Q1. A man rows upstream 16 km and downstream 27 km talking 5 hours each time. What is the velocity of current?
(a) 2 km/hr
(b) 2.1 km/hr
(c) 1.1 km/hr
(d) 1.4 km/h
(e) None of these
Q2. A boat moves downstream at the rate of one km in 7(1/2) minutes and upstream at the rate of 5 km an hour. What is the velocity of current?
(a) 1.3 km/hr
(b) 1.2 km/hr
(c) 1.6 km/hr
(d) 1.5 km/hr
(e) None of these
Q3. A person rows a kilometre down the stream in 10 minutes and upstream in 30 minutes. Find velocity of the stream.
(a) 1 km/hr
(b) 2 km/hr
(c) 3 km/hr
(d) 4 km/hr
(e) None of these
Q4. A man can row three quarters of a km against the stream in 11 minutes 15 seconds ad return in 7 minutes 30 seconds. Find the speed of the man in still water and also the speed of the stream
(a) 5 km/hr, 2 km/hr
(b) 5 km/hr, 1 km/hr
(c) 6 km/hr, 2 km/hr
(d) 4 km/hr, 1 km/hr
(e) None of these
Q5. A boat moves downstream at the rate of 1 km in 6 minutes and upstream at the rate of 1 km in 10 minutes. The speed of the current is
(a) 2 km/hr
(b) 1 km/hr
(c) 1.5 km/hr
(d) 2.5 km/hr
(e) None of these
Q6. A pharmaceutical company received Rs. 3 million in royalties on the first Rs. 20 million in sales of the generic equivalent of one of its products and then Rs.9 million in royalties on the next Rs. 108 million in royalties on the next Rs. 108 million in sales. By approximately what percent did the ratio of royalties to sales decrease from the first Rs. 20 million in sales to the next Rs. 108 million in sales?
(a) 10.27%
(b) 20.63%
(c) 38.6%
(d) 44.44%
(e) None Of these.
Q7. In Chittaranjan, only two newspapers Jan Jagran and Jan Khabar are published. It is known that 25% of the city population reads Jan Jagran and 20% reads Jan Khabar while 8% reads both the newspapers. It is also known that 30% of those who read Jan Jagran but not Jan Khabar look into advertisement and 40% of those who read Jan Khabar but not Jan Jagran look into advertisement while 50% of those who read both the newspapers look into advertisements. What is the percentage of the population who read an advertisement?
(a) 13.9%
(b) 15.8%
(c) 17.2%
(d) 21.4%
(e) None of these
Q8. In my office, at least 50% of the people read an e-newspaper. Among those who read an e-newspaper, at most 25% read more than one e-paper. Only one of the following statements follows from the statements given below. Which one is it?
(a) At the most 37.5% read exactly one e-paper.
(b) At least 37.5% read exactly one e-paper.
(c) At the most 19.8% read exactly one e-paper.
(d) At least 19.8% read exactly one e-paper.
(e) none of these
Q9. In Times Model School, 60% of the students are boys. In an aptitude test, 80% of the girls scored more than 40 marks (out of a maximum possible 150 marks). If 60% of the total students scored more than 40 marks in the same test, find the fraction of the boys who scored 40 marks or less?
(a) 3/5
(b) 6/7
(c) 5/7
(d) 7/15
(e) none of these
Q10. In a recent opinion poll held during April, 60% of the respondents favoured India Against Corruption (IAC) while the rest favoured Indian political parties (IPP). It was found in May polls that 10% of IAC supporters switched their preference to IPP, while the same percentage of IPP’s supporters also switched their preference to IAC. What percentage of the electorate should now switch their preference from IAC to IPP so that they are equal?
(a) 14%
(b) 19%
(c) 24%
(d) 29%
(e) None of these
Solutions
S1. Ans.(c)
Sol. Man’s rate upstream=16/5 km/hr
Man’s rate downstream=27/5 km/hr
Velocity of the current=1/2 (27/5-16/5) km/hr=1.1 km/hr
S2. Ans.(d)
Sol. Rate downstream=(2/15 *60) km/hr=8 km/hr
Rate upstream=5 km/hr
Velocity of the current=1/2 (8-5) km/hr=1.5 km/hr
S3. Ans.(b)
Sol. Rate downstream=1/10 *60 = 6 km/hr
Rate upstream=1/30 *60 = 2 km/hr
Velocity of the stream=1/2 (6-2) = 2 km/hr
S4. Ans.(b)
Sol. Rate upstream=3/4 * 4/45 * 60=4 km/hr
Rate downstream=3/4 * 2/15 * 60=6 km/hr
Speed of the man in still water (6+4)/2=5 km/hr
Speed of the stream=(6-4) ½=1 km/hr
S5. Ans.(a)
Sol. D=60/6 =10 km/hr
U=60/10=6 km/hr
Y= 1/2 (10-6)=2 km/hr
S6. Ans.(d)
Sol. The ratio of royalties to sales for the first Rs. 20 million in sales is 3/20, and the ratio of royalties to sales for the next Rs. 108 million in sales is 9/108=1/12. The percent decrease in the royalties to sales ratios is
S7. Ans.(a)
Sol. Let the population of the city be 100. Then,
People reading Jan Jagran=25
People reading Jan Khabar=20
People reading both=8
People reading only Jan Jagran=17
People reading only Jan Khabar=12
Therefore, required percentage of people who read an advertisement=(5.1+4.8+4)=13.9%.
S8. Ans.(b)
Sol. Let the number of people in my office=100
At least 50 people read an e-newspaper.
At most 12.5 people read more than one e-newspaper.
Therefore, at least 37.5 people read only one e-newspaper.
Hence, at least 37.5% read exactly one e-newspaper.
S9. Ans.(d)
Sol. Let the total number of students be y. Then,
Number of boys=3y/5
Number of girls=2y/5
Number of girls scoring more than 40 marks=4/5×2y/5=8y/25
Total number of students scoring more than 40 marks=3y/5
∴ Required fraction =7/25×5/3=7/15
Hence, the fraction of the boys who scored 40 marks or less is 7/15.
S10. Ans.(a)
Sol. Let the total number of respondents=100
People favoured IAC=60
People favoured IPP=40
New no. of people favouring IAC = 60+4-6 = 58
New no. of people favouring IPP = 40+6-4 = 42
Required percentage= (58-50)*100/58=14%Approx
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