Question

If the ratio of mode and median us 9:7,then find the ratio of mean and mode

Answer 1

$\bold{\sf{\underline{\underline{\huge{AnsWer:}}}}}$

Ratio of mean and mode = 2:3

$\bold{\sf{\underline{\underline{\large{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• The ratio of mode and median is 9:7

To FiNd :

• Ratio of mean and mode.

SoLuTiON :

Let the common multiple of the ratio 9:7 be x.

•°• Mode $\longrightarrow$ 9x

Medium $\longrightarrow$ 7x

FoRmUlA :

$\bold{\large{\boxed{\sf{blue{3\:Median\:=\:Mode\:+\:2\:Mean}}}}}$

Blocking in the values,

$\longrightarrow$ $\sf{3\:\times\:7x=\:9x\:+\:2\:\times\:Mean}$

$\longrightarrow$ $\sf{21x\:=\:9x\:+\:2\:\times\:Mean}$

$\longrightarrow$ $\sf{21x\:-\:9x\:=\:2\:\times\:Mean}$

$\longrightarrow$ $\sf{12x\:=\:2\:\times\:Mean}$

$\longrightarrow$ $\sf{\dfrac{12x}{2}\:=\:Mean}$

$\longrightarrow$ $\sf{6x\:=\:Mean}$

•°• Mean = 6x

Now, ratio of mean and mode :

$\longrightarrow$$\sf{\dfrac{Mean}{Mode}}$

Block in the values,

$\longrightarrow$ $\sf{\dfrac{6x}{9x}}$

Divide by 3,

$\longrightarrow$ $\sf{\dfrac{2x}{3x}}$

$\longrightarrow$ $\sf{\dfrac{2}{3}}$

•°• Ratio of mean and mode = 2 : 3