# Problems on Percentages

Lets do some problems on Percentages

• 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

• 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

• 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/-
• 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 %

• 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% 1. Mam I have a ques. When I worked it for the 1st time it was correct but now its wrong. ITS :-
*X spends 20% of his salary on food, 15% on conveyance, 10% on education and 35% on house rent. If he spends Rs.1950 on education, how much does he spend on conveyance?
Here 100-(10+15+20+35)=Rs.20\$
So, 20%(Rs. 20\$ answer) = 1950*100/20 = 9750
And 15% of salary (Conveyance) = 9750*15/100 = 1462.5
1st I got it right when I took 10 instead of 20 (100-80), but how mam? 20 is the remaining of 100. Its correct with 10.
What should I do?
Is 20 the remaining of 100 or should I take 10% on education value for 1st factor?

1. ya you should take 10 % because he spend 10 % on Education

2. 1950*100/10=19500
15% of conveyance :19500*15/100=2925

3. 10% on Eductation
Total salary 19500/-
So On con 19500X15/100= 2925

2. 3. 4. it's very useful for me

5. it is very useful.. great work...

6. confusing ....

7. Very helpful than for providing such a useful
site

8. EXCELLENT

9. 10. 11. Good for non coaching candidate only

12. this site is very good

13. very good for all students

14. is there any shortcut for doing sums like :
40% of 1740 +X=38% of980 +150 % of 850

15. Its very us full for all exams

16. It is very use full for all exams

17. pls explain the logic of question related to class.

18. 19. Mr. Jones gave 40% of the money he had to his wife. He also gave 20% of the remaining amount to each of his three sons. Half of the amount now left was spent on miscellaneous items and the remaining amount of Rs. 12,000 was deposited in the bank. How much money did Mr. Jones have initially?

1. the ans should be 25000.
the equation goes like this, let the total amt be x, therefore,
x=40/100(x) + 20/100(x-(40/100(x))) + 12000
solving for x we get 25000 as the final ans...
Ma'am please let me know if this approach is wrong.

2. hi frnd,

i think the ans is 60000

see he gave 40 % to his wife
20 % to sons
in the balance 40% half of the amount goes to miscellaneous i.e., 20 % goes to miscellaneous.
Now he have 20% balance in bank = 12000

40%(WIFE)+20%(sons)+20%(mis)+20%(savings = 12000)= 60000

pls verify.. else explain ur views

3. hi frnd,

i think the ans is 60000

see he gave 40 % to his wife
20 % to sons
in the balance 40% half of the amount goes to miscellaneous i.e., 20 % goes to miscellaneous.
Now he have 20% balance in bank = 12000

40%(WIFE)+20%(sons)+20%(mis)+20%(savings = 12000)= 60000

pls verify.. else explain ur views

4. ans is 60000

5. 12000/24*100=50000

6. 12000/24*100=50000

7. 12000/24*100=50000

8. 12000*100*100*100/60*80*50 = 50000

Ans: 50000

9. ans is 100000

20. 100-40=60
60*20%=12 now 12*3=36
60-36=24
24*1/2=12now
12=12000 then 100=100000

21. first example is not clear,
the ans must b A and C both have equal salary.

22. to whom salary we assume 100 between d given ppl??

23. TO WHOM SALARY WE CAN ASSUME 100?? BETWEEN D GIVEN PPL

1. (12000*100)/20=60000
24. 