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If a, b, c, d and e are positve numbers,...

If a, b, c, d and e are positve numbers, and it is given that ,
`{:(a + b = c + d ),(b + d = 2a),(d + e gt a + b and ),(c + d gt a + e ):}`
then, which of the following statement is true ?

A

`d gt a gt b gt e gt c`

B

`d gt b gt e gt a gt c`

C

`a gt b gt c gt d gt e`

D

`a gt b fr b gt e gt c`

Text Solution

Verified by Experts

The correct Answer is:
A
`a+b = c +b` (i)
`2a=b+d....(ii) rArr b,a,d in AP`
(ii) - (i)
`a-b=c+d`
`rArr d+e gt C + d`
`rArr e gt c`
Again , `c + d gt a+e rArr a+b gt a+e`
`rArr b gt e`
`rAr c lt e lt b`
Combing , the results we can conclude :
`d gt a gt b gt e gt c`
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