Question : In a bag, the number of INR 5 coins is 8 more than the number of INR 10 coins but 20% less than the number of INR 2 coins. If the total amount in the bag is INR 270, what is the number of INR 5 coins?
Option 1: 15
Option 2: 20
Option 3: 25
Option 4: 18
Correct Answer: 20
Solution :
Let's assume the number of INR 2, INR 5 and INR 10 coins are 'a', 'b', and 'c' respectively.
In a bag, the number of INR 5 coins is 8 more than the number of INR 10 coins but 20% less than the number of INR 2 coins.
⇒ b = c + 8
⇒ c = (b – 8)
⇒ b = (100 – 20)% of a
⇒ b = 80% of a
⇒ b = 0.8a
⇒ a = $\frac{b}{0.8}$
The total amount in the bag is INR 270. We can write this as:
⇒ 2a + 5b + 10c = INR 270
⇒ 2 × $\frac{b}{0.8}$ + 5b + 10 × (b - 8) = 270
⇒ 2.5b + 5b + 10b - 80 = 270
⇒ 17.5b = 350
⇒ b = 20
Therefore, the number of INR 5 coins is 20.
Hence, the correct answer is 20.
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