If the difference of Mode and Median of a data is 24 . . .

Question : If the difference of Mode and Median of a data is 24, then the difference of median and mean is 

a) 8

b) 12

c) 24

d) 36

Doubt by Aditi

Solution : 

Median - Mean = ?
Mode-Median = 24 (Given)
Mode = 24+Median — (1)

We know, 

3 Median = 2 Mean + Mode

3 Median = 2Mean + 24 + Median 

[Using eq (1)]

3Median-Median-2Mean = 24
2Median - 2Mean = 24
2(Median-Mean)=24

Median - Mean = 24/2
Median - Mean = 12

Hence, b) would be the correct option.