(a) The assumption of diminishing marginal rate of substitution states that the consumer will be willing to sacrifice lesser units of Good Y, so as to gain additional unit of the Good X. This is an extention of law of diminishing marginal utility. Diminishingmarginal rate of substitution is the reason behind convexity of Indifference Curve to the origin. 

The following table shows, bundles of Good X and Y which provide same level of satisfaction to the consumer:- 

The above schedule shows that for each additional unit of Good X, consumer is willing to sacrifice lesser and lesser units of Good Y. 

(b) Marginal rate of substitution (MRS) is the rate at which consumer is willing to trade-off one good for the other. It depends on the quantity of the two goods s/he is consuming. A rational consumer will sacrifice lesser units of Good Y so as to acquire additional units of Good X, due to the application of law of diminishing marginal utility. 

MRS should be diminishing as additional consumption of Commodity X, symbolises fall in marginal utility due to which the consumer will not further increase its consumption. If it does not fall, s/he will keep on increasing the consumption of Commodity-X and will not reach a stable equilibrium.