Two stations P and Q are D km apart. Train M departs from P towards Q at a speed of 96 kmph and halts for 3 minutes after every 32 km. Train N departs from Q towards P at a speed of 60 kmph, but starts 9 minutes after Train M departs. Both trains meet exactly 1 hour and 24 minutes after Train M starts, and the number of stoppages Train M made before meeting Train N is exactly 3. Which of the following statement(s) is/are true?
I. Nearest perfect square number to D is 196.
II. LCM of (D − 5) and (D + 1) is 18620.
III. Sum of each digit of D is 15.

Time for which train M stops = 3 × 3 = 9 min Time for which train M travels = 84 − 9 = 75 min Distance travelled by Train M = 96 × (75/60) = 120 km Time for which train N travels = 84 − 9 = 75 minutes Distance travelled by Train N = 60 × (75/60) = 75 km Total distance D = 120 + 75 = 195 km Required value of D = 195 Statement I:
Nearest perfect square number to 195 is 196.
So, Statement I is true. Statement II:
D − 5 = 195 − 5 = 190
D + 1 = 195 + 1 = 196
LCM of 190 and 196 = 18620
So, Statement II is true. Statement III:
Sum of Digit of 195 = 1 + 9 + 5 = 15
So, Statement III is true. Hence, option E (All I, II and III).