correct answer is: a) ₹\;25506

Explanation

According to the question,
The co-operative society can spend ₹\;77575 in a year.
It distributes ₹\;42150 as dividend among the members.
So that,
Remaining money =₹\left(77575-42150\right)
\rightarrow ₹\;35425.
Here,
Remaining money is distributes as the ratio of 7\;:\;18.
Let’s,
Money required to distributes as salary is =\;₹\;7x.
Money required to invested as loan is =\;₹\;18x.
So that,
₹\left(7x+18x\right)=₹35425
\rightarrow 25x=35425
\rightarrow x=\large\frac{35425}{25}
\rightarrow x=1417
\therefore Money invested as loan =\;₹\;18x
\rightarrow ₹ \left(18\times1417\right)
\rightarrow ₹\;25506.
Ans: ₹\;25506 is invested as loan.

Another method to articulate this particular math query is available:

1. Within a year, a customer co-operative society disperses ₹ 42150 as dividends among its members from its available funds. The residual amount is apportioned as staff salaries and loans in a ratio of 7 : 18. Given that the society’s yearly expenditure totals ₹ 77575, ascertain the portion allocated for loans.
2. In a year, a customer co-operative society spends ₹ 77575, with ₹ 42150 being distributed as dividends among its members. The residual amount is divided as staff salaries and loans in a ratio of 7 : 18. Determine the sum designated for loans.
3. A customer co-operative society allocates ₹ 42150 as dividends among its members from its annual expenditure. The remainder is distributed as staff salaries and loans in a ratio of 7 : 18. If the society’s annual expenditure amounts to ₹ 77575, determine the sum designated for loans.