1. 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?
A. 60%
B. 70%
C. 80%
D. 90%
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Ans: C. 80%
Explanation :
Let total number of men = 100
80 men are less than or equal to 50 years old
(Since 80% of the men are less than or equal to 50 years old)
=> 20 men are above 50 years old (Since we assumed total number of men as 100)
20% of the men above the age of 50 play football⇒Number of men above the age of 50 who play football = 20×20/100=4
Number of men who play football = 20 (Since 20% of all men play football)
Percentage of men who play football above the age of 50 = 4/20×100=20%
=>Percentage of men who play football less than or equal to the age 50 = 100%−20%=80%.
2. A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
a) 10 km/hr
b) 2.5 km/hr
c) 5 km/hr
d) 7.5 km/hr
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Ans: b) 2.5 km/hr
Explanation:
Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream =x
Then speed downstream =2x
we have, 1/2(x+2x)= speed in still water
⇒1/2(3x)=7.5
⇒3x=15
⇒x=5
i.e., speed upstream = 5 km/hr
Rate of stream =1/2(2x−x)=x/2=5/2=2.5 km/hr
3. What is the probability of drawing a “Queen” from a deck of 52 cards?
a) 1/2
b) 1/13
c) 1/6
d) 1/3
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Ans: b) 1/13
Explanation :
Total number of cards, n(S) = 52
Total number of “Queen” cards, n(E) = 4
P(E) = n(E)/n(S)=4/52=1/13
4. A letter is randomly taken from English alphabets. What is the probability that the letter selected is not a vowel?
a) 525
b) 225
c) 526
d) 21/26
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Ans: d) 21/26
Explanation
Total number of alphabets, n(S) = 26
Total number of characters which are not vowels, n(E) = 21
P(E) = n(E)/n(S)=21/26
5. Father is aged three times more than his son Sunil. After 8 years, he would be two and a half times of Sunil’s age. After further 8 years, how many times would he be of Sunil’s age?
a) 4 times
b) 4 times
c) 2 times
d) 3 times
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Ans: c) 2 times
Explanation:
Assume that Sunil’s present age = x.
Then father’s present age = 3x + x = 4x
After 8 years, father’s age = 212212 times of Sunils’ age
=> (4x+8) = 2(1/2)(x+8)
=> 4x + 8 = 5/2(x + 8)
=> 8x + 16 = 5x + 40
=> 3x = 40 – 16 = 24
=> x = 24/3 = 8
After further 8 years,
Sunil’s age = x + 8 + 8 = 8 + 8 + 8 = 24
Father’s age = 4x + 8 + 8 = 4 × 8 + 8 + 8 = 48
Father’s age/Sunil’s age = 48/24 = 2.
6. Six years ago, the ratio of the ages of Vimal and Saroj was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Saroj’s age at present?
a) 18
b) 17
c) 16
d) 15
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Ans: c) 16
Explanation:
Given that , six years ago, the ratio of the ages of Vimal and Saroj = 6 : 5
Hence we can assume that
age of Vimal six years ago =6x
age of Saroj six years ago =5x
After 4 years, the ratio of their ages = 11 : 10
=> (6x+10):(5x+10)=11:10
=> 10(6x+10)=11(5x+10)
=> 5x=10
=> x=10/5=2
Saroj’s present age =(5x+6)=5×2+6=16
7. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. What is his profit percentage?
a) 6%
b) 5%
c) 4%
d) 7%
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Ans: b) 5%
Explanation :
CP of 1st variety rice=20
CP of 2nd variety rice=36
CP of the 56 kg rice mixture = (26×20+30×36)=520+1080=1600
SP of the 1 kg rice mixture=30
SP of the 56 kg rice mixture=30×56=1680
Gain=SP−CP=1680−1600=80
Gain%=Gain/CP×100=80/1600×100=100/20=5%
8. Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is
a) 10.8 s
b) 12 s
c) 9.8 s
d) 8 s
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Ans: a) 10.8 s
Explanation :
Distance = 140+160 = 300 m
Relative speed = 60+40 = 100 km/hr = (100×10)/36 m/s
Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s
9. A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?
a) 62 m
b) 54 m
c) 50 m
d) 55 m
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Ans: c) 50 m
Explanation :
Let x is the length of the train in meter and v is its speed in kmph
x/9 = ( v-2) / (10/36) —(1)
x/10 =( v-4) / (10/36) — (2)
Dividing equation 1 with equation 2
10/9 = (v-2)/(v-4)
=> 10v – 40 = 9v – 18
=> v = 22
Substituting in equation 1, x/9 = 200/36 => x = 9×200/36 = 50 m
10. Arun took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If he paid Rs.686 as interest at the end of the loan period, what was the rate of interest?
a) 8%
b) 6%
c) 4%
d) 7%
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Ans: d) 7%
Explanation :
Let rate = R%
Then, Time, T = R years
P = Rs.1400
SI = Rs.686
SI= PRT/100
⇒686 = (1400 × R × R)/100
⇒686=14 R^2
⇒49=R^2
⇒R=7
i.e.,Rate of Interest was 7%
