Q11 of 40 Page 210

There are four unknown numbers. The mean of the first two numbers is 4 and the mean of the first three is 9. The mean of all four number is 15, if one of the four number is 2 find the other numbers.

Given: There are 4 unknown numbers, but one of the number is 2.

Let x1 = 2, x2 = ?, x3 = ? and x4 = ?


According to the question, mean of first two numbers = 4


Mean of first two numbers is given by,



⇒


⇒


⇒ 8 = 2 + x2


⇒ x2 = 8 – 2 = 6


We have x1 = 2 and x2 = 6. …(i)


Also, according to the question, mean of first three numbers = 9



⇒


⇒ [from (i)]


⇒ 27 = 8 + x3


⇒ x3 = 27 – 8


⇒ x3 = 19


We have now, x1 = 2, x2 = 6 and x3 = 19 …(ii)


Also, according to the question, mean of all four numbers = 15



⇒


⇒ 60 = 2 + 6 + 19 + x4 [from (ii)]


⇒ 60 = 27 + x4


⇒ x4 = 60 – 27


⇒ x4 = 33


Thus, we have x1 = 2, x2 = 6, x3 = 19 & x4 = 33.


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