Number Problem 22

From Homeworkwiki

A, B and C got a total income of $ 5000. Out of the amount possessed by them, they spend 80%, 85% and 87.5% respectively.
Now their balance are in the ratio of 12 : 10 : 5. Find the amount that each had.

Solution: Let the amount possessed by A, B and C be $ x, $ y and $ z respectively.

The amount left with A after spending = x X 20/100 = $ x/5

The amount left with B after spending = y X 15/100 = $ 3y/20

The amount left with C after spending = z X 12.5/100 = $ z/8

Therefore, x/5 : 3y/20 : z/8 = 12 : 10 : 5

i.e. 8x : 6y : 5z = 12 : 10 : 5

8x : 6y = 12 : 10 => 80x = 72y i.e. x : y = 9 : 10

6y : 5z = 2 : 1 i.e. 6y = 10z or y : z = 10 : 6

Therefore, x : y : z = 9 : 10 : 6

Dividing $ 5000 in the ratio 9 : 10 : 6 we get x = 5000 X 9/25 = $ 1800

y = 5000 X 10/25 = 2000

z = 5000 X 6/25 = $ 1200

Therefore, A, B and C had $ 1800, 2000 and 12000 respectively.