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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 the one-rupee coin is:
- a)65
- b)66
- c)77
- d)78
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A box has 210 coins of denominations one-rupee and fifty paise only. ...
The respective ratio of the number of coins;
View all questions of this test
= 13 : 11 × 2
= 13 : 22
So, Number of 1 rupee coins;
= 78
Hence, the correct option is (D).
Most Upvoted Answer
A box has 210 coins of denominations one-rupee and fifty paise only. ...
Given information:
- The box has 210 coins of denominations one-rupee and fifty paise only.
- The ratio of their respective values is 13 : 11.
To find: The number of one-rupee coins in the box.
Solution:
Let the number of one-rupee coins be x.
Then, the number of fifty paise coins will be (210 - x).
According to the given ratio,
- Value of x one-rupee coins = 13y (where y is the value of one fifty paise coin)
- Value of (210 - x) fifty paise coins = 11y
Total value of the coins in the box can be calculated as follows:
Value of x one-rupee coins + Value of (210 - x) fifty paise coins = Total value of coins
13xy + 11y(210 - x) = Total value of coins
Simplifying the above equation, we get:
2xy + 11y(210) = Total value of coins
2xy + 2310y = Total value of coins
y(2x + 2310) = Total value of coins
Since the total value of coins is a multiple of 50 paise, y must be a multiple of 0.5.
Let y = 0.5.
Then, 2x + 2310 = Total value of coins / 0.5
2x + 2310 = 2 * Total value of coins
2x + 2310 = 26x + 22(210 - x)
2x + 2310 = 26x + 4620 - 22x
24x = 2310 + 4620 - 2310
24x = 2310
x = 2310 / 24
x = 96.25
Since the number of one-rupee coins must be a whole number, the closest whole number to 96.25 is 96.
Therefore, the number of one-rupee coins in the box is 96. Answer: (d) 78.
- The box has 210 coins of denominations one-rupee and fifty paise only.
- The ratio of their respective values is 13 : 11.
To find: The number of one-rupee coins in the box.
Solution:
Let the number of one-rupee coins be x.
Then, the number of fifty paise coins will be (210 - x).
According to the given ratio,
- Value of x one-rupee coins = 13y (where y is the value of one fifty paise coin)
- Value of (210 - x) fifty paise coins = 11y
Total value of the coins in the box can be calculated as follows:
Value of x one-rupee coins + Value of (210 - x) fifty paise coins = Total value of coins
13xy + 11y(210 - x) = Total value of coins
Simplifying the above equation, we get:
2xy + 11y(210) = Total value of coins
2xy + 2310y = Total value of coins
y(2x + 2310) = Total value of coins
Since the total value of coins is a multiple of 50 paise, y must be a multiple of 0.5.
Let y = 0.5.
Then, 2x + 2310 = Total value of coins / 0.5
2x + 2310 = 2 * Total value of coins
2x + 2310 = 26x + 22(210 - x)
2x + 2310 = 26x + 4620 - 22x
24x = 2310 + 4620 - 2310
24x = 2310
x = 2310 / 24
x = 96.25
Since the number of one-rupee coins must be a whole number, the closest whole number to 96.25 is 96.
Therefore, the number of one-rupee coins in the box is 96. Answer: (d) 78.
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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 the one-rupee coin is:a)65b)66c)77d)78Correct answer is option 'D'. Can you explain this answer?
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