
Rupee: The indian rupee (INR) is India's money. INR is the International Organisation for the
standardization of the Indian Rupee Currency Code, for which the emblem of the currency is
a component.
We know that ${\rm{1}}$ rupee = $100$ paise. When we convert rupees into paise, we
multiply by $100$. To convert from paise to rupees we divide it by $100$.
In step I, assign the values of ${\rm{1}}$ rupee, ${\rm{50}}$ paise, and ${\rm{10}}$ paise
considering a variable $x$.
In step II, add the numbers with respect to their corresponding ratios to the total amount of
money.