Friday, May 9, 2014

Solved problems on Percentages

1. The ratio  5:4 expressed as percent equals:

(a) 12.5%                                (b) 40%
(c) 80%                                   (d)  125%

Answer:(d) 
Solution:

Applying the formula for percentage,

required percentage = 5/4 x 100 = 125 %  


3, Half of 1 percent written as a decimal is :
(a)0.005                              (b) 0.05
(c) 0.02                                (d) 0.2

Answer:  (a)

Solution: 
Half of 1 percent is 0.5 % = 0.5/100 = .005

(to convert % to decimal you divide it by 100)


4. what is 15 percent of Rs. 34?
(a) Rs. 3.40                               (b) Rs. 3.75
(c) Rs. 4.50                               (d) Rs. 5.10


Answer:  (d)



Solution:
Applying the formula for conversion of percentage to actual
Actual = (x %/100) x N where x is the percentage given and N is the total Amount.
Here, x = 15 %, N= 34. 
Now, put the values to get (15/100) x 34 =  0.15 x 34 = 5.1 


5. 63% of 3 x (4/7) is :
(a) 2.25                                   (b) 2.40
(c) 2.50                                       (d) 2.75

Answer:  (a)
Solution:
First convert the mixed fraction 3 (4/7) to fraction which is = (21 + 4)/7 = 25/7.
Now, to calculate 63% of 25/7. 
we have,
( 63/100)  x (25/7) =  9/4 = 2.25


6. 88% of 370 + 24% of 210 - ? = 118
(a) 256                                       (b) 258
(c) 268                                         (d) 358

Answer:(b)

Solution :
88 % of 370 =  0.88 x 370 = 325.6
               24 % of 210 = 0.24 x 210 =  50.4
            put these terms in the equation and let the unknown be x then we have,
              325.6 + 50.4 - x = 118
              376 - x = 118
               x =  258            


7. 860% of 50 +50% of860 =?
(a) 430                                     (b) 516
(c) 860                                     (d) 960

Answer: (c)

Solution:
              860 % of 50 = 8.6 x 50 = 430
              50% of 860 = 0.5 x 860 =  430
 put the values in the above equation to get 430 + 430 = 860

8. 45% of 750 - 25% of 480 = ?
(a) 216                                (b) 217.50
(c) 236.50                            (d) 245

Answer: (b)
Solution: 45 % of 750 = 337.5
              25 % of 480 = 120
Put the values in the above equations to get 337.5 - 120 = 217.5


9. 40% of  1640 + ? = 35%of 980 +150%of 850
(a) 372                                          (b) 842
(c) 962                                          (d) 1052
 
Answer: (c)
Solution:
               40% of 1640 =  656
                 35% of 980 = 343
               150% of 850 = 1275
Put these values and x as the unknown value in the equation to get
 656 + x = 343 + 1275 
            x =  1618 - 656
            x =  962


10. 218%  of 1674 = ? x 1800
(a) 0.5                                (b) 4
(c) 6                                 (d) none of these

Answer:(d)
Solution:
218% of 1674 = 2.18 x 1674 = 3649.32
Put this value in the above equation to get
3649.72 = x x 1800
x = 2.0274

11. 60% of 246 is the same as :
(a) 10% of 44                              (b) 15% of 1056
(c) 30% of 132                           (d) none of these

Answer:(d)
Solution:

60% 0f 246 = 0.6 x 246 = 147.6

or  
Checking the options
(a) => 4.4
(b) => 158.4
(c)=> 39.6

12. 270 candidates appeared for an examination, of which 252 passed . the pass percentage
(a) 80%                                             (b) 83(1/3) %
(c) 90(1/3) %                                    (d) 93(1/3)

Answer:(d)
Solution:
Using the formula for calculating percentage  we have,
(Total passed/ Total appeared ) x 100 = (252/270 ) x 100 = 93(1/3)

13 .  0.01 is what percent of 0.1
 (a) (1/100)                               (b)  (1/10)
 (c) 10                                      (d) 100

Answer:(c)
Solution:
(0.01/0.1) x 100 = (1/10) x 100 = 10 %

14 . what percent of Rs. 2650 is Rs 1987.50
 (a) 60%                                  (b) 75%
 (c) 80 %                                 (d) 90%

Answer: (b)
Solution:
(1987.50/2650) x 100 = 75 %

15. What percent of a day is 3 hours?
(a) 12(1/2)%                           (b) 16(2/3)%
(c)  18(2/3)%                          (d) 22(1/2)%

Answer:(a)
Solution: 
(3/24) x 100 = 12 (1/2) %


16. It costs Re 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after first 1000 sheets. How much will it cost to copy 5000 sheets of paper?
(a)Rs. 3920                            (b) Rs. 3980
(c)Rs. 4900                            (d) Rs. 4920

Answer: (d)
Solution:
Cost of photocopying first 1000 sheets = Rs 1000
Cost of photocopying next 4000 sheets is = 4000 - 0.02 x 4000 = 3920
Therefore total cost = 4920


17. A housewife saved Rs. 2.50 in buying an item on sale.If she spents Rs. 25 for the item, approximately how much percent she saved in the transaction?
(a) 8%                                 (b) 9%
(c)10%                               (d) 11%

Answer: (b)
Solution:
Total saved 2.5 
Total Spent after the discount = 25
Therefore original cost of item = 27.5
And percentage saved = (2.5/27.5)x 100 = 9.09



18.The number which exceeds 16% of  it by 42 is :
(a)50                                   (b)52
(c) 58                                  (d)60

Answer: (d)
Solution:
Let the number be x then 
{(x - 42) /x} x 100 = 16
(x - 42) x 100 = 16x
100x  - 4200 = 16x
84x = 4200
x =  50


19. If 15% of 40 is greater than 25% of number by 2. then the number is :
(a)12                                     (b)16
(c)24                                    (d)32

Answer : (b)
Solution:  Making it an equation and converting the % into numbers and unknown into x
0.15 x 40 - 0.25 x  X = 2
 6 - 0.25X = 2
4 = 0.25 X
X = 16



20 . The sum of two numbers is 2490. if 6.5% of one number is equal to 8.5% of the other
(a)989,1501                             (b)1011,1479
(c)1401, 1089                         (d)1411,1079

Answer: (d)
Solution:
We will have two equations in two variables
i.e. x + y = 2490
    65  x =85 y
Solving these equation , we will have y = 1079 and x = 1411
21. The difference of two numbers is 20% of the larger number . if the smaller number is 20, then the larger number is :
(a)25                                         (b)45
(c)50                                         (d)80

Answer: (a)
Solution:
Writing the above condition into equations,
( x - y ) = 0.2 x x
( x - 20 ) = 0.2 x x
0.8 x = 20
x = 25

22. If one number is 80%  of the other and 4 times the sum of their squares is 656, then the numbers are :
(a)4,5                                        (b)8,10
(c)16,20                                     (d) None of these

Answer:(b)
Solution:
Here we can check for options or form two equations in two variable to get the answer.
We will follow the first approach
We can observe that the first condition is satisfied by the first three options.
Now check for second condition
(a) 4 ( 16 +25) = 4 (41) = 164   Not satisfied
(b) 4 ( 64 + 100) 4 (164) = 656 satisfied. Hence this is the answer.

23. A person who spends 66(2/3)% of his income is able to save Rs. 1200 per month. His monthly expenses ( in Rs. ) are :
(a)   Rs. 1200                         (b) Rs. 2400
(c)   Rs. 3000                         (d) Rs. 3200

Answer: (b)
Solution: 
His saving in Percentage is 33 (1/3) % and it is equal to 1200
Therefore,  x x (100/3%) = 1200
                  x / 3 = 1200
                  x = 3600
And expense = 3600  - 1200 = 2400


24. 10% of of the voters did not cast their in an election between two candidates. 10% of the votes polled were found invalid;id.The successful candidate got 54% of the valid votes and won by a majority of 1620 votes. The number of voters enrolled on the voters' list was:
(a)  25000                               (b) 33000
(c)  35000                            (d)  40000

Answer:(a)
Solution:

First we calculate the valid votes, They are divided into two candidates and the winning candidate got 54 %  and losing got 46 %.  the difference is 8 % and it is equal to 1620.
i.e. 0.08 x x = 1620
      x =  20250 Votes that were valid
and since 10 % votes were invalid.

0.9 x  vote polled = 20250

Votes polled = 22500

And Since 10 % did not cast their votes
i.e.e0.9 x  Total Voters = 22500
Total Voters =  25000


25. Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(a)   Rs. 200                         (b) Rs. 250
(c)   Rs. 300                         (d) None of them

Answer: (b)
Solution:
Total Paid to tailor in 1 week = 550
Let Y is Paid at the rate of P per week
Then X is paid at the rate of 1.2 P per week
And this total comes to be 550 = 1P + 1.2P
2.2P = 550
P= 250


26 . 1100 boys and 700 girls are examined in a test , 42 %  of the boys and 30 % of the girls pass . the percentage of the total who failed is :
 (a)58%                              (b) 62(2/3) %
 (c)64%                              (d) 78%

Answer: (b)
Solution:
42% boys passed that means 58 boys failed which is equal to   = 638
30% girls passed that means 70 % girls failed  which is equal to = 490
Total Appeared = 1800
Total Failed % = (1128/1800) x 100 = 62 (2/3)

27 . If 20% of a= b, then b% of 20 is the same as :
(a) 40%o of a                         (b)5% of a
(c)20% of a                            (d)None of these

Answer: (a)
Solution:
Given ,
0.2 x a = b
Then ,
b% X 20 = (b/100) x 20 = {(0.2 x a)/100} x 20 = 0.4 x a or 40 percent of a


29 If p% of p is 36, then p is equal to :
(a) 15                                   (b)60
(c) 600                                 (d)3600

Answer: (b)
Solution:
Given
(p/100) x p = 36
P X p = 3600
p = 60


30. If x % of y is 100 and y% of z is 200 then find a relation between x and z
(a)z= (x/ 2)                              (b) z = 2 x
(c) z= (x/4)                               (d)z=4 x

Answer: (a)
Solution:
First
(x/100) y = 100
(xy) = 10000 --------- (i)

And (y/100)z = 200
(yz)=20000------- (ii)

Dividing Equation (i) by equation (ii) we get
(x/z) = (1/2)
2x = z
z = (x/2)


31. A man loses 20(1/2) % of his money and after spending 80% of the 
     remainder, he is left with 159. How much money did he have first?
 (a) 800    (b)  1000
 (c) 1,200 (d)   500

Answer: (b)  1000
Solution:
Let the money was Rs x .Then after losing 20.5 % he is left with (0.795)x
Now, he spend 80% of the remainder and left with 159. 
This means 20% of 0.795x is 159.
            =>     (0.795x)(0.20) = 159
            =>     0.159x = 159
            =>             x  = 159/0.159 = 1000 
 
32. If 120% of a is equal to 80% of b, then (b+a)/(b-a) is equal to
(a) 5    (b) 6
(c) 7    (d) 8



Answer:(a) 5
Solution:
Given that 120% of a = 80% of b, 
     => 1.20 x a = (0.80)b
     => a = (8/12)b
     => a = (2/3)b

Thus, (b+a)/(b-a) = {b+(2/3)b }/{b - (2/3)b}  
                          = (5/3)/(1/3) = 5

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