71. Groundnut oil is now being sold at ₹ 27 per kg. During last month its cost was ₹ 24 per kg. Find by how much % a family should reduce its consumption, so as to keep the expenditure same.
(a) \(\displaystyle 11\frac{1}{9}\%\)
(b) \(\displaystyle 11\frac{1}{{11}}\%\)
(c) \(\displaystyle 11\frac{9}{{10}}\%\)
(d) \(\displaystyle 9\frac{1}{{10}}\%\)
(e) None of these
Solution: (a)
% change in rate =(27-24)/24×100=100/8%
For fixed expenditure, % change in consumption
=\(\displaystyle \frac{{\%changeinrate}}{{100+\%changeinrate}}\times 100\)
=\(\displaystyle \frac{{100/8}}{{100[1+\frac{1}{8}]}}\times 100=\frac{{100}}{9}\%=11\frac{1}{9}\%\)
72. If 50% of a certain number is equal to \(\displaystyle \frac{3}{4}\) th of another number, what is the ratio between the numbers ?
(a) 3 : 2
(b) 2 : 5
(c) 5 : 2
(d) 3 : 4
(e) 4 : 3
Solution: (a)
First number = x
Second number = y
Therefore, \(\displaystyle x\times \frac{{50}}{{100}}=y\times \frac{3}{4}\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{2}=y\times \frac{3}{4}\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{x}{y}=\frac{3}{4}\times 2=\frac{3}{2}\)
73. A petrol pump owner mixed leaded and unleaded petrol in such a way that the mixture contains 10% unleaded petrol. What quantity of leaded petrol should be added to 1 litre mixture so that the percentage of unleaded petrol becomes 5%?
(a) 900 ml
(b) 1000 ml
(c) 1800 ml
(d) 1900 ml
(e) None of these
Solution: (b)
In 1 litre quantity of unlead petrol = 100 ml (given 10%)
Let x ml leaded petrol be added, then
5% of (1000 + x) = 100 ml
or, 5(1000 + x) = 100 × 100
\(\displaystyle \Rightarrow \)\(\displaystyle x=\frac{{5000}}{5}=1000ml\)
74. A man losses 20% of his money. After spending 25% of the remaining, he has ₹ 480 left. What is the amount of money he originally had?
(a) ₹600
(b) ₹ 720
(c) ₹ 800
(d) ₹ 840
(e) None of these
Solution: (c)
Let man has originally ₹x
After 20% loss = \(\displaystyle \frac{{x\times 80}}{{100}}=\frac{{8x}}{{10}}\)
After spending 25% = \(\displaystyle \frac{{8x}}{{10}}\times \frac{{75}}{{100}}=\frac{{8x}}{{10}}\times \frac{3}{4}\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{8x}}{{10}}\times \frac{3}{4}=480\)
Therefore, \(\displaystyle \frac{{480\times 4\times 10}}{{8\times 3}}=800\)
75. A person could save 10% of his income. But 2 years later, when his income increased by 20%, he could save the same amount only as before. By how much percentage has his expenditure increased?
(a) \(\displaystyle 22\frac{2}{9}\%\)
(b) \(\displaystyle 23\frac{1}{3}\%\)
(c) \(\displaystyle 24\frac{2}{9}\%\)
(d) \(\displaystyle 25\frac{2}{9}\%\)
(e) None of these
Solution: (a)
Let income be ₹ 100
Expenditure amount = \(\displaystyle 100\times \frac{{90}}{{100}}\)
Now, income increased by 20% = \(\displaystyle 100\times \frac{{120}}{{100}}\)
Expenditure amount = (120 – 10) = ₹110
Increase in expenditure = 110 – 90 = ₹ 20
Increase in % of expenditure = \(\displaystyle \frac{{20}}{{90}}\times 100\)
= \(\displaystyle \frac{{200}}{9}=22\frac{2}{9}\%\)
76. Sujata scored 2240 marks in an examination that is 128 marks more than the minimum passing percentage of 64%. What is the percentage of marks obtained by Meena if she scores 907 marks less than Sujata?
(a) 35
(b) 40
(c) 45
(d) 36
(e) 48
Solution: (b)
If total maximum marks be x, then,
\(\displaystyle \frac{{x\times 64}}{{100}}2240-128=2112\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{2112\times 100}}{{64}}=3300\)
Marks obtained by Meena = 2240 – 907 = 1333
Required percentage = \(\displaystyle \frac{{1333}}{{3300}}\times 100=40\)
77. Ms. Pooja invests 13% of her monthly salary, i.e.,₹ 8554 in Mediclaim Policies, Later she invests 23% of her monthly salary on Child. Education Policies; also she invests another 8% of her monthly salary on Mutual Funds. What is the total annual amount invested by Ms. Pooja?
(a) ₹ 28952
(b) ₹ 43428
(c) ₹ 347424
(d) ₹ 173712
(e) None of these
Solution: (c)
Let Ms. Pooja monthly salary = ₹ x
According to the question,
13% of the x = ₹8554
\(\displaystyle \Rightarrow \)\(\displaystyle x=\frac{{8554\times 100}}{{13}}\)
= Rs. 65800
Total monthly investment in percentage= 13 + 23 + 8 = 44
Therefore, Total monthly investment = 44% of ₹65800
=\(\displaystyle \frac{{44\times 65800}}{{100}}\)
= ₹ 28952
Therefore, total annual investments= (12 × 28952)
= 347424
78. In a class of 240 students, each student got sweets that are 15% of the total number of students. How many sweets were there?
(a) 3000
(b) 3125
(c) 8640
(d) Cannot be determined
(e) None of these
Solution: (c)
Number of sweets received by each student= 15% of 240
=\(\displaystyle \frac{{15\times 240}}{{100}}=36\)
Therefore, total number of sweets = 240 × 36 = 8640
79. What is the value of three fourth of sixty percent of 480?
(a) 216
(b) 218
(c) 212
(d) 214
(e) None of these
Solution: (a)
Required Value = \(\displaystyle 480\times \frac{{60}}{{100}}\times \frac{3}{4}=216\)
80. It is required to get 40% marks to pass an exam. A candidate scored 200 marks and failed by 8 marks. What were the maximum marks of that exam?
(a) 530
(b) 540
(c) 502
(d) Cannot be determined
(e) None of these
Solution: (e)
Maximum marks = \(\displaystyle \frac{{100\times 208}}{{40}}=520\)
