investment

[grandh01]

Last year Luis invested x dollars for
one year, half at 8 percent simple
annual interest and the other half at
12 percent simple annual interest.
Now he wants to reinvest the x
dollars for one year in the same two
types of investments, but the lower
rate has decreased. If the higher rate
is unchanged, what fraction of the x
dollars must he reinvest at the 12
percent rate so that the total interest
earned from the x dollars will be the
same for both years ?
(1) The lower rate is now 6 percent.
(2) The total amount of interest
earned from the two investments
last year was $3,000.

OA is A

[niketdoshi123]

Last year Luis invested x dollars for
one year, half at 8 percent simple
annual interest and the other half at
12 percent simple annual interest.
Now he wants to reinvest the x
dollars for one year in the same two
types of investments, but the lower
rate has decreased. If the higher rate
is unchanged, what fraction of the x
dollars must he reinvest at the 12
percent rate so that the total interest
earned from the x dollars will be the
same for both years ?
(1) The lower rate is now 6 percent.
(2) The total amount of interest
earned from the two investments
last year was $3,000.

Last Year

Interest earned from 8% S.I = 8% of x/2 = .04x
Interest earned from 12% S.I = 12% of x/2 = .06x
Total interest earned = .1x

This Year

Total interest earned = .1x (same as that of last year)
Let $y & $x-y he reinvest at 12% & new rate respectively to earn .1x interest

=> .1x = 12% of y + (new rate)% of (x-y)
=> (10 - new rate)% of x = (12 -new rate)% of y

So if we know the new rate , we can find the fraction of the $x he must reinvest.

statement 1:
it gives the new rate = 6%
Hence sufficient

statement 2:
we don't have any information about the new rate.
Hence insufficient