Question

a bag had 500 rs in the form of 1 rs, 50 paise and 25 paise coins coins in the ratio 3:8:12, find the number of each type of coins

Answer 1

Question :

a bag had 500 rs in the form of 1 rs, 50 paise and 25 paise coins coins in the ratio 3:8:12, find the number of each type of coins

To find :

The total number of coins in the bag

Let us assume :

According to the question

1 rs , 50 paise and 25 paise are in the ratio → 3 : 8 : 12

By taking the variable as x we get

number of 1 rs coins → 3x

number of 50 paise coins → 8x

number of 25 paise coins → 12x

Solution :

Value of 3x rs 1 coins

→ ₹ 1 × 3x

→ ₹ 3x

Value of 8x 50 paise coins

→ 8x × 50 paise

$\sf \small \rarr \frac{8x \times 50}{100}$

$\sf \small \rarr 4x \: rs$

Value of 12x 25 paise coins

→ 12x × 25 paise

$\sf \small \rarr \frac{12x \times 25}{100}$

$\sf \small \rarr3x \:rs$

Total amount in the bag → ₹ 500

Value of 1 rs coins + 50 paise coins + 25 paise coins = ₹ 500

Putting the values we get,

$\sf \small \rarr3x + 4x + 3x = 500$

$\sf \small \rarr10 x = 500$

$\sf \small \rarr x = \frac{500}{10}$

$\sf \small \rarr x = 50$

Putting the values of x we get

No. of 1 rs coins 3x = 3 × 50 = 150 coins

No. of 50 paise coins 8x =8 × 50 = 400 coins

No. of 25 paise coins 12x = 12 × 50 = 600 coins

Total number of coins = 150 + 400 + 600 → 1150 coins

There were 1150 coins in the bag

Answer 2

According to the question

1 rs , 50 paise and 25 paise are in the ratio → 3 : 8 : 12

By taking the variable as x we get

number of 1 rs coins → 3x

number of 50 paise coins → 8x

number of 25 paise coins → 12x

Solution :

Value of 3x rs 1 coins

→ ₹ 1 × 3x

→ ₹ 3x

Value of 8x 50 paise coins

→ 8x × 50 paise

8x × 50/100

Value of 12x 25 paise coins

→ 12x × 25 paise

12x × 25/100

rs→3xrs

Total amount in the bag → ₹ 500

Value of 1 rs coins + 50 paise coins + 25 paise coins = ₹ 500

Putting the values we get,

3x + 4x + 3x = 500→3x+4x+3x=500

10 x = 500→10x=500

x = 500/10

x=50

Putting the values of x we get

No. of 1 rs coins 3x = 3 × 50 = 150 coins

No. of 50 paise coins 8x =8 × 50 = 400 coins

No. of 25 paise coins 12x = 12 × 50 = 600 coins

Total number of coins = 150 + 400 + 600 → 1150 coins

There are 1150 coins in the bag