A total of 384 rupees are in a bag in the form of 50p, 25p and 10p coins. If the coins are in the ratio 7: 8: 9 respectively, then the number of 10p coins are 500. (a) True (b) False
Question
A total of 384 rupees are in a bag in the form of 50p, 25p and 10p coins. If the coins are in the ratio 7: 8: 9 respectively, then the number of 10p coins are 500. (a) True (b) False
Solution
To solve this problem, we first need to understand that the total value of the coins is given in rupees, but the value of the coins themselves is given in pence. Therefore, we need to convert the total value to pence.
1 rupee = 100 pence, so 384 rupees = 38400 pence.
The ratio of the coins is 7:8:9. This means for every 7 coins of 50p, there are 8 coins of 25p and 9 coins of 10p.
Let's denote the common ratio as x. So, the number of 50p coins is 7x, the number of 25p coins is 8x, and the number of 10p coins is 9x.
The total value of the coins can be calculated as follows:
50p * 7x + 25p * 8x + 10p * 9x = 38400p
350x + 200x + 90x = 38400
640x = 38400
Solving for x gives x = 60.
So, the number of 10p coins is 9x = 9*60 = 540.
Therefore, the statement "the number of 10p coins are 500" is (b) False.
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