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A box has 210 coins of denominations one-rupee and fifty paise only. The ratio of their respective values is 13 : 11. The number of one-rupee coin is
- a)65
- b)66
- c)77
- d)78
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A box has 210 coins of denominations one-rupee and fifty paise only. T...
To solve this problem, we need to set up a system of equations based on the given information. Let's assume that the number of one-rupee coins is x and the number of fifty paise coins is y.
1. Setting up the equations:
We are given that the ratio of the values of one-rupee coins to fifty paise coins is 13:11. This means that the value of one-rupee coins is 13 times the value of fifty paise coins.
Therefore, we can write the equation:
1 * x = 13 * 0.50 * y
We are also given that the total number of coins is 210. So we can write another equation:
x + y = 210
2. Solving the equations:
First, let's simplify the first equation:
x = 6.50y
Now substitute this value of x into the second equation:
6.50y + y = 210
7.50y = 210
y = 210 / 7.50
y = 28
Now substitute the value of y back into the second equation to find x:
x + 28 = 210
x = 210 - 28
x = 182
So, the number of one-rupee coins (x) is 182.
3. Finding the correct answer:
We need to find the number of one-rupee coins, which is 182. Among the given options, option D states that the number of one-rupee coins is 78. This is incorrect.
Therefore, the correct answer is option D. The number of one-rupee coins is actually 182.
1. Setting up the equations:
We are given that the ratio of the values of one-rupee coins to fifty paise coins is 13:11. This means that the value of one-rupee coins is 13 times the value of fifty paise coins.
Therefore, we can write the equation:
1 * x = 13 * 0.50 * y
We are also given that the total number of coins is 210. So we can write another equation:
x + y = 210
2. Solving the equations:
First, let's simplify the first equation:
x = 6.50y
Now substitute this value of x into the second equation:
6.50y + y = 210
7.50y = 210
y = 210 / 7.50
y = 28
Now substitute the value of y back into the second equation to find x:
x + 28 = 210
x = 210 - 28
x = 182
So, the number of one-rupee coins (x) is 182.
3. Finding the correct answer:
We need to find the number of one-rupee coins, which is 182. Among the given options, option D states that the number of one-rupee coins is 78. This is incorrect.
Therefore, the correct answer is option D. The number of one-rupee coins is actually 182.
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Community Answer
A box has 210 coins of denominations one-rupee and fifty paise only. T...
Respective ratio of the Number of coins;
= 13 : 11 × 2 = 13 : 22
Hence, Number of 1 rupee coins;
= 13 : 11 × 2 = 13 : 22
Hence, Number of 1 rupee coins;
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