Question

I had $Rs.14.40$ in one- rupee coins and $20{\text{ paise}}$ coins when I went out shopping. When I returned, I had as many $1{\text{ rupee}}$ coins as I originally had $20{\text{ paise}}$ coins and as many $20{\text{ paise}}$ coins as I originally had $1{\text{ rupee}}$ coins. Briefly I came back with about one third of what I had started out with. How many $1{\text{ rupee}}$coins did I have initially?
A)$10$
B)$12$
C)$14$
D)$16$

Answer 1

Hint: Let us assume the number of $1{\text{ rupee}}$coins be $x$ and the number of $20{\text{ paise}}$ coins be $y$. And we know $20{\text{ paise}}$ is equal to $0.2{\text{ Rupees}}$ . So, initially, he has $Rs.14.40$ . So, equation is written as
$x + 0.2y = 14.40$
After shopping, the number of one-rupee coins and the number of $20{\text{ paise}}$ coins interchange and the amount left becomes one-third of $Rs.14.40$ . So, generate a new equation and solve it.

Complete step-by-step answer:
So, in question, we are given that we have $Rs.14.40$ in one-rupee coins and $20{\text{ paise}}$ coins. So, let us assume the number of one-rupee coins to be $x$ and the number of $20{\text{ paise}}$ coins be $y$. So,
$x + 0.2y = 14.40$ we can write this formula as $20{\text{ paise}}$ is equal to $0.2{\text{ Rupees}}$. So,
$x + 0.2y = 14.40$ (1)
After shopping, he had one-rupee coins as originally he had $20{\text{ paise}}$ coins initially and he had $20{\text{ paise}}$ coins as he initially had one-rupee coins. So, after shopping, we can write this:
The number of $20{\text{ paise}}$ coins becomes $x$ and the number of $1{\text{ rupee}}$coins becomes $y$ .
And he had left with one-third of the given money he took while going for the shopping.
Money left after shopping$ = \dfrac{1}{3} \times 14.40 = 4.80$
So, after shopping, we can write
$0.2x + y = 4.80$ (2)
Now from equation (1), we get
$
  x + 0.2y = 14.40 \\
  x = 14.40 - 0.2y \\
 $
Putting $x$ in equation (2)
$
  0.2\left( {14.40 - 0.2y} \right) + y = 4.80 \\
  2.88 - 0.04y + y = 4.80 \\
  0.96y = 1.96 \\
  y = 2 \\
 $
And now, putting $y = 2$ in equation (1)
$
  x = 14.40 - 0.2y \\
   = 14.40 - 0.2\left( 2 \right) \\
   = 14.40 - 0.40 \\
   = 14 \\
 $
So, number of one-rupee coins we assumed be $x$

So, here, $x = 14$.

Note: We know that $1{\text{ Rupee = 100 paise}}$. So,
$
  1{\text{ paisa = }}\dfrac{1}{{100}}{\text{ Rupees}} \\
   \Rightarrow {\text{20 paisa = 0}}{\text{.2 Rupees}} \\
 $
So, we cannot add rupees and paise, so we need to convert paisa into rupees to get the equation
$x + 0.2y = 14.40$