At 9 o'clock, the hour hand is at 9 and the minute hand is at 12. it means that the two hands are 15 min spaces apart .To be in the same straight line (but not together ), they will be 30 min space apart .
∴ The minute hand will have to gain (30 - 15) = 15 min space over the hour hand .

Correct Option: C

At 9 o'clock, the hour hand is at 9 and the minute hand is at 12. it means that the two hands are 15 min spaces apart .To be in the same straight line (but not together ), they will be 30 min space apart .
∴ The minute hand will have to gain (30 - 15) = 15 min space over the hour hand .

As we Know, 55 min spaces are gained in 60 min.
∴ 15 min will be gained in (60/55 x 15) min = 180/11 = 16⁴ /₁₁ min

Hence, the hands will be in the same straight line but not together at 16⁴/ ₁₁ min past 9.

Given that n = 2 and (n + 1) = 3(n < 6)
The hands will be at the same straight line at
⇒ (5n + 30) x 12/11 min past n.

Correct Option: A

Given that n = 2 and (n + 1) = 3(n < 6)
The hands will be at the same straight line at
⇒ (5n + 30) x 12/11 min past n.
⇒ (5 x 2 + 30 ) x 12/11 min past 2.
⇒ (10 + 30) x 12/11 min past 2.
⇒ 40 x 12/11 min past 2.
⇒ 480/11 min past 2.

Time from 6 am on a day to 11 pm on 4th day = 89 h
Now, 23 h 44 min of this clock = 24 h of correct clock
89 h of this clock = 24 x (15/356) x 89 h of correct clock = 90 h of correct clock

Correct Option: A

Time from 6 am on a day to 11 pm on 4th day = 89 h
Now, 23 h 44 min of this clock = 24 h of correct clock
89 h of this clock = 24 x (15/356) x 89 h of correct clock = 90 h of correct clock
∴ Correct time will be 12 o' clock (mid-night).

Time from 9 pm in a day to 2 pm on the following day = 29 h.
24 h 10 min of this clock = 24 h of the correct clock
or 145/6 h of this clock = 24 h of the correct clock
29 h of this clock = 24 x (6/145) x 29 h of the correct clock
= 28 h 48 min of correct clock

Correct Option: C

Time from 9 pm in a day to 2 pm on the following day = 29 h.
24 h 10 min of this clock = 24 h of the correct clock
or 145/6 h of this clock = 24 h of the correct clock
29 h of this clock = 24 x (6/145) x 29 h of the correct clock
= 28 h 48 min of correct clock
∴ The correct time is 28 h 48 min after 9 am. This will be 48 min past 1.

Given that, time to overtake = 70 min

The required result = [(720/11) - N) ] x [(60 x 24)/N) min
= [(720/11) - 70) ] x [(60 x 24)/70) min

Correct Option: B

Given that, time to overtake N = 70 min

The required result = [(720/11) - N) ] x [(60 x 24)/N) min
= [(720/11) - 70) ] x [(60 x 24)/70) min
= [(720 - 770) / 11] x [(60 x 24) / 70] min
= - (50/11) x [(6 x 24)] / 7 min = -7200/77 min
-ve sign indicates that there is a loss.