SOLUTION: 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

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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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