Question

I had Rs $14.40$ in one rupee coins and $20$ paise coins when I went out shopping. When I returned, I had as many $1$ rupee coins as I originally has $20$ paise coins and as many $20$ paise coins as I originally had $1$ rupee coins. Briefly I came back with about one third of what I had started out with. How many $1$ rupee coins did I have initially?

• A. $10$
• B. $12$
• C. $14$
• D. $16$

Answer 1

The correct option is C $14$

Let the number of $1$ rupee coins be $x$ and that of $20$ paise coins be $y$

Then the total amount $=1\times x+0.2\times y=14.40$

$⟹10x+2y=144$

$⟹5x+y=72$

$⟹y=72-5x$ .......... $\left(i\right)$

Also, after shopping, the number of $1$ rupee coins $=y$ and that of $20$ paise coins $=x$.

The total amount this time is one third of the previous amount.

i.e.$1\times y+0.2\times x=4.8$

$⟹2x+10y=48$

$⟹x+5y=24$

$⟹y=\frac{24-x}{5}$ ............ $\left(ii\right)$

Comparing $\left(i\right)$ and $\left(ii\right)$, we get

$72-5x=\frac{24-x}{5}$

$⟹24x=336$

$⟹x=14$

$\therefore$ The number of rupee $1$ coins $=14$.