If the mean exceeds the mode by 48 and the median is 12, find the mean.

Question: If the mean exceeds the mode by 48 and the median is 12, find the mean.

Solution:
Given,
Median = 12
Mean - Mode = 48

We know,
Mode = 3Median - 2Mean

So,
Mean - Mode = Mean - (3Median - 2Mean)
= Mean - 3Median + 2Mean
= 3Mean - 3Median
= 3(Mean - Median)

Therefore, Mean - Mode = 3(Mean - Median)
⇒ 48 = 3(Mean - 12)
⇒ Mean - 12 = 48/3
⇒ Mean - 12 = 16
⇒ Mean = 16 + 12
∴ Mean = 28

Answer: গ) 28