Question

I have a total of ₹ 300 in coins of denomination ₹1, ₹2 and ₹5. The number of ₹2 coins is three 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 number of ₹1, ₹2, ₹5 be X, y, z

Given:

* x+2y+5z=300 - - - - > 1

* y=3z - - - - - - - - - - > 2

*x+y+z=160 - - - - - - - -> 3

Solution

Sub eq 2 in eq 1

1 => x+2(3z)+5z=300 x+6z+5z=300

x+11z=300 - - - - - > 4

Sub eq 2 in eq 3

3 => x+3z+z=160

x+4z=160 - - - - - - - - > 5

SUBTRACT 5 from 4

4 – 5 => x+11z–(x+4z)=300–160 x+11z–x–4z=140

(x–x)+(11z–4z)=140 0+7z=140

z=140/7

z=20

Sub z=20 in eq 5 & eq 2

5 => x+4(20)=160

x+80=160

x=160–80

x=80

2 => y=3(20)

y=60

*Number of ₹1 coin, x=80

*Number of ₹2coin, y=60

*Number of ₹5coin, z=20

Hope u got it

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