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A group wanted to renovate their club. Each member contributed an amount equal to twice the number of members in the club. But the government contributed same amount as the number of members. If each member had contributed the same amount as the number of members and the government had given an amount twice the number of members, then they would have Rs. 210 less. How many members are there?
  • a)
    7
  • b)
    14
  • c)
    25
  • d)
    15
Correct answer is option 'D'. Can you explain this answer?
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Understanding the Problem:
The problem states that each member contributed an amount equal to twice the number of members in the club, and the government contributed the same amount as the number of members. If the contributions were different, they would have had Rs. 210 less. We need to find the number of members in the club.

Let's Solve the Problem:
Let's assume the number of members in the club is 'x'.

Given Conditions:
1. Each member contributed 2x.
2. The government contributed x.
3. The difference in contributions is Rs. 210.

Equation:
Total contribution with original plan = x * 2x + x = 2x^2 + x
Total contribution with modified plan = x * x + 2x = x^2 + 2x

Given Difference:
2x^2 + x - (x^2 + 2x) = 210
x^2 - x = 210
x^2 - x - 210 = 0
(x - 15)(x + 14) = 0

Therefore, the Number of Members is:
Since the number of members cannot be negative, the number of members is 15.
Therefore, the correct answer is option D) 15.
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A group wanted to renovate their club. Each member contributed an amount equal to twice the number of members in the club. But the government contributed same amount as the number of members. If each member had contributed the same amount as the number of members and the government had given an amount twice the number of members, then they would have Rs. 210 less. How many members are there?a)7b)14c)25d)15Correct answer is option 'D'. Can you explain this answer?
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