Let’s calculate the percentage of these problems

Hyderabad: This article is in continuation to the last article focusing on the percentage topic. Here are some practice questions along with solutions on the percentage topic that will you in your preparation for the State government recruitment jobs. 1. In a library 60% of the books are in arithmetic, 60% of the remaining are […]

Hyderabad: This article is in continuation to the last article focusing on the percentage topic. Here are some practice questions along with solutions on the percentage topic that will you in your preparation for the State government recruitment jobs.

1. In a library 60% of the books are in arithmetic, 60% of the remaining are in reasoning and rest of the books are in mathematics. If there are 3,600 books in reasoning, then the total number of books in mathematics is?
a) 3400 b) 2400 c) 2300 d) 3200
Ans: b

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Solution: Let the total number of books = x
Arithmetic = 60/100 × x = 60x/100
Reasoning = 40/100 × 60% = 24x/100
Mathematics = 16x/100
R: M = 3:2
3 ->; 3600
2 ->; ?
3600 × 2/3 = 2400

2. In an examination, 19% students failed in mathematics and 10% students failed in English. If 7% of all students failed in both the subjects, then the number of students passed in both the subjects is
a) 78% of all subjects b) 68% of all subjects
c) 65% of all subjects d) 75% of all subjects
Ans: a

Solution: M E
19 12 7 3 10
The percentage of students are failed in either one or two subjects = 12 7 3 = 22
Therefore, the percentage of students passed in both the subjects
= 100 – 22 = 78%

3. In an examination 80% of the boys passed in English and 85% passed in Mathematics, while 75% passed in both. If 45 boys failed in both, the number of boys who sat for the examination was?
a) 225 b) 375 c) 350 d) 450
Ans: d

Solution :
E     M
80 5 75 10 85
Passed in English or Mathematics or both
= 5 75 10 = 90%
Failed = 10%
10% = 45
100% = ?
? = 450

4. In a group of students 70% can speak English and 65% can speak Hindi. If 27% of the students can speak none of the two languages, then what percent of group can speak both the languages?
a) 62% b) 64% c) 55% d) 52%
Ans: a

Solution: Let total number of students = 100
Students who can speak none of the languages = 27
Remaining students = 100 – 27 = 73
Students who know both the languages
= 70 65 – 73 = 62%

5. In an examination 60% of the candidates passed in English and 70% of the candidates passed in Mathematics, but 20% failed in both of these subjects. If 2500 candidates passed in both subjects, the number of candidates who appeared at the examination was
a) 4000 b) 5500 c) 5000 d) 4500
Ans: c

Solution: Let the total number of candidates = x
Number of candidates passed in at least one subject
= x – 20x/100 = 80x/100 = 0.8x
E           M
0.6x 2500 0.7x
0.6x 0.7x – 2500 = 0.8x
0.5x = 2500
x = 2500/0.5 = 5000

6. In an examination 70% of the candidates passed in English and 80% passed in Mathematics, while 10% failed in both the subjects. If 144 candidates passed in both, the total number of candidates was?
a) 220 b) 240 c) 230 d) 225
Ans: b

Solution: Let the total number of candidates = 100
English             Mathematics
Passed Failed Passed Failed
70       30       80         20
10 candidates failed in English and Mathematics both
30 20
E 20 10 10 M
Therefore, the total number of failed candidates = 20 10 10 = 40
=>; 100 – 40 = 60 candidates passed in both the subjects
100 ->; 60
? ->; 144
? = 144 × 100/60 = 240

7. In a class of MBA students 16.66% students are from commerce background, 12.5% students are from science background, 6.66% students from engineering background and rest are from arts background. The minimum possible students of arts background are?
a) 44 b) 55 c) 66 d) 77
Ans: d
Solution: 16.66% = 1/6, 12.5% = 1/8, 6.66% = 1/15
Let total number of students = x
x – ( x/6 x/8 x/15)
x – (43x/120) = 77x/120
When x = 120 (The least possible number)
Then the number of arts background students = 77

To be continued..