It is between 3 pm and 4 pm and the distance between the hour hand and the minute hand of clock is 18 minutes spaces. What time does the clock show ?

At 3 o'clock, the minute hand is 15 minute spaces behind the hour hand.
Thus, the minute hand has to gain (15 + 18) = 33 minute spaces
55 minutes are gained in 60 minutes.
33 minutes are gained in $$\left( {\frac{{60}}{{55}} \times 33} \right)$$   = 36 minutes
∴ The hands will be 18 minutes spaces apart at 3 : 36 pm.