41. When 75 is added to 75% of a number, the answer is the number. Find 40% of that number.
(a) 100
(b) 80
(c) 120
(d) 160
(e) 180
Solution: (c)
If the number be x, then
\(\displaystyle x\times \frac{{75}}{{100}}+75=x\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{3x}}{4}+75=x\)
\(\displaystyle \Rightarrow \)\(\displaystyle x-\frac{{3x}}{4}=75\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{4}=75\)
\(\displaystyle \Rightarrow \)\(\displaystyle x=4\times 75=300\)
Therefore, 40% of 300
= \(\displaystyle \frac{{300\times 40}}{{100}}=120\)
42. In an office, 40% of the staff is female. 70% of the female staff and 50% of the male staff are married. The percentage of the unmarried staff in the office is
(a) 64
(b) 60
(c) 54
(d) 42
(e) 45
Solution: (d)
Total staff strength in the office = 100 (let)
Females = 40
Males = 60
Married females = \(\displaystyle \frac{{40\times 70}}{{100}}=28\)
Unmarried females = 40 – 28 = 12
Unmarried males = 30
Therefore, unmarried staff = 30 + 12 = 42
i.e. 42%
43. A boy found the answer for the question “subtract the sum of \(\displaystyle \frac{1}{4}\) and \(\displaystyle \frac{1}{5}\) from unity and express the answer in decimals” as 0.45. The percentage of error in his answer was
44. Two numbers are less than a third number by 30% and 37% respectively. The per cent by which the second number is less than the first is
(a) 10%
(b) 7%
(c) 4%
(d) 3%
(e) 5%
Solution: (a)
Third number = 100
First number = 70
Second number = 63
Therefore, required percentage
= \(\displaystyle \frac{7}{{70}}\times 100=10\)
45. 28% members of a certain group are married. What is the respective ratio between the number of married members to the number of unmarried members ?
46. 52% students from a college participated in a survey. What is the respective ratio between the number of students who did not participate in the survey to the number of students who participated?
(a) 11 : 13
(b) 12 : 13
(c) 12: 17
(d) Cannot be determined
(e) None of these
Solution: (b)
Required ratio = 48 : 52 = 12 : 13
47. In an examination it is required to get 55% of the aggregate marks to pass. A student gets 520 marks and is declared failed by 5% marks. What are the maximum aggregate marks a student can get?
(a) 960
(b) 1250
(c) 1040
(d) Cannot be determined
(e) None of these
Solution: (c)
Let maximum aggregate marks be x.
Student gets 520 marks and is declared failed by 5% marks it means student get 50% marks
50% of x = 520
\(\displaystyle \frac{x}{2}\) = 520
x = 1040
48. The product of 5% of a positive number and 2% of the same number is 211.6. What is half of that number?
(a) 230
(b) 460
(c) 920
(d) 115
(e) None of these
Solution: (a)
Let the number be x. Then, according to the question,
\(\displaystyle \frac{{5x}}{{100}}\times \frac{{2x}}{{100}}=211.6\)
or \(\displaystyle {{x}^{2}}=\frac{{211.6\times 100\times 100}}{{5\times 2}}=211600\)
x = + 460
Therefore, half of eight number = 230
49. In an examination, the maximum aggregate marks a 1020. In order to pass the exam a student is required to obtain 663 marks out of the aggregate marks. Shreya obtained 612 marks. By what percent did Shreya fail the exam?
50. The product of 5% of a positive number and 3% of the same number is 504.6. What is half of that number?
(a) 290
(b) 340
(c) 680
(d) 580
(e) None of these
Solution: (d)
Let the positive number be x
Then, \(\displaystyle \frac{{5x}}{{3x}}\times \frac{{3x}}{{100}}=504.6\)
\(\displaystyle \frac{{15{{x}^{2}}}}{{10000}}=504.6\)
or, \(\displaystyle {{x}^{2}}=\frac{{504.6\times 10000}}{{15}}\)
Therefore, x = 580
