Quantitative Aptitude- For Upcoming Exams
1). 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
2). 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
3). 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
4). 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
5). 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
6). 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.
7). 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
8). 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
9). In Times
Model School
a) 3/5
b) 6/7
c) 5/7
d) 7/15
e) none of these
10). 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
SOLUTION
Solution:
1). C)
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
2). D)
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
3). B)
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
4). B)
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
5). A)
D=60/6 =10 km/hr
U=60/10=6 km/hr
Y= 1/2 (10-6)=2 km/hr
6). D)
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
{ [(1/12) – (3/20)] / (3/20) } ×
100 = [(1/12) – (3/20)] × (20/3) × 100
= [ (5-9) / 60 ] × (20/3) × 100
= (-4/60) × (20/3) × 100
= (-4/60) × (20/3) × 100 = (-4/9) × 100
= -0.4444 × 100 = -44.44
= 44.44% decrease
7) . A)
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%.
8). B)
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.
9). D)
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.
10). A)
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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