Q 64. Percentage
Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?
- Let the total number of votes = V.
- As per the condition given in question,
- Number of votes that were casted = 80 × V / 100 = 0.8 × V
- Numbers of votes received by X = 56 × 0.8 × V / 100.
- Percentage of the votes candidate Y got = 100- 56 = 44%
- Given that, X votes – Y votes = 1440
- Thus, 80V/100 (56-44)/100 = 1440
- 0.8 × 0.12 × V = 1440
- V = 12,000/0.8
- Total votes V =15,000.
Q 9. Percentage
In a class, 60% of students are from India and 50% of the students are girls. If 30% of the Indian students are girls, then what percentage of foreign students are boys?
- Let total number of students in the class be 100.
- Indian students = 60% of 100 = 60.
- So, foreign students = 100 – 60 = 40 students.
- Total number of girls students = 50% of 100 = 50.
- Total number of Indian girl students = 30% of 60 = 18 students.
- So, foreign girl students = 50 – 18 = 32.
- As total foreign students = 40.
- So, foreign boy students = 40 – 32 = 8.
- So, percentage of boys among foreign students = (8/40) × 100 = 20%.
- Hence, option (d) is the correct answer.
Q 30. Percentage
A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks?
- Let total marks in each subject be 100.
- Therefore, total marks for all 6 subjects = 600
- Overall marks scored = 60% of 600 = 360
- Given Ratio of marks= 5:6:7:8:9:10.
- Now 5x+6x+7x+8x+9x+10x= 360.
- Then x= 360/45= 8
- Now marks in different subjects are- 40; 48; 56; 64; 72; 80.
- Hence, in 3 subjects the student has scored less than 60% marks.
Q 46. Percentage
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct?
- Given: 50 percent villagers have their own houses.
- 20 percent of the villagers cultivate paddy.
- 33.33 percent of the villagers are literate.
- 80 percent of the villagers are below twenty-five.
- If we take literate villagers on one side, then there will be at least 13.33 of the villagers who must be below twenty-five as there are 80% villagers are below twenty-five.
- Hence, at least 13.33 percent literate villagers must be below twenty-five.
Q 54. Percentage
P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score?
- P scored 40 marks more than Q.
- If we take marks of Q as ‘q’ then marks of P= q + 40.
- Q scored 10% less marks than P i.e., q = 90% of P.
- Then, q= (90/100)* (q - 40).
- Or 10q = 9q + 360
- So, q = 360.
- So, Q scored 360 marks.
Q 40. Percentage
A person bought a car and sold it for ₹3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car?
• Let CP be Rs. x
SP of car = Rs 3,00,000; Loss percent = 20%
∴ 80% of x = 300000
Or x = 300000 × (100/80)
Or x = Rs. 3,75,000
Q 55. Percentage
In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marriєв more than one man; and there are no widows and widowers?
Number of married men and women must be equal.
So, 40% of men = 30% of women
Let there be 300 men and 400 women in the city. Hence, there are a total of 700 adults.
Number of married men = 40% of 300 = 120
Number of married women = 30% of 400 = 120
So, Number of married adults = 120 + 120 = 240
Percentage of married adults in the population = (240 / 700) × 100 = 34 2/7 %
Q 11. Percentage
A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?
• Let the weight of A be 100 kg.
• So, the combined weight of A + B will 160 kg. Out of this 160 kg, 60 kg is reduced now.
• 60 of 160 gives 60×100/160 = 37.5%.
Q 17. Percentage
Raju has ₹9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows ₹2000 from a friend. Then
• In this question Rs. 9000 is 75% of the cost of mobile phone.
• So total cost of mobile phone is Rs. 12000 ( = 9000 / 0.75).
• Now, as he borrows Rs. 2000, he will be still short of Rs.1000 to buy the phone.
Q 31. Percentage
All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data?
1. 40% members went for shopping as well as sightseeing.
2. 20% members went for only shopping.
Select the correct anser using the code given below:
Those who went for either or both 100%-10%(those who took rest)= 90%
Who went for sightseeing and shopping both 80%+50%-90%= 40%
Members who went only for shopping = 80% - 40% = 40%
40% members went for shopping as well as sightseeing. Thus statement 1 is correct.
Q 34. Percentage
In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored?
• We check with options directly.
• Start with (a). If B is 360, A will be 380. Now, 5% of 380 = 19. So B will become 380 – 19 = 361. Hence this option is wrong (B is 360, not 361).
• If B is 380, A will be 400. Now, 5% of 400 = 20. So B will be 400 – 20 = 380. Hence (b) is correct.
Q 50. Percentage
If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is
Q 41. Percentage
A student has to get 40% marks to pass in an examination. Suppose he gets 30 marks and fails by 30 marks, then what are the maximum marks in the examination?
- Let maximum marks in the examination be x.
- Pass marks = 40% of x
- After getting 30 marks, the student fails by 30 marks. So, passing marks are 60.
- 40% of x = 60
- x = 150
Q 30. Percentage
P (40% of A) + (65% of B) and Q = (50% of A) + (50% of B), where A is greater than B. In this context, which of the following statements is correct?
- According to the question, P = (40% of A) + (65% of B) and
Q = (50% of A) + (50% of B), where A > B
- Now, P – Q = (40% of A) + (65% of B) - (50% of A) - (50% of B) = (15% of B) - (10% of A)
- As the numerical values of A and B will diverge, the answers will start to change from initial assumptions.
- Hence, nothing can be said about the relation between P and Q.
Q 42. Percentage
In a city, 12% of households earn less than ₹ 30,000 per year, 6% households earn more than ₹ 2,00,000 per year, 22% households earn more than ₹ 1,00,000 per year and 990 households earn between ₹ 30,000 and ₹ 1,00,000 per year. How many households earn between ₹ 1,00,000 and ₹ 2,00,000 per year?
According to the question:
- Total households are 100%, then if 12% are below Rs.30000, X % are between 30,000 and 1,00,000, and 22% are above 1,00,000.
- So, we get : 12 + X + 22 = 100 => X = 66%. This 66% is given to us as 990 households.
- So the total population = (990 x 100) / 66 = 1500 households.
- Now 22% of 1500 are above Rs.1,00,000.
- But 6% are above Rs.2,00,000.
- So households between Rs.1,00,000 and Rs.2,00,000 are 16% of 1500 ( = 22% - 6%), which is 240.
Q 40. Percentage
Anita's mathematics test had 70 problems carrying equal marks i.e., 10 arithmetic, 30 algebra and 30 geometry. Although she answered 70% of the arithmetic, 40% of the algebra and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is:
- Let every question carry 1 mark. So total number of marks is 70.
- Therefore passing marks = 60% of 70 = 42 marks.
- Anita answered 70% of Arithmetic (10 Q) = 7
- 40% of Algebra (30 Q) = 12
- 60% of Geometry (30 Q) = 18
- So, Anita's total marks = 7 + 12 +18 = 37 marks which is 5 short of 42.
- So 5 more marks are required to pass the exam.
Q 47. Percentage
Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X?
- Let third number Z be 100.
- Therefore X will be 80 & Y will be 72.
- Hence Y is 10% less than X. Hence, answer is (b)
Q 15. Percentage
In a test, a candidate attempted only 8 questions and secured 50% marks in each of the questions. If he obtained a total of 40% in the test and all questions in the test carried equal marks, how many questions were there in the test?
Let marks of each question be 10 Then, total marks got by the students = 8 x 5 = 40 marks
40% = 40 ; 100% = 100
⸫ Total number of questions = 100 / 10 =10
Q 31. Percentage
In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine?
Ans: (c) According
to the venn diagram,
Given, d + g = 30%, e + g = 15%, f + g = 25%, g =10%
On solving, we get d = 20%, e = 5% and f = 15%
⸫ a = A - (d + f + g) = 0%
b = B - (d + e + g) = 20%
and c = C - (e + f + g) = 10%
⸫ Percentage of those who do not read any magazine (n)
= Total percentage - (a + b + c + d + e + f + g)
= 100 - (0 + 20 + 10 + 20 + 5 + 15 + 10) = 20%
Q 80. Percentage
Candidates in a competitive examination consisted of 60% men and 40% women. 70% men and 75% women cleared the qualifying test and entered the final test where 80% men and 70% women were successful. Which of the following statements is correct?
Let there are 100 persons in which 60 are men and 40 are women.
⸫ Number of men who cleared the qualifying test = 70 x 60 / 100 = 42
Number of women who cleared the qualifying test = 40 x 3 / 4 = 30
Number of men who get success in final test = 42 x 4 / 5 = 33.6
Number of women who get success in final test = 30 x 70 / 100 = 21
Hence, more men cleared the examination than women.
Q 48. Percentage
A and B decide to travel from place X to place Y by bus. A has ₹10 with him and he finds that it is 80% of the bus fare for two persons. B finds that he has ₹3 with him and hands it over to A. In this context, which one of the following statements is correct?
Let the fair of bus for two passengers be Rs. x.
Now, A has Rs. 10, i.e. 80% of total fair.
⸫ 80% of x = 10
]
⸫
Now, B has given Rs.3
Now, total amount A has = 10 + 3 = Rs.13
Money left after purchasing 2 tickets = 13 - 12.5 = Rs.0.5 = 50 paise
⸫ After buying the two tickets, A will be left with 50 paise. Hence, option (c) is correct.
Q 49. Percentage
As per agreement with a bank, a businessman had to refund a loan in some equal instalments without interest. After paying 18 instalments he found that 60 percent of his loan was refunded. How many instalments were there in the agreement?
In this question, the loan is refunded with equal instalment and without interest.
Initially the man had to pay x instalments.
Now, after paying 18 instalments 60% of loan is refunded.
⸫ 60% of x = 18
]
⸫
⸫ There were 30 instalments in the agreement. Hence, option (c) is correct
Q 42. Percentage
There are 100 students in a particular class. 60% students play cricket, 30% student play football and 10% students play both the games. What is the number of students who play neither cricket nor football?
If 60% play cricket, and 30% play football then total percentage that plays both = 60 + 30 = 90% But out of these, 10% that play both need to be subtracted as they are counted twice. So, 80% play both. Those who play neither will be 100-80 = 20%.
Q 50. Percentage
In a group of persons, 70% of the persons are male and 30% of the persons are married. If two-sevenths of the males are married, what fraction of the females is single?
70% males, so 30% females. If 2/7th of males are married, this means 2/7 (70 %) = 20% males are married. So, 10% females are married (out of 30% total married). So, single females will be 20% out of total 30% females. The fraction is 2/3.