## Problems on Percentages

1. A’s income is 20% more than that of B while B’s income is 20% less than that of C. Whose income is the highest amongst all?
Sol : Let the income of C be Rs. 100/-
So, The income of B is Rs. 80/-
A’s income is 20% more than B = (120/100) X 80 = Rs. 96/-
So, obviously C’s income is Highest

2. A’s income exceeds that of B’s by Rs.600 while B’s income is 20% less than that of C’s. If total income of all of them put together is Rs. 3.850, what is the income of C ?

Sol : Let the income of C be Rs. X
B’s income is 20% less than C’s

So, B’s income is 80% of  X  = 4 X  / 5

So, A’s income is (4 X /5) + 600

=>  ((4 X /5)+600) + (4 X /5) +  X  = 3,850

=> (8 X  / 5) +  X  = 3,250

=>  13  X  = 5 x 3,250

X  = (5 x 3,250) / 13 = Rs. 1,250

3. Shivani spends 15% of her salary on Shopping, 20% on House – Rent, 50 % on Food and the remaining on Education of Her children. If education costs her Rs 3000, how much does she spend on House – Rent ?

Sol :  Let the salary of Shivani is Rs. 100
So, amount spent on Education = 100 – ( 15 + 20 + 50) = Rs. 15
But, her expences towards education is Rs. 3000
So, 15% of salary = (3000 x 100) / 15  = Rs. 20,000
She spent 20% of her salary on house rent
So, 20% of 20,000 = Rs. 4000/-
4. In a class, 30% students passed in Maths, 50% students passed in English and 10% students passed in Both. What per cent of students failed in both of these subjects?

Sol : Let the number of total students = 100
So, Number of students passed in Maths = 30
Number of students passed in English = 50
Number of students passed in Maths and English = 10
So, total number of students passed = (30 + 50 – 10) = 70
Number of students failed = 30
So,     Percentage of Students failed = 30 %
5. A trader announced 10% reduction in the unit price of an article. As a result, the sales volume went up by 10%. What was the net effect on the sales revenue?
Sol : Let the unit price be Rs. 10/-
Let the number of articles sold = 10
So, the sales revenue = 10 x 10 = Rs. 100
The trader has reduced the unit price by 10%
So, Reduced price = 90% of Rs 10 = Rs. 9 /-
and, increase in the sales volume = 10%
= 110% of 10 = 11
So, The net effect = 9 x 11 = Rs. 99
The sales revenue has come down by Re. 1/-
So, the sales revenue has come down by 1%
Note : There is a short cut for these type of problems.
If price is reduced by X% and sales increase by Y%, the total effect on sales revenue :
=      increased % value – Decreased % value = (Increased % value x Decreased % value) / 100
The effect on revenue is increased or decreased according to the positive or negative sign otained
=  10 – 10 – ((10 x 10) / 10)) = 0 – 1 = -1

The sign obtained is negative. Thus, the total revenue decreases by 1%