Robert, Adam and Elli together earned #$807000#, If Robert's expenses are #75%#, Adam's expenses are #85%# and Elli's savings are #10%#. If their savings are in the ratio of #16:17:12#, what are their savings?

Question

Eva Abramson · Accepted Answer

Savings of Robert are #43426.01# rupees, that of Adam are #46140.13# rupees and income of Elli is #=32569.51# rupees.

Let the income of Robert be #x# rupees and that of Adam be #y#. Then income of Elli is #807000-x-y#. As Robert's expenses are #75%#, his savings are #(25x)/100#; Adam's expenses are #85%#, his savings are #(15y)/100# and Elli's income are #807000-x-y#, her savings are #(10(807000-x-y))/100=(807000-x-y)/10#. As savings are in the ratio of #16:17:12#, we should have #((25x)/100)/16=((15y)/100)/17=((807000-x-y)/10)/12# or #x/64=(3y)/340=(807000-x-y)/120# Let this be #k#, then #x=64k#, #y=(340k)/3# and hence #(807000-64k-(340k)/3)/120=k# or #807000-64k-(340k)/3=120k# or #2421000-192k-340k=360k# i.e. #892k=2421000# or #k=2421000/892# Hence savings of Robert are #64xx2421000/892xx25/100=43426.01# rupees, that of Adam are #340/3xx2421000/892xx15/100=46140.13# rupees and income of Elli is #43426.01/16xx12=32569.51# rupees.

HIX Tutor · Answer

undefined Let's start by finding the total expenses for Robert, Adam, and Elli.

1. To find Robert's expenses, we multiply his share (75%) by the total amount earned: 75% x $807,000 = $605,250.
2. To find Adam's expenses, we multiply his share (85%) by the total amount earned: 85% x $807,000 = $686,950.
3. Since Elli's savings are given, we need to find her expenses first. We know that her savings are 12 out of 16+17+12 = 45 parts of the total. So, her savings' fraction is 12/45. We can find her expenses by subtracting her savings' fraction (12/45) from 1: 1 - 12/45 = 33/45. To find the value of her expenses, we multiply this fraction (33/45) by the total amount earned: (33/45) x $807,000 = $594,400.

Now, let's find their savings:

4. Robert's savings can be found by subtracting his expenses from the total amount earned: $807,000 - $605,250 = $201,750.
5. Adam's savings can be found by subtracting his expenses from the total amount earned: $807,000 - $686,950 = $120,050.
6. Elli's savings can be found by multiplying her savings' fraction (12/45) by the total amount earned: (12/45) x $807,000 = $214,800.

So, their savings are:

- Robert: $201,750
- Adam: $120,050
- Elli: $214,800