Question

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

Answer 1

We can assume 1x + 2y +5z= 300 ---> (1)

Total no.of coins , x+y+z = 160 --->(2)

y=3z -->(3)

Subtituting value of (3) in (1) and (2)
1x + (2) * 3z + 5z= 300 
ie; 1x + 6z+5z=300 = x + 11z=300 --> (3)
x+3z+z=160 --> (4)

Considering eqn (3) and (4)

x+11z=300
x+4z=160

then  7z=140 as x cancelled each other.
then z= 20

Now we can calculate rest...

z=20
y = 3z = 60

x+2y+5z=300

then x = 300 -120-100
          = 80

x = 80
y=60
z=20

Solved...

Answer 2

Answer:

Total no. of coins = 160

The no. of 5 rs coins be x

The no. of 2 rs coins be 3x

The no. of 5 rs coins be 4x

The no. of coins => 1 coins 160 - ( 3x + x)

= 160 - 4x

Amount of 5 rs coins = 5x

Amount of 2 rs coins = 2x × 2 = 6x

Amount of 1 rs coin = 60 - 4x

.•. -> 5x + 6x + 160 - 4x = 300

-> 11x + 160 - 4x = 300

-> 7x + 160 - 4x + 160 = 300

-> 7x = 140

-> x = 140 / 7 = 20