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Investment

by mgmt_gmat » Fri Feb 12, 2010 2:15 am
A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?
(1) x = 43y
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.
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Source: — Data Sufficiency |
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by ajith » Fri Feb 12, 2010 6:46 am
mgmt_gmat wrote:A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?
(1) x = 43y
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.
say a was the amount invested with rate x 60000-a was invested with a rate y

now ax/100 + (60000-a)*y/100 = 4080 ------(1)

1) x =43 y

43ay/100 + (60000-a)*y/100 = 4080

42ay/100 +60000y/100 = 4080

Insufficient

2) ( ax/100) /((60000-a)*y/100) =3/2

2/3( ax/100) = (60000-a)*y/100

Substituting in 1


ax/100 + 2/3 ax/100 = 4080

5/3 ax/100 = 4080
ax/100 = 4080/5*3 = 2448
(60000-a)*y/100 = 4080 -2448 =1632

Insufficient

Combining 1&2 we can solve and find out a, x and y

C
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by kstv » Tue Feb 16, 2010 8:15 am
In data sufficiency exact solution may not be needed . In this example. The Principle is 60,000. Ratio 3: 2 implies than the two sums are 36,000 and 24,000.

SI = PRT/100.
Px is 36,000 & Py is 24,000. Rate is x and y , from the eq x = 43 y, x can be expressed in terms of y.
T is one year.

Total SI =4080 = SIx + SI y = 36000 X 43y / 100 + 24000 X y /100

Thats enough

Hence C
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by thephoenix » Wed Feb 17, 2010 2:50 am
mgmt_gmat wrote:A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?
(1) x = 43y
(2) The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 2.
si=PRT/100

here there are two int and corresponding prt are
p1=say n
r=x%
t=1
si1=nx/100

similarly si2=(60000-n)y/100
tot si=nx/100 + (60000-n)y/100=4080.....eqn1

we have three variables or two more independent eqn so we need to know at least two to get an ans
let us c the statements
s1)gives one more eqn
; but still left with one more..........insuff

s2)same.insuff

s1+s2= total 3 eqn and 3 variables hence ans is possible and therefore
C
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