PERCENTAGE

    Q1.  A PC is sold for Rs. 16000 at a reduction of 20% on its recommended retail price. What was the computer’s original price?

            (a) 18000                 (b) 20000        

            (c)  18500                 (d) 21000        

    Q2.  Ketan has 32000 in a savings account. After a year, the bank pays him interest increasing his balance to 33600. What percentage rate was applied to the account?

            (a) 4%                      (b) 4.5%          

            (c)  5%                      (d) 4.75%        

    Q3.  Rajesh won some money on the lottery and deposited it in the bank. At the end of one year he got 8% interest, and then had Rs. 4320 in his account. How much did he win?

            (a) 4100                   (b) 4050          

            (c)  4230                   (d) 4000          

    Q4.  If the cost of petroleum decreases by 15%, what will be the change in percentage consumption in case the budget stays the same?

            (a) 16 %                   (b) 15%           

            (c)  16.6%                 (d) 16.67%      

    Q5.  If the cost of petrol increases by 40%, Rohan reduces his annual consumption by 20 %. Find the percentage change in his annual expenditure on petrol.

            (a) 8%                      (b) 12%           

            (c)  10%                    (d) 16%      

    Q6.  Ravi got 30% of the total marks and failed by 10 marks. Ranjan who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What were the passing marks in the examination?

            (a) 80                        (b) 95   

            (c)  90                        (d) 85   

    Q7.  The difference between the value of a number increased by 15% and the value of the original number decreased by 25% is 50. What is the original number?

            (a) 125                     (b) 100

            (c)  110                     (d) 120

    Q8.  Ram sells his goods 10 % cheaper than Ravi and 10 % dearer than Bhuvan; how much percent are Bhuvan’s rates lower than Ravi’s?

            (a) 18%                    (b) 17.5%        

            (c)  19%                    (d) 18.19%      

    Q9.  A fruit seller sells 50 percent of apples of and throws away 20 percent of the remainder. Next day he sells 60 percent of the remainder and throws away the rest. What percent of his apples does he throw?

            (a) 26%                    (b) 32%           

            (c)  36%                    (d) 30%           

  Q10.  In an examination, 70 % of the students passed in math; 74 % in English, 25 % failed in both subjects and 138 passed in both subjects. Find the number of students.

            (a) 190                     (b) 210

            (c)  200                     (d) 230

  Q11.  In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, Each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60 % of the total marks.  (CAT QUESTION)

            (a) 1                          (b) 2     

            (c)  3                          (d) Cannot be determined

  Q12.  If group C contains 8 questions and group B carries at least 20 % of the total marks, which of the following best describes the number of questions in group B?

(CAT QUESTION)

            (a) 11 or 12              (b) 12 or 13     

            (c)  13 or 14              (d) 14 or 15     

  Q13.  Fresh grapes contain 90% water; dry grapes contain 20 % water. From 20 kg fresh grapes, how many kg of dry grapes can be obtained? (CAT QUESTION)

            (a) 2.4                       (b) 2.5  

            (c)  2.2                       (d) None of these       

  Q14.  40% of the employees of a certain company are men and 75% of the men earn more than Rs 25000 per year. if 45% of the company’s employees earn more than Rs 25000per year ,what fraction of the women employed by the company earn Rs 25000 per year or less?     (CAT QUESTION)

            (a) 1/3                       (b) 2/11           

            (c)  3/4                       (d) 1/4  

Solutions

Ans1: (b) Selling price of PC = 16000, discount = 20%, so 16000 is 80% of the original price

                  Let the original price of the PC = A

                  Therefore  80/100 × A = 16000, A = 20,000

Ans2: (c)  Principal = 32000

                  Current balance = 33600

                  Increase = interest = 33600 – 32000 = 1600

                  Rate =  1600/32000 × 100 = 5 %

Ans3: (d) Let the money won be A

                  Rate = 8%, current amount = 4320

                  Therefore A + 8/100A      = 4320

                                    1.08 A = 4320

(student should be able to do this in one step)

                                            A = 4320/1.08  = 4000

Ans4: (d) As per the formula,  r/(100- r) × 100

                  Since rate = 15, therefore  15/90 × 100 = 16.67%

Ans5: (b) Suppose initial price of petrol was Rs. 10/litre and initial consumption of Rohan is A litres. Therefore his initial expenditure = 10A

                  Current price of petrol (40% increase)

= 1.40 × 10 = Rs.14/litre

                  Current consumption (20% decrease) = 0.80A

                  Current expenditure = 14 × 0.8 A = 11.2 A

                  Difference in consumption         = 11.2A – 10A

                                                         = 1.2 A

                  Percentage difference = 1.2A/10A× 100 = 12 %

Ans6: (d) Let total marks = A and passing marks be ‘P’

                  Therefore Ravi got 0.3A, and P = 0.3A + 10

                  And Ranjan got 0.4A and P = 0.4A – 15

                  Therefore 0.3A + 10        = 0.4A – 15

                                            0. = 25

                                            A = 250

                  By first equation P = 0.3(250) + 10 = 85         

Ans7: (a) Suppose original number = A

                  Increased value = 1.15A

                  Decreased value = .75A

                  Difference = 50   = 1.15A – .75A

                                      A =  50/.40 = 125

Ans8: (d) Suppose Ravi sells the goods at 100

                  Then Ram sells at 90(10% cheaper), which is 10% more than Bhuvan (90/1.1)

                  Therefore Bhuvan sells at 81.81

                  Ravi – Bhuvan     = 100 – 81.81

                                        = 18.19 over 100,

                                           therefore 18.19%

Ans9: (a) Let the total number of apples he had were 100

                  On day one he sells 50(50%), he is left with 50, out which he throws 20% which is 10, so for day two he is left with 40.

                  On day two he sells 60% of the remainder, which is 24 and throws away the rest which is 16

                  Total thrown away = 26, which is 26% of the total

Ans10:     (c)  Let the number of students = 100

                  As per the question 70 passed in math, 74 in English and 25 in both

                  Also 30 failed in math out of which 25 failed in both, so 5 failed in math alone

                  Also 26 failed in English out of which 25 failed in both, so 1 failed in English alone

                  Total (failed in both or either) = 5 + 1 + 25 = 31

                  Therefore passed in both = 100 – 31 = 69, which is 69% as base is 100

                  Now 69% is given as 138,

                  Total students = 138 ×  = 200

Ans11:     (d) Cannot be determined

                  The least number of questions in group A is 60 of 60 marks.

                  Group B contains 23 questions of 46 marks. There is no knowledge of exact number of questions in group A and total marks.

Ans12:     (b) 12 or 13

                  8 questions carry maximum 20% marks, therefore 20% of total marks =  24

                  Total marks =  20

                  20% 0f 120  = 24

                  Thus number of questions in group  =  12

Ans13:     (b) 2.5kg

                  Let weight of dry grapes  = x kg

                  For 20 kg of fresh grapes

                  Solid content of fresh grapes  =  solid content of dry grapes

                  Thus 10/100 × 20            =  80/100x

                                             x =  2.5 kg

Ans14:     (c)  3/4

                  Suppose total no. of employees = 100

                                                Thus    n(M)    = 40

                                                            n(W)    =  60

                  Let E denote the set of employees earning more than Rs 25000.

                  Since 75% of men earn more than Rs 25000

                  Then number of men earning less than Rs 25000  =  10

                  And number of women earning less than 25000  =  60 – 15  =  45

                  Hence required fraction = 45/60 = 3/4