Question

Question 15
I have a total of ₹300 in coins of denomination ₹1, ₹2 and ₹5.The number of ₹2 coins is 3 times the number of ₹5coins. The total number of coins is 160. How many coins of each denomination are with me?

Answer 1

Total sum of money = ₹300
Let the number of ₹5 coins be x,
Number of ₹2 coins be 3x and
Number of ₹1 coins be $160-(x+3x)=(160-4x)$.

According to question,
$5\times x+2\times \left(3x\right)+1\times (160-4x)=300$

$\Rightarrow 5x+6x+160-4x=300$
$\Rightarrow 7x+160=300$
$\Rightarrow 7x+160-160=300-160$ [Subtracting 160 from both sides]
$\Rightarrow 7x=140$
$\Rightarrow \frac{7x}{7}=\frac{140}{7}$ [Dividing both sides by 7]
$\Rightarrow x=20$

Hence,the number of coins of ₹5 denomination
$=20$

Number of coins of ₹2 denomination
$=3\times 20=60$

Number of coins of ₹1 denomination
$=160–4\times 20=160–80=80$