Question

the mean of certain no. of observations is 46.if 4 observations whose mean is 52 is removed,the mean becomes 44.5.the original number of observations is
A)35
B)20
C)15
D)12

Answer 1

$\huge\pink{\underline{\red H\orange e\purple l\blue l\green o}}$

$\huge\orange{\mid{\overline{\underline{\mathfrak{Solution:-}}}}\mid}$

➡️ Let the number of observations be x.

➡️Mean of observations = 46

➡️Total number of observations = 46x

Now,

⏩ Value removed = 52×4 = 208

➡️Remaining value = 46x-208

➡️Remaining observations = x-4

⏩Mean = 44.5

➡️Value = 44.5(x-4) = 44.5x-178

According to question,

➡️ 46x-208 = 44.5x-178

➡️ 46x-44.5x = 208-178

➡️ 1.5x = 30

➡️ x = 30/1.5 = 20

Hence, Total number of terms are 20.

⏩⏩ (B) 20

$\large\red{\underline {Hope\:it\:helps}}$