Question

I have a total of ₹300 in coins of denomination ₹1, ₹2 amd ₹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?​

Answer 1

Step-by-step explanation:

let the no. of rs 5 coins be x

& the no. of rs 1 coin be y

& no. of rs 2 coins be 3 x

a.q.t total no. of coins = 160

x + 3x+y = 160

4x + y = 160 eq. 1

again a.q.t total rs = 300

5x + 2(3x) + 1y = 300

11x + y = 300 eq. 2

by elimination method

on subtracting both the equations

4x + y = 160

-11x -y = -300

=-7x =-140

x =20

on putting the the value of x in eq 2

4(20) + y =160

80 + y = 160

y =80

now,

no of rs 2 coins = 3(20)

= 60

no. of rs 5 coins = 20

no. of rs 1 coins=80

Please mark as brainliest

Answer 2

Given :

Total amount in coins : ₹300

Denomination of coins : ₹1, ₹2, ₹3

Total number of coins : 160

Number of ₹2 coins is 3 times the number of ₹5 coins.

To find :

The number of denominations' coins in each case.

Solution :

Let the number of ₹5 coins be x.

Let the number of ₹2 coins be 3x.

Let the number of ₹1 coins be 160-(x + 3x).

Now, we should find the amount in each type of coins in variable form.

Let the amount in ₹5 coins be 5x.

Let the amount in ₹2 coins be 6x.

Let the amount in ₹1 coins be 160 - 4x.

Number of ₹5 coins :

According to the question,

$\sf \dashrightarrow 5x + 6x + (160 - 4x) = 300$

$\sf \dashrightarrow 160 - 4x + 5x + 6x = 300$

$\sf \dashrightarrow 160 - 7x = 300$

$\sf \dashrightarrow 7x = 300 - 160$

$\sf \dashrightarrow 7x = 140$

$\sf \dashrightarrow x = \dfrac{140}{7}$

$\sf \dashrightarrow x = 20$

Number of ₹2 coins :

$\sf \dashrightarrow 3(x) = 3(20)$

$\sf \dashrightarrow 60$

Number of ₹1 coins :

$\sf \dashrightarrow 160 - (x + 3x)$

$\sf \dashrightarrow 160 - {20 + 3(20)}$

$\sf \dashrightarrow 160 - (20 + 60)$

$\sf \dashrightarrow 160 - (80)$

$\sf \dashrightarrow 80$

Hence, the number of ₹1, ₹2 and ₹5 coins are 80, 60 and 20 coins respectively.