Question

A brother and a sister invested part of their $600 of allowance money at 4% and the remainder as 7%. Their annual income from these two investments was equivalent to an income of 6% on the entire sum. How much was invested at each rate?

Answer 1

Given :

Total investment amount = $600

The first investment amount = 4% of part of $600

The second investment amount = 7% of part of $600

Total income from 6% of entire sum = 6% of $600

To Find :

The investment amount at 4%

The investment amount at 7%

Solution :

Let The investment amount at 4% = $x

So, First investment amount = 4% of $x

                                       = 0.04 x

The investment amount at 7% = $(600 - x)

So, Second investment amount = 7% of $(600 - x)

                                       = 0.07 × $(600 - x)

∵ Total income amount = 6% × $600

                                      = $\dfrac{6}{100}$ × $600

                                      = $ 36

Again

Investment amount at 4% +  Investment amount at 7% =   Total income amount at 6%

i.e  0.04 x + 0.07 × $(600 - x) = $36

Or, 0.04 x + 42 - 0.07 x = 36

Or, 0.03 x = 6

∴            x = $\dfrac{6}{0.03}$

i.e          x = $200

So, Investment at 4% = x = $200

And The investment at 7% =  $(600 - x) = 600 - 200 = $400

Hence,  The investment amount at 4% rate is $200

And The investment amount at 7% rate is $400       Answer