‘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 143:100:163, respectively. Which of the following statement(s) is/are true regarding ‘y’?
I. Sum of squares of each digit of ‘y’ is 50.
II. 12y < √900 × √900
III. The tens digit of ‘y’ is a prime 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 = 143:100 Or, 12,000 + 24y = 13,680 Or, 24y = 1,680 Or, ‘y’ = 70 Statement I:
Required sum = 7² + 0² = 49 + 0 = 49
Statement says 50 → false. Statement II:
12y = 12 × 70 = 840
√900 × √900 = 30 × 30 = 900
Here, 12y < √900 × √900
So, statement II is true. Statement III:
Tens digit of ‘y’ = 7, which is a prime number.
So, statement III is true. Therefore, both II and III are true.