Problem Solving

if x dollars are invested at 10 percent for one year and y dollars are invested at 8% for one year, the annual income from the 10% will exceed the annual income from 8% in 56 dollars. if the total invested was 2000, how much was invested in both of them?

OA: 892 and 1,108

if x dollars are invested at 10 percent for one year and y dollars are invested at 8% for one year, the annual income from the 10% will exceed the annual income from 8% in 56 dollars. if the total invested was 2000, how much was invested in both of them?

======================
PTR/100 - ptr/100 = 56
(2000-x)*1*10/100 - x*1*8/100 = 56
(2000-x)*10 - 8x = 5600
20000 - 5600 = 18x
=> x = 14400/18 = 800
so y = 1200

why your OA is different, r u considering compound interest....

I ran the answers you provided and I came up with something else. I must be confused on the question. When you wrote "will exceed the annual income from 8% in 56 dollars," do you mean "by" $56? And are you asking how much was invested in each of them, rather than both?

mkbigmoz wrote:I ran the answers you provided and I came up with something else. I must be confused on the question. When you wrote "will exceed the annual income from 8% in 56 dollars," do you mean "by" $56? And are you asking how much was invested in each of them, rather than both?

yup by 56

[spoiler]Lets consider the OA.


$892 was invested in Bank X at 10% interest for one year.

892 * 1.1 = 981.20


$1108 was invested in Bank Y at 08% interest for one year.

1108 * 1.08 = 1196.64


(1196.64-1108) - (981.20-892) doesnt equal 56.


Can you explain how you came up with 56 with a spoiler, as to not ruin the question for others please? Thanks!


[/spoiler]

maihuna wrote:if x dollars are invested at 10 percent for one year and y dollars are invested at 8% for one year, the annual income from the 10% will exceed the annual income from 8% in 56 dollars. if the total invested was 2000, how much was invested in both of them?

======================
PTR/100 - ptr/100 = 56
(2000-x)*1*10/100 - x*1*8/100 = 56
(2000-x)*10 - 8x = 5600
20000 - 5600 = 18x
=> x = 14400/18 = 800
so y = 1200

why your OA is different, r u considering compound interest....

You're on the right track you just mixed up x & y. x is at 10% and y is at 8%.

so it should be

(2000 - y).10 - .08y = 56
200-.10y-.08y = 56
.18y = 144
y = 800
x = 1200

I got the same answer as you all