Question

Please solve this question​

Answer 1

Question :

A bag contains one rupee, 50 paise and 25 paise coins. The ratio of the number of 1 rupee coins to 50 paise coins is 5 : 9 and the ratio number of 50 paise coins to that of 25 paise coins is 2 : 1. Find the value of 50 paise coins in the bag if the total value of the coins in the bag is Rs. 425.

1. Rs. 254
2. Rs. 180
3. Rs. 78
4. Cannot be determined

Answer :

Let the number of 1 rupee coins be W

Let the number of 50 paise coins be F

Let the number of 25 paise coins be T

Value of 1 rupee coins in the bag = Rs. 1 × W = Rs. W

Value of 50 paise coins in the bag = Rs. 50/100 × F = Rs. F/2

Value of 25 paise coins in the bag = Rs. 25/100 × T = Rs. T/4

Given :

Ratio of number of 1 rupee coins to 50 paise coins = 5 : 9

⇒ W / F = 5 / 9

⇒ W = 5F / 9 → ( 1 )

Given :

Ratio of number of 50 paise coins and 25 paise coins = 2 : 1

⇒ F / T = 2 / 1

⇒ T / F = 1 / 2

⇒ T = F / 2 → ( 2 )

Given :

Total value of the coins in the bag = Rs. 425

⇒ W + F/2 + T/4 = 425

⇒ ( 4W + 2F + T ) / 4 = 425

⇒ 4W + 2F + T = 425 × 4

⇒ 4W + 2F + T = 1700

From ( 1 ) & ( 2)

⇒ 4( 5F / 9 ) + 2F + F/2 = 1700

⇒ 20F/9 + 2F + F/2 = 1700

⇒ ( 40F + 36F + 9F ) / 18 = 1700

⇒ 85F / 18 = 1700

⇒ F = 1700 × ( 18 / 85 )

⇒ F = 360

∴ there are 360 fifty paise coins

Value of 50 paise coins = F/2 = 360/2 = Rs. 180

Therefore the value of 50 paise coins in the bag is Option ( 2 ) Rs. 180.