Problems on Percentage

Question 1: Ram gets 55 % of total valid votes in an election. If the total votes were 9000, what is the number of valid votes that the other candidate Shyam gets if 30 % of the total votes were declared invalid? 
Solution: Total votes= 9000 
Total valid votes=70 % of 9000 = 6300 
Shyam gets 45 % of 6300 =(45/100) * 6300 = 2835 votes

Question 2: A number is mistakenly divided by 2 instead of being multiplied by 2. Find the percentage change in the result. 
Solution: Let the number be N. 
2N is the correct outcome. 
0.5N is the mistakenly calculated outcome. 
Change in the number= 2N – 0.5N = 1.5N 
Percentage change= 1.5N * [100/(2N)]= 75%

Question 3: A rectangular plot length and breadth are increased by 10 % and 30 % respectively. Find the increased percentage area of the rectangular plot. 

Solution: Let 100 is the length of the plot.  

       10%               30% 
100 ---------->110 ---------->143

Hence the increased percentage area is 43%.

Question 4: Radha’s salary is 50% more than Seeta’s salary. Radha got a raise of 40% on her salary while Seeta got a raise of 30% on her salary. By what percent is Radha’s salary more than Seeta’s? 

Solution: Let Seeta’s salary = Rs 100 
Then Radha’s salary = 100 * 50% + 100 = 150 
Radha got a raise of 40% then 150 *40% + 150 = 210 
Seeta got a raise of 30% then 100*30% + 100 = 130 
Now Radha salary more than Seeta salary by 80 
Percent = 80/130 * 100 = 61.53%

Question 5: In school, three rows are formed of the students. First row has 50% more students than the second row and the third row has 50% less students than the second row. If the total number of students in all the rows is 900, then find the number of students in the third row. 

Solution: Let the number of students in the second row is 100. 
Then number of students in first row is 150 and number of students in third row is 50. 
Total students = 150 + 100 + 50 = 300 
Given = 900 
Then 900/300 = 3 
Third row has 50 * 3 =150 students. 

Question 6: 40 litre of mixture of milk and water contains 25% of water. When 10 liters of water is added, what will be the percentage of milk in the final mixture? 

Solution: 25% of 40 litre = 10 litre. 
10-liter water is present in the mixture. 
When 10 liters more water is added in the mixture then the final mixture contains 20 liters water and 30 liters milk. 
% of milk in final mixture= 30/50 * 100 = 60%

Question 7: A number is divided into two parts in such a way that 60% of 1st part is 2 more than the 40% of 2nd part and 60% of the 2nd part is 1 more than the 40% of 1st part. Find the numbers. 

Solution: Acc. to question 
60% a – 40% b = 2 
(60/100)a – (40/100)b = 2 
6a – 4b = 20…………(1) x4 

and 60% b – 40% a = 1 
(60/100)b – (40/100)a = 1 
6b – 4a = 10………….(2) x6 

From (1) and (2) 
36b – 16b = 140 
20b = 140 
b= 7 
Put b in 1, we get a=8 
Hence, the number is (7+8)=15

Question 8: The percentage of metal extracted from a mine of lead ore is 50%.Now the percentage of gold is 4/5 % of the metal and the rest is lead. If the mass of ore extracted from the mine is 6000kg, the mass of the lead is 

Solution: Given mass of lead ore=6000 kg 
Mass of metal is 50% of 6000 = 3000 kg 
Mass of gold is 4/5% of 3000 = 24 kg 
Mass of lead=Mass of metal−Mass of gold
Mass of lead = 3000 – 24 = 2976 kg