31. Sujata invests 7% i.e. ₹ 2170 of her monthly salary in mutual funds. Later she invests 18% of her monthly salary in recurring deposits also; she invests 6% of her salary on NSC’s. What is the total annual amount invested by Sujata?
(a) ₹ 1,25,320
(b) ₹ 1,13,520
(c ) ₹ 1,35,120
(d) ₹ 1,15,320
(e) None of these
Solution: (d)
Let her monthly salary be ₹ x.
According to the question
\(\displaystyle \frac{7}{{100}}\times x=2170\)
\(\displaystyle \Rightarrow \)x= \(\displaystyle x=\frac{{2170\times 100}}{7}=31000\)
Total monthly investment = (18 + 6 + 7)% of 31000
\(\displaystyle \frac{{31}}{{100}}\times 31000=9610\)
Total annual investment = 12 × 9610 = ₹ 115320
32. If tax on a commodity is reduced by 10%, total revenue remains unchanged. What is the percentage increase in its consumption?
(a) \(\displaystyle 11\frac{1}{9}\%\)
(b) 20%
(c) 10%
(d) \(\displaystyle 9\frac{1}{{11}}\%\)
(e) None of these
Solution: (a)
Percentage increase in the consumption
=\(\displaystyle \frac{{10}}{{100-10}}\times 100=\frac{{100}}{9}=11\frac{1}{9}\%\)
33. Five-ninths of a number is equal to 25% 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% of the first number?
(a) 88.8
(b) 99.9
(c) 66.6
(d) Can’t be determined
(e) None of these
Solution: (b)
Second number = \(\displaystyle \frac{1}{4}\times 2960=740\)
Let the first number be x.
\(\displaystyle \frac{5}{9}x=\frac{{25}}{{100}}\times 740\)
\(\displaystyle x=\frac{9}{5}\times \frac{1}{4}\times 740=333\)
30% of 1st number = \(\displaystyle \frac{{30}}{{100}}\times 333=99.9\)
34. If 8% of x is the same as 4% of y, then 20% of x is the same as:
(a) 10% of y
(b) 16% of y
(c) 80% of y
(d) 50% of y
(e) 70% of y
Solution: (a)
\(\displaystyle \frac{{8x}}{{100}}=\frac{{4y}}{{100}}\)
\(\displaystyle \Rightarrow \)y = 2x
Therefore,
20% of x = 10% of y.
35. In a school 40% of the students play football and 50% play cricket. If 18% of the students neither play football nor cricket, the percentage of the students playing both is:
(a) 40%
(b) 32%
(c) 22%
(d) 8%
(e) 20%
Solution: (d)
Since 18% of the students neither play football nor cricket. It means 82% of the students either play football or cricket or both.
Using set theory
\(\displaystyle n(A\cup B)=n(A)+n(B)-n(A\cap B)\)
\(\displaystyle \Rightarrow \)82 = 40 + 50 –\(\displaystyle n(A\cap B)\)
\(\displaystyle \Rightarrow \)\(\displaystyle n(A\cap B)\) =90-82=8
Therefore, 8% students play both games.
36. If 120% of a is equal to 80% of b, then \(\displaystyle \frac{{b+a}}{{b-a}}\) is equal to
37. The population of a village is 25,000. One fifth are females and the rest are males. 5% of males and 40% of females are uneducated. What percentage on the whole are educated?
38. The sum of the numbers of boys and girls in a school is 150. If the number of boys is x, the number of girls becomes x% of the total number of students. The number of boys is :
39. Due to 25% fall in the rate of eggs, one can buy 2 dozen eggs more than before by investing Rs.162. Then the original rate per dozen of the eggs is
(a) Rs. 22
(b) Rs. 24
(c) Rs. 27
(d) Rs. 30
(e) Rs.32
Solution: (c)
Let Initial price of eggs = Rs. X per dozen
New price = Rs. 3x/4 per dozen
According to the question,
\(\displaystyle \frac{{162}}{{\frac{{3x}}{4}}}-\frac{{162}}{x}=2\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{162\times 4}}{{3x}}-\frac{{162}}{x}=2\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{216}}{x}-\frac{{162}}{x}=2\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{54}}{x}=2\)
\(\displaystyle \Rightarrow \)2x = 54
\(\displaystyle \Rightarrow \) x = Rs. 27 per dozen
40. A supply of juice lasts for 35 days. If its use is increased by 40% the number of days would the same amount of juice lasts, is
(a) 25 days
(b) 30 days
(c) 24 days
(d) 27 days
(e) 29 days
Solution: (a)
Required time = \(\displaystyle \frac{{35\times 100}}{{140}}\)
=25 days
