Income of Riya is Rs. (124n + 1680). She spends 75% of her income and saves the rest. Savings of her friend Mehul is Rs. 960 more than that of her. Mehul saves 50% of his income. If average expenditure of Riya and Mehul is Rs. (74n - 360). Which of the following statement(s) is/are true?
I. 'n' is less than the square of 12
II. (n - 41) is a perfect square
III. Sum of each digit of 'n' is 5

Expenditure of Riya = 0.75 × (124n + 1680) = Rs. (93n + 1260)

Savings of Riya = 124n + 1680 - 93n - 1260 = Rs. (31n + 420)

Savings of Mehul = 31n + 420 + 960 = Rs. (31n + 1380)

Income of Mehul = (31n + 1380) ÷ 0.5 = Rs. (62n + 2760)

Expenditure of Mehul = 62n + 2760 - 31n - 1380 = Rs. (31n + 1380)

(93n + 1260 + 31n + 1380) ÷ 2 = 74n - 360

Or, 124n + 2640 = 148n - 720

Or, 62n + 1320 = 74n - 360

Or, 12n = 1680

Or, 'n' = 140

Statement I:

Square of 12 = 144

140 < 144

So, statement I is true.

Statement II:

140 - 41 = 99, which is not a perfect square

So, statement II is false.

Statement III:

Required sum = 1 + 4 + 0 = 5

So, statement III is true.

Therefore, statements I and III are true.