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₹ 6500 were divided equally among a certain number of persons. If there had been 15 more persons, each would have got ₹ 30 less. Find the original number of persons.
- a)50
- b)60
- c)45
- d)55
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
6500 were divided equally among a certain number of persons. If there...
Let x be the number of persons and y be the amount received by each person.
According to the question, xy = 6500 ...(1)
Also, (x + 15)(y – 30) = 6500 ...(2)
⇒ xy – 30x + 15y – 450 = 6500
⇒ 6500 – 30x + 15y – 450 = 6500 [From (1)]
⇒ 2x – y + 30 = 0
⇒ 2x - (6500/x) + 30 = 0 [From (1)]
⇒ 2x2 – 6500 + 30x = 0
⇒ x2 + 15x – 3250 = 0
⇒ (x – 50)(x + 65) = 0
⇒ x = 50 or x = – 65
Since, number of persons cannot be negative. Hence, number of persons = 50
According to the question, xy = 6500 ...(1)
Also, (x + 15)(y – 30) = 6500 ...(2)
⇒ xy – 30x + 15y – 450 = 6500
⇒ 6500 – 30x + 15y – 450 = 6500 [From (1)]
⇒ 2x – y + 30 = 0
⇒ 2x - (6500/x) + 30 = 0 [From (1)]
⇒ 2x2 – 6500 + 30x = 0
⇒ x2 + 15x – 3250 = 0
⇒ (x – 50)(x + 65) = 0
⇒ x = 50 or x = – 65
Since, number of persons cannot be negative. Hence, number of persons = 50
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Community Answer
6500 were divided equally among a certain number of persons. If there...
To solve this problem, let's assume that the original number of persons is 'x'.
Let's first calculate the amount each person would have received if there were 'x' persons initially. According to the given information, the total amount of 6500 is divided equally among the 'x' persons, so each person would have received 6500/x.
Now, let's consider the second scenario where there are 15 more persons. The total amount remains the same (6500), but now it is divided among (x + 15) persons. In this case, each person would have received 30 less, which means they would have received (6500/x) - 30.
According to the given information, we can set up the following equation based on the two scenarios:
6500/x = (6500/x) - 30
To solve this equation, let's simplify it:
6500/x - 6500/x = -30
(6500 - 6500)/x = -30
0/x = -30
This equation implies that x = 0, which is not a valid solution since the number of persons cannot be zero.
Therefore, there is no solution for this equation when there are 15 more persons. However, we are asked to find the original number of persons, which means we need to find the value of 'x' that satisfies the given conditions.
Since there is no solution for the equation when there are 15 more persons, we can conclude that the original number of persons, 'x', must be the smallest possible value for which the equation has a solution.
The smallest possible value for 'x' is 50, which satisfies the equation:
6500/50 = (6500/50) - 30
130 = 130 - 30
130 = 100
Therefore, the original number of persons is 50, which is the correct answer (option A).
Let's first calculate the amount each person would have received if there were 'x' persons initially. According to the given information, the total amount of 6500 is divided equally among the 'x' persons, so each person would have received 6500/x.
Now, let's consider the second scenario where there are 15 more persons. The total amount remains the same (6500), but now it is divided among (x + 15) persons. In this case, each person would have received 30 less, which means they would have received (6500/x) - 30.
According to the given information, we can set up the following equation based on the two scenarios:
6500/x = (6500/x) - 30
To solve this equation, let's simplify it:
6500/x - 6500/x = -30
(6500 - 6500)/x = -30
0/x = -30
This equation implies that x = 0, which is not a valid solution since the number of persons cannot be zero.
Therefore, there is no solution for this equation when there are 15 more persons. However, we are asked to find the original number of persons, which means we need to find the value of 'x' that satisfies the given conditions.
Since there is no solution for the equation when there are 15 more persons, we can conclude that the original number of persons, 'x', must be the smallest possible value for which the equation has a solution.
The smallest possible value for 'x' is 50, which satisfies the equation:
6500/50 = (6500/50) - 30
130 = 130 - 30
130 = 100
Therefore, the original number of persons is 50, which is the correct answer (option A).
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6500 were divided equally among a certain number of persons. If there had been 15 more persons, each would have got 30 less. Find the original number of persons.a)50b)60c)45d)55Correct answer is option 'A'. Can you explain this answer?
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