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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.
- Rs. 254
- Rs. 180
- Rs. 78
- 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