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 ₹5 coins. The total number of coins is 160. How many coins of each denomination are with me?

As per the ratio given,
Let the number of ₹5 coins be x.

Number of ₹2 coins = 3x

Total number of coins = 160

Number of ₹1 coin = 160 – (x + 3x) = 160 – 4x

Converting the number of coins into rupees, we have

x coins of ₹5 amount = ₹5x

3x coins of ₹2 amount = ₹ 3x × 2 = ₹6x

and (160 – 4x) coins of ₹ 1 amount =₹1 × (160 – 4x) =₹(160 – 4x)

As per the conditions given, we got

5x + 6x + 160 – 4x = 300

\(\Rightarrow\) 7x + 160 = 300

\(\Rightarrow\) 7x = 300 – 160 (transposing 160 to RHS)

\(\Rightarrow\) 7x = 140

\(\Rightarrow\) x = 140 ÷ 7 (transposing 7 to RHS)

\(\Rightarrow\) x = 20

Thus, number of ? 5 coins = 20

Number of ₹2 coins = 3 × 20 = 60

and Number of ₹ 1 coins = 160 – 4 × 20 = 160 – 80 = 80