Let's break down the information given:
1. The total profit the man wants to make is Rs. 10,000.
2. The total amount borrowed is Rs. 25,000.
3. The repayment will be done in 10 installments.
4. Each installment is Rs. 200 less than the preceding one.
The sum of the arithmetic progression formula can be used to solve this problem:
Sum of the first n terms of an arithmetic progression: S = n/2 * [2a + (n-1)d]
Where:
S = Sum of the terms (Rs. 10,000 + Rs. 25,000)
n = Number of terms (10 installments)
a = First term (the first installment)
d = Common difference (-Rs. 200)
Given that S = 10,000 + 25,000 = Rs. 35,000, n = 10, and d = -200, we can solve for 'a':
35,000 = 10/2 * [2a + (10-1)(-200)]
35,000 = 5 * [2a - 1800]
7,000 = 2a - 1800
2a = 7,000 + 1800
2a = 8,800
a = 8,800 / 2
a = 4,400
Therefore, the man's first installment should be Rs. 4,400.