Question

I have total 300 coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is three times the number ₹5 coins. The total number of coins is 160. How many coins of each denominations are with me?

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

80

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Total value of coins = Rs. 300

Total coins = 160

The number of Rs.2 coins are 3 times the number of Rs. 5 coins.

To Find :

Coins of each denominations.

Solution :

Let a be number of ₹1 coins, b number of ₹2 coins and c number of ₹ 5 coins

Because you have a total of ₹300 in denomination of ₹1 , ₹2 and ₹5

$\implies a + 2b + 5c = 300$ (i)

The total number of coins is 160

So,

$\implies a + b + c = 160$ (ii)

Subtract (ii) from (i)

$\implies b + 4c = 140$ (iii)

But b = 3c ( As The number of ₹2 coins is 3 times the number of ₹5 coins )

Substituting value of b in (iii)

$\implies 3c + 4c = 140$

$\implies 7c = 140$

$\boxed{ c = 20}$

Substituting the value of c in (iii)

$\implies b + 4 x 20 = 140$

$\implies b = 140 - 80$

$\boxed{b = 60}$

Substituting the values of b and c in (ii)

$\implies a + 60 + 20 = 160$

$\boxed{a = 80}$

★Verification★

$\implies 1\times80+2\times60+ 5 \times 20$

$\implies 80 + 120 + 100 = 300$

Answer 2

Let the number of ₹5 coins be x.

Then,

number ₹2 coins = 3x

and, number of ₹1 coins = (160 – 4x) Now,

Value of ₹5 coins = x × 5 = 5x

Value of ₹2 coins = 3x × 2 = 6x

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

According to the question,

5x + 6x + (160 – 4x) = 300

⇒ 11x + 160 – 4x = 300

⇒ 7x = 140

⇒ x = 140/7

⇒ x = 20

Number of ₹5 coins = x = 20

Number of ₹2 coins = 3x = 60

Number of ₹1 coins = (160 – 4x) = 160 – 80 = 80