Question

At what time between $\text{3 o ' clock and 4 o ' clock}$, both the needles of the clock will coincide each other ?

• A. $16\frac{4}{11}\text{minutes past 3}$.
  
• B. $\frac{2}{11}(3\times 30+0)\text{minute past 3}$
• C. $\frac{3}{11}(3\times 30+0)\text{minute past 3}$
• D. $\frac{4}{11}(3\times 30+0)\text{minute past 3}$

Answer 1

The correct option is A $16\frac{4}{11}\text{minutes past 3}$.

⇒⇒ At 3 o ' clock3 o ' clock, minute hand is 1515 minute apart from hour hand
To coincide with hour hand, it must gain 1515 minutes space 5555 minutes are gained in 6060 minutes
1515 minutes are gained in 6055×15=16411min6055×15=16411min
Hands coincide at 16411minutes past 316411minutes past 3.
Another Method
Using formula T=211(Hour hand position×30+Angle difference)T=211(Hour hand position×30+Angle difference)
Here, Hour hand position =3=3
Angle difference =0=0
∴T=211(3×30+0)minute past 3