Why should the consumer be willing to sacrifice less and less amount of Good-Y for every successive unit of Good-X?

Ria,

As a consumer gets more amount of good X, he will like to obtain less units of good X. It means the marginal utility he derive from good X will decline(as per law of diminishing marginal utility). Also, if more amount of good Y is being sacrificed, consumer will like to have more units of good Y. So, marginal utility from good Y will increase. This is the reason that a consumer is willing to sacrifice less and less amount of good Y for every successive unit of good X. So, $\frac{∆Y}{∆X}$ will decrease implies a fall in MRS.