Question

A purse contains coins of denominations of 2 rupees, 5 rupees and 1 rupee in the ratio 8:6:5. Find the amount in the purse if the value of 5 rupees coin is 56 rupees more than the value of 2 rupees coins​

Answer 1

Answer:

$\bigstar{\bold{Amount\:of\:money=Rs\:204}}$

Step-by-step explanation:

$\Large{\underline{\underline{\sf{Given:}}}}$

• Ratio of 2 rupee, 5 rupee and 1 rupee coin = 8 : 6 : 5
• Value of 5 rupee coins = 56 + value of 2 rupee coins

$\Large{\underline{\underline{\sf{To\:Find:}}}}$

• The total amount in the purse

$\Large{\underline{\underline{\sf{Solution:}}}}$

→ Let the number of 2 rupee coins be 8x

→ Let the number of 5 rupee coins be 6x

→ Let the number of 1 rupee coins be 5x

→ By given we know that

  Value of 5 rupee coins = 56 + value of 2 rupee coins---(1)

→ Value of 5 rupee coins = 5 × 6x

  Value of 5 rupee coins = 30x rupees---(2)

→ Value of 2 rupee coins = 2 × 8x

  Value of 2 rupee coins = 16x rupees-----(3)

→ Substituting equation 2 and 3 in 1

  30x = 56 + 16x

  30x - 16x = 56

  14x = 56

      x = 56/14

      x = 4

→ Amount of money in the purse = Value of 2 rupee coins + Value of 5 rupee coins + Value of 1 rupee coins.

  Amount of money in the purse = 2 × 8x + 5 × 6x + 1 × 5x

→ Substituting the value of x,

  Amount of money in the purse = 16 × 4 + 30 × 4 + 5 × 4

  Amount of money in the purse = 64 + 120 + 20

  Amount of money in the purse = 204 rupees

$\boxed{\bold{Amount\:of\:money=Rs\:204}}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

→ Value of 5 rupee coins = 56 + value of 2 rupee coins

  5 × 6x = 56 + 2 × 8 x

  5 × 6 × 4 = 56 + 2 × 8 × 4

  120 = 56 + 64

  120 = 120

→ Hence verified.