Solution: (a)
Let the number be x.
According to the question,
\(\displaystyle x\times \frac{{18}}{{100}}=75\times \frac{{12}}{{100}}\)
\(\displaystyle \Rightarrow \)\(\displaystyle x=\frac{{75\times 12}}{{18}}=50\)
92. If X is 20% less than Y, then find the values of \(\displaystyle \frac{{Y-X}}{Y}\) and \(\displaystyle \frac{X}{{X-Y}}\) .
(a) \(\displaystyle \frac{1}{5},-4\)
(b) \(\displaystyle 5,-\frac{1}{4}\)
(c) \(\displaystyle \frac{2}{5},-\frac{5}{2}\)
(d) \(\displaystyle \frac{3}{5},-\frac{5}{3}\)
(e) \(\displaystyle \frac{4}{5},-\frac{4}{3}\)
Solution: (a)
X is 20% less than Y.
If Y = 100, X = 80
\(\displaystyle \frac{{Y-X}}{Y}=\frac{{100-80}}{{100}}\)
=\(\displaystyle \frac{{20}}{{100}}=\frac{1}{5}\)
\(\displaystyle \frac{X}{{X-Y}}=\frac{{80}}{{80-100}}\)
=\(\displaystyle \frac{{80}}{{-20}}=-4\)
95. If 60% of A = 30% of B, B = 40% of C, C = x% of A, then value of x is
(a) 200
(b) 500
(c) 800
(d) 300
(e) 400
Solution: (b)
According to the question, \(\displaystyle \frac{{60A}}{{100}}=\frac{{30B}}{{100}}\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{3A}}{5}=\frac{{3B}}{{10}}=\frac{3}{{10}}\times \frac{{40}}{{100}}C\)
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{3A}}{5}=\frac{{3C}}{{25}}=\frac{3}{{25}}\times A\times \frac{X}{{100}}\) \(\displaystyle \frac{3}{5}=\frac{{3X}}{{2500}}\)
\(\displaystyle \Rightarrow \)5X=2500
\(\displaystyle \Rightarrow \)\(\displaystyle X=\frac{{2500}}{5}=500\)
96. 50% of a number when added to 50 is equal to the number. The number is
(a) 50
(b) 75
(c) 100
(d) 150
(e) 200
Solution: (c)
Let the number be x.
According to the question,
\(\displaystyle \frac{{x\times 50}}{{100}}+50=x\)
\(\displaystyle \frac{x}{2}+50=x\)
\(\displaystyle x-\frac{x}{2}=50\)
\(\displaystyle \frac{x}{2}=50\)
\(\displaystyle \Rightarrow \)x=100
97. 51% of a whole number is 714. 25% of that number is
(a) 350
(b) 450
(c) 550
(d) 250
(e) 650
Solution: (a)
Let the whole number be x.
According to the question, 51% of x = 714
\(\displaystyle \Rightarrow \)\(\displaystyle \frac{{x\times 51}}{{100}}=714\)
\(\displaystyle \Rightarrow \)X=\(\displaystyle \frac{{714\times 100}}{{51}}=1400\)
\(\displaystyle \Rightarrow \)25% of 1400= \(\displaystyle \frac{{1400\times 25}}{{100}}=350\)
98. There are 950 employees in an organization, out of which 28% got promoted. How many employees got promoted?
(a) 226
(b) 256
(c) 266
(d) 216
(e) None of these
Solution: (c)
Number of promoted employees = \(\displaystyle \frac{{950\times 28}}{{100}}=266\)
99. Arjun kapoor and Anil Kapoor appear for a test. For each correct answer is awarded 1 mark and for each wrong answer 1/2 mark is deducted. Arjun kapoor answers some questions and gets 10% of his answers wrong. He secures a score of 85% which is 6 marks more than the pass marks. Anil Kapoor also answers some questions and gets 20% of his answers wrong. He gets a score of 70% which is 3 marks less than the pass mark. No marks are awarded or deducted for the unanswered questions. What is the pass mark?
(a) 64
(b) 51
(c) 45
(d) 25
(e) None of these
Solution: (c)
Let Arjun kapoor attempt x questions, he gets 10% of the answers wrong.
Arjun kapoor’s score = \(\displaystyle 0.9x-(0.1x)\times \frac{1}{2}=0.85x\)
\(\displaystyle 0.85x=0.85z\), where z is the total number of marks as well as total number of marks possible.
So, x = z
\(\displaystyle \Rightarrow x=100\%ofz\)
Similarly let Anil Kapoor attempt y questions
Anil kapoor’s score = \(\displaystyle 0.8y-(0.2y)\times \frac{1}{2}=0.7y\)
\(\displaystyle 0.7y=0.7z\)
\(\displaystyle \Rightarrow y=100\%ofz\)
Now, \(\displaystyle 0.85z=P+6\), where P is pass mark …….. (i)
Also, \(\displaystyle 0.7z=P-3\)…….. (ii)
From (i) and (ii), we get
\(\displaystyle 0.15z=9\)
\(\displaystyle \Rightarrow z=60\)
Putting the value of z in (ii), we get
\(\displaystyle 0.7\times 60=P-3\)
\(\displaystyle P=42+3=45\)
100. The production of a company has ups and downs every year. The production increases for two consecutive years consistently by 15% and in the third year it decreases by 20%. Again in the next two years it increases by 25% each year and decreases by 10% in the third year. If we start counting from the year 2014 approximately what will be the effect on the production of the Company in 2018?
(a) 22
(b) 32
(c) 30
(d) 20
(e) None of these
Solution: (b)
Suppose the production of the company in the year 2014 be x.
Then production of the company in year 2018
\(\displaystyle =x\times \frac{{115}}{{100}}\times \frac{{115}}{{100}}\times \frac{{80}}{{100}}\times \frac{{125}}{{100}}=1.32x\)
Therefore, Increase % in the production in year 2018
\(\displaystyle =\frac{{(1.32x-x)}}{x}=32\%\)
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