Some members of a social service organization in Kolkata decide to prepare 2400 laddoos to gift to children in various orphanages and slums in the city, during Durga puja. The plan is that each of them makes the same number of laddoos. However, on the laddoo-making day, ten members are absent, thus each remaining member makes 12  laddoos more than earlier decided.

How many members actually make the laddoos?

Initially considering the number of members = a

The number of ladoos each member is required to make as per the original plan = b.

Given : a*b = 2400.

Given that 10 members were absent and each member had to make an additional 12 ladoos :

(a-10)*(b+12) = 2400.

ab - 10b+12a-120 = 2400.

Since a*b = 2400.

Hence 12a-10b = 120.

Substituting b = 120/a.   $$12a\ -\ 10\cdot\left(\frac{2400}{a}\right)\ =\ 120$$

= $$\ 12a^2-24000-\ 120a\ =\ 0$$

The roots are a = 50, a = -40.

Hence a = 50, b = 48.

The number of people who took part in making ladoos = a - 10 = 40