## 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%