Why does time pass faster in moon than the earth? One of my friends said that,

time passes faster in moon than the earth

Why does time pass faster on the moon than on the earth?
Okay, this question is actually quite simple and requires some background on the relations between gravity and time.
The property that can be used to answer this question is :

Time is affected by gravity in the following way : Imagine you are on an exoplanet. The gravity there is twice that gravity here on Earth. Now, assuming that we take Earth Time as standard, the Exoplanet's time should be slower than Earth-Time.

Basically, the property states that the greater the gravity of the place, the greater will be the time dilation effect.
Here, for your question, we can apply the same principle. Since Moon-Gravity is 1/6th of Earth's, time should pass faster there.
@MarkAdler has given an excellent answer here, on the Stack Exchange for Space Exploration. To quote his answer :

Time passes about 0.66 parts per billion faster on the Moon than on Earth, due to not being in as strong a gravity field. The dilation, including all the effects of being further from the Earth's gravity field, being in the Moon's gravity field, and the velocity of the Moon, could easily be measured in sum by comparing good atomic clocks on the Earth and the Moon.

He has also posted some maths on the same, so I recommend checking out the link above :
Hope this answer helps,