Which of the following statements is true?
Statement 1: MRS is simply the rate at which the consumer will substitute bananas for mangoes, so that her total utility remains constant.
Statement 2: As we move down along the indifference curve, MRS falls. 

Both the statements are true.

Both the statements are true in themselves. MRS is the slope of indifference curve and at all the points on the indifference curve the total satisfaction of consumer remains same and for that to happen, if one commodity is increased, the other has to be sacrificed. MRS measures the sacrifice made in order to have more of another product. And MRS also diminishes as we increase consumption of one commodity and decreases the consumption of another.