11. Mathew scored 42 marks in Biology, 51 marks in Chemistry, 58 marks Mathematics, 35 marks in Physics and 48 marks in English. The maximum marks a student can score in each subject are 60. How much overall percentage did Mathew get in this exam?
(a) 76
(b) 82
(c) 68
(d) 78
(e) None of these
Solution: (d)
Total maximum marks of 5 subjects = 60 × 5 = 300
Total marks of Mathew = 42 + 51 + 58 + 35 + 48 = 234
% of Marks = \(\displaystyle \frac{{234}}{{300}}\times 100=78\%\)
12. The respective ratio of salaries of A and B is 8 : 7. If the salary of B increases by 20% and the salary of A increases by 21%, the new ratio becomes 96 : 77 respectively. What is A’s salary?
a) ₹ 22560
(b) ₹21600
(c) ₹ 20640
(d) ₹ 23040
(e) Cannot be determined
Solution: (e)
\(\displaystyle \frac{{A’ssalary}}{{B’ssalary}}=\frac{8}{7}\)
A’s salary= \(\displaystyle \frac{{8x}}{{15}}\)
B’s salary=\(\displaystyle \frac{{7x}}{{15}}\)
Now, A’s salary= \(\displaystyle \frac{{8x}}{{15}}+\frac{{8x}}{{15}}\times \frac{{21}}{{100}}=\frac{{8x+1.68x}}{{15}}=\frac{{9.68x}}{{15}}\)
Now B’s salary= \(\displaystyle \frac{{7x}}{{15}}+\frac{{7x}}{{15}}\times \frac{{20}}{{100}}=\frac{{7x+1.4x}}{{15}}=\frac{{8.4x}}{{15}}\)
Therefore, \(\displaystyle \frac{{9.68x}}{{15}}\times \frac{{15}}{{8.4x}}=\frac{{96}}{{77}}\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{9.68}}{{8.4}}=\frac{{96}}{{77}}\)
Here x is cancelled. So, salary of A can’t be determined.
13. A merchant bought some goods worth Rs. 6000 and sold half of them at 12% profit. At what profit percent should he sell the remaining goods to make and overall profit of 18%?
(a) 24
(b) 28
(c) 18
(d) 20
(e) 26
Solution: (a)
Profit on all the goods = 18% of 6000 = ₹ 1080
Profit on half of the goods = 12% of 3000 = ₹ 360
Therefore, the profit on remaining half of the objects
= 1080 – 360 = ₹ 720
Hence, required profit percentage=\(\displaystyle \frac{{720}}{{3000}}\times 100\%=24\%\)
14. Prema decided to donate 15% of her salary to an orphanage. On the day of donation she changed her mind and donated ₹ 1,896 which was 80% of what she had decided earlier. How much is Prerna’s salary?
(a) ₹18,500
(b) ₹ 10,250
(c) ₹15,800
(d) Cannot be determined
(e) None of these
Solution: (c)
Let Prerna’s salary be ₹ x
According to the question,
80% of 15% of x = 1896
\(\displaystyle \Rightarrow \)\(\displaystyle x\times \frac{{15}}{{100}}\times \frac{4}{5}=1896\)
Therefore, \(\displaystyle x=\frac{{1896\times 5\times 100}}{{15\times 4}}=₹15800\)
15. If the numerator of a fraction is increased by 600% and the denominator is increased by 200%, the resulting fraction is \(\displaystyle 2\frac{4}{5}\) What was the original fraction?
(a) \(\displaystyle \frac{4}{7}\)
(b) \(\displaystyle \frac{13}{12}\)
(c) \(\displaystyle \frac{11}{12}\)
(d) \(\displaystyle \frac{6}{5}\)
(e) None of these
Solution: (d)
Let the original fraction is \(\displaystyle \frac{a}{b}\)
Numerator is increased by 600%,
\(\displaystyle a\to a+\frac{{600}}{{100}}\times a=7a\)
Denominator is increased by 200%,
\(\displaystyle b\to b+\frac{{200}}{{100}}\times b=3b\)
According to the question \(\displaystyle \frac{{7a}}{{3b}}=\frac{{14}}{5}\)
Therefore, \(\displaystyle \frac{a}{b}=\frac{{14\times 3}}{{5\times 7}}=\frac{{42}}{{35}}\)
or \(\displaystyle \frac{a}{b}=\frac{6}{5}\)
16. If the numerator of a fraction is increased by 20% and the denominator is increased by 25%, the fraction obtained is \(\displaystyle \frac{3}{5}\). What was the original fraction?
(a) 5/7
(b) 4/7
(c) 3/8
(d) Cannot be determined
(e) None of these
Solution: (e)
Let fraction be \(\displaystyle \frac{x}{y}\)
According to the question \(\displaystyle \frac{{x\times 120\%}}{{y\times 125\%}}=\frac{3}{5}\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{y}=\frac{3}{5}\times \frac{{125}}{{120}}=\frac{5}{8}\)
17. Mr Alok spends 50% of his monthly income on household items and out of the remaining he spends 50% on transport, 25% on entertainment, 10% on sports and the remaining amount of ₹900 is saved. What is Mr Alok’s monthly income?
(a) ₹ 6000
(b) ₹9000
(c) ₹12000
(d) Cannot be determined
(e) None of these
Solution: (c)
Let total monthly income of Mr. Alok be ₹ x.
According to question,
Therefore, \(\displaystyle x\times \frac{{50}}{{100}}\times \frac{{15}}{{100}}=900\)
x = ₹ 12000
Hence, monthly income of Mr. Alok = ₹12000
18. The salaries of A,B,C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
(a) 3 : 3 : 10
(b) 10 : 11 : 20
(c) 23 : 33 : 60
(d) Cannot be determined
(e) None of these
Solution: (c)
Let A = 2k, B = 3k and C = 5k.
A’s new salary = \(\displaystyle \frac{{115}}{{100}}\times 2k=\frac{{23}}{{10}}k\)
B’s new salary = \(\displaystyle \frac{{110}}{{100}}\times 3k=\frac{{33}}{{10}}k\)
C’s new salary = \(\displaystyle \frac{{120}}{{100}}\times 5k=6k\)
Therefore, New ratio = \(\displaystyle \frac{{23k}}{{10}}:\frac{{33k}}{{10}}:6k=23:33:60\)
19. Barath spends 25 per cent of his salary on house rent, 5 percent on food, 15 percent on travel, 10 percent on clothes and the remaining amount of ₹ 27,000 is saved. What is Barath’s income?
(a) ₹60,000
(b) ₹60,500
(c) ₹60,700
(d) ₹70,500
(e) None of these
Solution: (a)
Saving percentage = (100 – 55) % = 45%
If the income of Barath be ₹ x, then,
\(\displaystyle \frac{{45\times x}}{{100}}=27000\)
\(\displaystyle \Rightarrow \)x = \(\displaystyle x=\frac{{27000\times 100}}{{45}}=60000\)
20. Five-ninths of number is equal to twenty five percent of the second number. The second number is equal to one-fourth of the third number. The value of the third number is 2960. What is 30 percent of the first number?
(a) 99.9
(b) 88.8
(c) 66.6
(d) Cannot be determined
(e) None of these
Solution: (a)
Second number = \(\displaystyle \frac{1}{4}\times 2960=740\)
Let the first number be x.
\(\displaystyle \frac{5}{9}x=\frac{{25}}{{100}}\times 740\)
x= \(\displaystyle x=\frac{9}{5}\times \frac{1}{4}\times 740=333\)
30% of 1st number
=\(\displaystyle \frac{{30}}{{100}}\times 333=99.9\)
