Simple Interest?

Given: $20 000

Place in two different investments (Silicon World and Solar Energy).

Let the amount placed in Silicon world be #x#

Silicon World offers an annual interest rate of 10%

So the interest on this amount will be given by:

#SI_1 = (PRT)/100 = (x xx10 xx 1)/100 = 0.1x#

where, P is principal amount invested
R is rate of interest, and
T is duration of investment which is given to be 1 year.

Now the amount invested in Solar Energy will be #20000 -x#
It offers a 6% annual interest rate, so the simple interest at the end of 1 year on this will be:

#SI_2 = (PRT)/100 = ((20000-x ) xx 6 xx 1 )/100 #

#SI_2 = (120000 - 6x)/100#

Given that: together the investments return a total of $1800 at the end of the year.

#=> SI_1 + SI_2 = 1800#

#=> 0.1x +(120000 - 6x)/100 = 1800#

#=> 10x +120000 - 6x = 180000#

#=> 4x = 180000-120000 = 60000#

#=> x = 15000#

#therefore # Amount of money placed in investment Silicon world is #$15000#
and Amount of money placed in Solar Energy was $20000-15000 = $5000#

Cross heck:

1 : Silicon world: Amount invested: $15000 at rate 10% for 1 year will return interest: #$15000 xx 10 /100xx 1 = $1500#
and
2: Solar energy : amount invested : $5000 at rate of 6% for 1 year will return interest : #$5000 xx 6/100 xx 1 = $300#

Total returns from 1 and 2 : #$1500 + $300 = $ 1800#