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The mean and the median of the following...

The mean and the median of the following ten numbers in increasing order 10, 22, 26, 29, 34, x, 42, 67, 70, y are 42 and 35 respectively, then `(y)/(x)` is equal to

A

`(7)/(3)`

B

`(7)/(2)`

C

`(8)/(3)`

D

`(9)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given ten numbers are
10, 22, 26, 29, 34, x, 42, 67, 70, y
and their mean `=42`
` therefore (10+ 22+ 26+ 29+ 34+ x+ 42+ 67+ 70+ y)/(10)=42`
`rArr (300+x+y)/(10)=42`
`rArr x+y=120 " …(i)" `
and their median (arranged numbers are in increasing order)`= 35`
`rArr (34+x)/(2)=35`
`rArr 34+x=70`
`rArr x=36`
On substituting `x=36` in Eq. (i), we get
`36+y=120`
`rArr y=84`
` therefore (y)/(x)=(84)/(36)=(7)/(3)`
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