| Directions: Read the following information to answer the given questions: |
| A bag contains coins of four different denominations viz. 1 rupee, 50-paise, 25-paise and' 10-paise. There are as many 50-paise coins as the value of 25-paise coins in rupee. The value of 1-rupee coins is 5 times the value of 50-paise coins. The ratio of the number of 10-paise coins to that of 1-rupee coins is 4:3, while the total number of coins in the bag is 325. |
A) 1 : 4
B) 2 : 5
C) 2 : 3
D) 1 : 3
Correct Answer: A
Solution :
10-paise coins = 4x; so 1-rupee coins = 3x. Value of 1-rupee coins = Rs 3x. Number of 50-paise coins say ?y?, then the value of 50-paise coins is Rs. \[\frac{y}{2}\]\[\Rightarrow \,\,3x=5,\frac{y}{2}\,\,or\,\,y=\frac{6x}{5}\] Also number of 50-paise coins \[=\frac{6x}{5}\] so this is also the value of 25-paise coins. Thus value of 25-paise coins = Rs \[\frac{6x}{5}\] let the number of 25-paise coins be Z so that its value is Rs \[\frac{Z}{4}\]\[\Rightarrow \,\,\,\frac{Z}{4}=\frac{6x}{5}\,\,or\,\,Z=\frac{24}{5}\,\,\,x\] \[\therefore \] Total number of coins \[=4x+\frac{24}{5}x+\frac{6x}{5}+3x=325\]\[\Rightarrow \,\,13x=325\,\,or\,\,x=25\]
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