Question

Fatima had 100 coins in her Piggy bank. It contained twice as many 1 rupee coins as 50 paise coins, and some 25 paise coins. The total amount of money was rupees 60. How many of each coin did she have?

Answer 1

Step 1: Let the number of 1 rupee coin be ‘x’.

According to the question, the number of 50 paise coins will be ‘$2\mathrm{x}$’.

It is given that in total there are 100 coins, so,

1 rupee coin + 50 paise coin + 25 paisa coin = 100

$x+2x+25$ paisa coin = 100

25 paise coin $=100-3x$

Step 2: Total amount of money is given as 60 rupees, so,

$x\times 1$rupee +$2x\times 50$paise $+(100-3x)\times 25$ paise = 60 rupees

We know that, $25$ paisa $=0.25$ and $50$ paisa $=0.50$ rupees, so, above equation can be written as,

$\Rightarrow 1x+0.50\times 2x+0.25\times (100-3x)=60$

$\Rightarrow 1x+1x+25-0.75x=60$

$\Rightarrow 1.25x=35$

$\Rightarrow x=\frac{35}{1.25}$

$\Rightarrow x=28$

So, $2x=2\times 28=56$

$(100-3x)=(100-3\times 28)=16$

Hence, the number of 1 rupee coin are 28, 50 paise coin are 56 and 25 paise coin are 16.