Question 1038194
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.