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?7151424

Let's denote the number of members in the club as 'x'.

According to the problem, each member contributed an amount equal to twice the number of members in the club. So, the total amount contributed by all members is x * 2x = 2x^2.

The government contributed the same amount as the number of members, which is x.

So, the total amount collected is 2x^2 + x.

The problem also states that if each member had contributed the same amount as the number of members (which is x) and the government had given an amount twice the number of members (which is 2x), then they would have Rs.210 less.

So, the total amount in this case would be x^2 + 2x, and according to the problem, this amount is Rs.210 less than the original amount collected.

Therefore, we can set up the following equation:

2x^2 + x = x^2 + 2x + 210

Solving this equation will give us the number of members in the club.

Subtract x^2 + 2x from both sides to get:

x^2 - x - 210 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it by factoring, completing the square, or using the quadratic formula.

Factoring the equation gives us:

(x - 15)(x + 14) = 0

Setting each factor equal to zero gives the solutions x = 15 and x = -14.

Since the number of members can't be negative, the club has 15 members.