If the ratio of mean and median of a certain data is 2 : 3, then the ratio of its mode and mean is

If the ratio of mean and median of a certain data is $2 : 3$ , then the ratio of its mode and mean is

A
$4 : 3$
B
$7 : 6$
C
$7 : 8$
D
$5 : 2$

Solution:

We have,

$\frac{Mean}{Median} = \frac{2}{3} \Rightarrow Mean = 2 λ and Median = 3 λ$

$∴$ $Mode = 3 Median - 2 Mean$

$\Rightarrow Mode = 9 λ - 4 λ = 5 λ$

$Mode: Mean = 5 λ : 2 λ = 5 : 2$

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