‘P’ and ‘Q’ started a business with investment of Rs. 3,000 and Rs. 4,200, respectively. After 8 months, ‘P’ increased his investment by Rs. ‘8y’. After another 8 more months, ‘Q’ decreased his investment by Rs. ‘8y’ and ‘R’ joined the business with Rs. 4,800. At the end of 32 months, the ratio of profit share of ‘P’, ‘R’ and ‘Q’ was 277:200:332, respectively. Which of the following statement(s) is/are true regarding ‘y’?
I. Sum of squares of each digit of ‘y’ is 45.
II. 12y < √625 × √729
III. The tens digit of ‘y’ is an even number.

Ratio of profit share of ‘P’, ‘Q’ and ‘R’, respectively: = [3,000 × 8 + (3,000 + 8y) × 24]:[4,200 × 16 + (4,200 − 8y) × 16]:[4,800 × 16] = (12,000 + 24y) : (16,800 − 16y) : 9,600 So, (12,000 + 24y):9,600 = 277:200 Or, 12,000 + 24y = 13,860 Or, 24y = 1,860 Or, ‘y’ = 54 Statement I:
Required sum = 5² + 4² = 25 + 16 = 41
So, statement I is false. Statement II:
12y = 12 × 54 = 648
√625 × √729 = 25 × 27 = 675
Here, 12y < √625 × √729
So, statement II is true. Statement III:
Tens digit of ‘y’ = 5, which is not even.
So, statement III is false. Therefore, only statement II is true.