Percentage problems
- 1. A city has a population of 300000 out of which 180000 are males. 50% of the population is literate. If 70% of the males are literate, the number of literate females is
Options- A. 24000
- B. 30000
- C. 54000
- D. 60000 Discuss
Correct Answer: 24000
Explanation:
Total population = 300000
Total number of males = 180000
Total Literates = 50% of total population = 150000
Number of literate males = 70% of males = 126000
? Number of literate females = 150000 - 126000 = 24000
- 2. If the price of mangoes is decreased by 40%, one could get 32 more mangoes for ? 120. Find the original price of each mango.
Options- A. ? 3.50
- B. ? 2.50
- C. ? 2.25
- D. ? 2.00 Discuss
Correct Answer: ? 2.50
Explanation:
Let the original price be ? N per kg.
New price per kg = 60% of N = 3N/5
? 120 / (3N/5) - 120/N = 32
? 600/3N - 120/N = 32
? 200/N - 120/N = 32
? 80/N = 32
? N = 80/32 = 2.5
So, the original price is ? 2.50
- 3. A student multiplied a number by 2/5 instead of 5/2. What is the percentage error in the calculation?
Options- A. 82%
- B. 86%
- C. 84%
- D. 89% Discuss
Correct Answer: 84%
Explanation:
Let the number be N.
Then, error = 5N/2 - 2N/5 = 21N/10
? Error percentage = (21N/10) x (2/5N) x 100 % = 84%
- 4. Anirudh secures 85%, 70%, 65% and 60% marks in test papers with 100, 120, 140 and 160, respectively as maximum marks. The percentage of his aggregate is?
Options- A. 652/3%
- B. 686/13%
- C. 661/4%
- D. 651/3% Discuss
Correct Answer: 686/13%
Explanation:
Marks secured by Anirudh = [(85/100) x 100] + [(70/100) x 120] + [(65/100) x 140] + [(60/100) x 160]
= (85 + 84 + 91 + 96) = 356
? Required percentage = [356/(100 + 120 + 140 + 160)] x 100 %
= (356/520) x 100% = 686/13%
- 5. In an examination, 950 boys and 250 girls appeared. 90 % of the boys and 60 % of the girl passed the examination. The percentage of candidates failed is?
Options- A. 16.25%
- B. 16.75%
- C. 16.50%
- D. None of these Discuss
Correct Answer: 16.25%
Explanation:
Number of failures = 10% of 950 + 40% of 250
= (10/100) x 950 + (40/100) x 250 = (95 + 100) = 195
Fail percentage = [195/(950 + 250)] x 100
= (195/1200) x 100 = 16.25%
- 6. The population of a town was 150000 three years ago. If it is increased by 2%, 2.5% and 4%, respectively in last 3 years, then the present population is?
Options- A. 163098
- B. 164049
- C. 163154
- D. 164145 Discuss
Correct Answer: 163098
Explanation:
Percentage population = 150000 x (1 + 2/100) x {1 + (5/2)/100} x (1 + 4/100)
= 150000 x (102/100) x (41/40) x (104/100)
= 163098
- 7. In a survey, it was found that 80% of those surveyed owned a car while 60% of those surveyed owned a mobile phone. If 55% owned both a car and a mobile phone, what percent of those surveyed owned a car or a mobile phone or both?
Options- A. 65%
- B. 80%
- C. 85%
- D. 97.5% Discuss
Correct Answer: 85%
Explanation:
Percentage of car owners = 80%
Percentage of mobile phone owners = 60%
Percentage of people having both car and mobile phone = 55%
Percentage of people having only car = 80 - 55 = 25%
Percentage of people having only mobile phone = 60 - 55 = 5%
Percentage of people having a car or a mobile phone or both = 55% + 25% + 5% = 85%
- 8. In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2 % took Mathematics. The total number of candidates was 2000. How many candidates took both Physics and Mathematics?
Options- A. 750
- B. 500
- C. 250
- D. 125 Discuss
Correct Answer: 500
Explanation:
Let x% candidates take both the subjects.
Percentage of candidates who opted Physics = 65.8%
and percentage of candidates who opted Mathematics = 59.2%
? x = (65.8 + 59.2 - 100)% = (125 - 100)% = 25%
Also, total number of candidates = 2000
? Number of candidates who opted both the subjects
= 25 x 2000/100 = 500
- 9. Two numbers X and Y are respectively 20% and 28% less then a third number Z. By what percentage is the number Y less than that of the number X?
Options- A. 8%
- B. 9%
- C. 10%
- D. 12% Discuss
Correct Answer: 10%
Explanation:
Here, Z = 100, X = 80 and Y = 72
Now according to the formula,
Percentage change = (New amount - Original amount)/Original amount
= [(80 - 72)/80] x 100%
= (8/80) x 100%
= 10%
? Y is less by X = 10%
- 10. The population of a city increases at the rate of 5% per annum. There is additional annual increases of 5% due to influx of job seekers. The percent increase in population after 3 yr, is?
Options- A. 33.1%
- B. 33%
- C. 34%
- D. 33.24% Discuss
Correct Answer: 33.1%
Explanation:
Total rate of increase in population per annum = 10%
Initially, let the population be 1000
population after 3 yr = 1000(1 + 10/100)3
= (1000 x 11/10 x 11/10 x 11/10) = 1331
? Increase in percentage = [(1331 - 1000)/1000] x 100%
= (331/1000) x 100%
= 33.1%
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