Question 1038194: Ram donated 1/10 of his salary to an orphanage , 1/3of his salary spent on food ,1/4of salary on rent and 1/20 of his salary on telephone . This month he donated Rs5000 inPM relief fund for uttarakhand victims. He was left with Rs3000 with him, find his monthly salary??
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x = salary
1/10 * x = orphanage money
1/3 * x = food money
1/4 * x = rent money
1/20 * x = telephone money.
this month he donated 5000 for uttarakhand victims.
he was left with 3000.
this money was in addition to what he spent on everything else.
you get:
x = 1/10 * x - 1/3 * x - 1/4 * x - 1/20 * x - 5000 = 3000
this means everything he spent subtracted from his salary left 3000 remaining.
if you add up all the normal subtractions, you get 1/10 + 1/3 + 1/4 + 1/20.
convert all these fractions to a common denominator and you get:
least common denominator appears to be 60.
1/10 = 6/60
1/3 = 20/60
1/4 = 15/60
1/20 = 3/60
add them up together and you get 44/60.
his normal monthly expenses are 44/60 of his salary.
the equation becomes x - 44/60 * x - 5000 = 3000
combine like terms and you get 16/60 * x - 5000 = 3000
add 5000 to both sides of this equation to get 16/60 * x = 8000
multiply both sides of this equation by 60/16 to get x = 8000 * 60/16
solve for x to get x = 30,000.
his monthly salary is 30,000
his normal expenses for the month are:
1/10 * x = orphanage money
1/3 * x = food money
1/4 * x = rent money
1/20 * x = telephone money.
orphanage money = 1/10 * 30,000 = 3,000
food money = 1/3 * 30,000 = 10,000
rent money = 1/4 * x = 7,500
telephone money = 1/20 * x = 1,500
total normal expenses for the month are 22,000
on top of his normal expenses, he donated 5,000 for uttarakhand victims.
that made his total expenses for this month = 27,000.
he was left with 3,000.
number check out so solution looks good.
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