20 Minutes Test
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Test Report
Question No 2
What was the day of the week on 28th May, 2006?
Select the correct answer
Solution!
28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) = 6 odd days
From January to 28 May (31 + 28 + 31 + 30 + 28 ) = 148 days
So, 148 days = (21 weeks + 1 day) = 1 odd day.
Total number of odd days = (0 + 0 + 6 + 1) = 7 = 0 odd day.
Hence Given day is Sunday.
28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)
Odd days in 1600 years = 0
Odd days in 400 years = 0
5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) = 6 odd days
From January to 28 May (31 + 28 + 31 + 30 + 28 ) = 148 days
So, 148 days = (21 weeks + 1 day) = 1 odd day.
Total number of odd days = (0 + 0 + 6 + 1) = 7 = 0 odd day.
Hence Given day is Sunday.
Question No 5
A 100 meters long train can cross a 150 meters long bridge in 20 seconds. What is the speed of the train?
Select the correct answer
Solution!
Length of the train = L1 = 100m
Length of the bridge = L2 = 150m
Time = t = 20s
Speed = v = ?
v = (L1+L2)/t
By putting values
v = (100+150)/20
v = 250/20 = 12.5m/s
Hence speed of train is 12.5m/s..
Length of the train = L1 = 100m
Length of the bridge = L2 = 150m
Time = t = 20s
Speed = v = ?
v = (L1+L2)/t
By putting values
v = (100+150)/20
v = 250/20 = 12.5m/s
Hence speed of train is 12.5m/s..
Question No 6
On 8th Dec, 2007 Saturday falls.What day of the week was it on 8th Dec, 2006?
Select the correct answer
Solution!
The year 2006 is an ordinary year. So, it has 1 odd day.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
Hence, 8th Dec, 2006 is Friday..
The year 2006 is an ordinary year. So, it has 1 odd day.
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
Hence, 8th Dec, 2006 is Friday..
Question No 7
A train travelling at he speed of 72km/h can cross a platform in 17 seconds. If length of the train is 180 meters, what is the length of the platform?
Select the correct answer
Solution!
Speed of train = v = 72Km/h = 72*(5/18) = 20m/s
Time = t = 17s
Length of the train = L1 = 180m
Length of the platform = L2 = ?
t = (L1+L2)/v
By putting values
17 = (180+L2)/20
340-180 = L2
L2 = 160m
Hence length of the platform is 160m..
Speed of train = v = 72Km/h = 72*(5/18) = 20m/s
Time = t = 17s
Length of the train = L1 = 180m
Length of the platform = L2 = ?
t = (L1+L2)/v
By putting values
17 = (180+L2)/20
340-180 = L2
L2 = 160m
Hence length of the platform is 160m..
Question No 8
One year ago, the ratio of Sooraj's and Vimal's age was 6/7 respectively. Four years hence, this ratio would become 7/8. How old is Vimal?
Select the correct answer
Solution!
Let take the age of Sooraj and Vimal, 1 year ago as 6x and 7x respectively.
Given that, four years hence, this ratio would become 7/8.
(6x + 5)/(7x + 5) = 7/8
48x + 40 = 49x + 35
x = 5
Vimal's present age = 7x + 1 = 7*5 + 1 = 36.
Let take the age of Sooraj and Vimal, 1 year ago as 6x and 7x respectively.
Given that, four years hence, this ratio would become 7/8.
(6x + 5)/(7x + 5) = 7/8
48x + 40 = 49x + 35
x = 5
Vimal's present age = 7x + 1 = 7*5 + 1 = 36.
Question No 9
Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is
Select the correct answer
Solution!
Ratio of times taken by Sakshi and Tanya = 125/100 = 5/4
Suppose Tanya takes x days to do the work.
5/4 = 20/x
x = (4*20)/5
x = 16 days.
Hence, Tanya takes 16 days to complete the work..
Ratio of times taken by Sakshi and Tanya = 125/100 = 5/4
Suppose Tanya takes x days to do the work.
5/4 = 20/x
x = (4*20)/5
x = 16 days.
Hence, Tanya takes 16 days to complete the work..
Question No 14
A father is 15 times as old as his son. however, 18 years later, he will be only thrice as old as the son. What is the father's present age?
Select the correct answer
Solution!
Let present age of the son is x and present age of Father is y.
Given that
y = 15x
15x-y = 0 ...(1)
and also given that
y+18 = 3(x+18)
y+18 = 3x+54
y-3x = 36 ...(2)
By simultaneously solving equation(1) and equation(2)
y = 45
Hence father's present age is 45 years..
Let present age of the son is x and present age of Father is y.
Given that
y = 15x
15x-y = 0 ...(1)
and also given that
y+18 = 3(x+18)
y+18 = 3x+54
y-3x = 36 ...(2)
By simultaneously solving equation(1) and equation(2)
y = 45
Hence father's present age is 45 years..
Question No 15
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?
Select the correct answer
Solution!
Let, 1 man's 1 day's work = x
and
1 woman's 1 day's work = y
Then, 4x + 6y = 1/8 nd 3x + 7y = 1/10
Solving the two equations, we get
x = 11/400
y = 1/400
So, One woman's 1 day's work = 1/400
10 women's 1 day's work = (1/400 * 10) = 1/40
Hence, 10 women will complete the work in 40 days..
Let, 1 man's 1 day's work = x
and
1 woman's 1 day's work = y
Then, 4x + 6y = 1/8 nd 3x + 7y = 1/10
Solving the two equations, we get
x = 11/400
y = 1/400
So, One woman's 1 day's work = 1/400
10 women's 1 day's work = (1/400 * 10) = 1/40
Hence, 10 women will complete the work in 40 days..
Question No 22
What is the speed of the train if it crosses a 175 meters long bridge in 41 seconds? Length of the train is 645 meters?
Select the correct answer
Solution!
Length of the train = L1 = 645m
Length of the bridge = L2 = 175m
Time = t = 41s
Speed = v = ?
v = (L1+L2)/t
v = (645+175)/41
v = 20m/s = 20 * 18/5 = 72 Km/h
Hence speed of the train is 72 Km/h..
Length of the train = L1 = 645m
Length of the bridge = L2 = 175m
Time = t = 41s
Speed = v = ?
v = (L1+L2)/t
v = (645+175)/41
v = 20m/s = 20 * 18/5 = 72 Km/h
Hence speed of the train is 72 Km/h..
Question No 25
If A + B means A is the sister of B; A x B means A is the wife of B, A % B means A is the father of B and A - B means A is the brother of B. Which of the following means T is the daughter of P?
Select the correct answer
Solution!
P x Q = P is the wife of Q
Q % R = Q is the father of R
R - T = R is the brother of T
T + S = T is the sister of S.
Therefore, T is the daughter of P..
P x Q = P is the wife of Q
Q % R = Q is the father of R
R - T = R is the brother of T
T + S = T is the sister of S.
Therefore, T is the daughter of P..
Question No 30
A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Select the correct answer
Solution!
Formula for converting from km/hr to m/s is
X km/hr = x * (5/18)m/s
Therefore,
Speed = 45 * (5/18) = 25/2 m/s
Total distance to be covered = (360 + 140) m = 500 m
Formula for finding Time = (Distance/Speed)
Hence, Required time = (500*2)/25
= 40 seconds.
Formula for converting from km/hr to m/s is
X km/hr = x * (5/18)m/s
Therefore,
Speed = 45 * (5/18) = 25/2 m/s
Total distance to be covered = (360 + 140) m = 500 m
Formula for finding Time = (Distance/Speed)
Hence, Required time = (500*2)/25
= 40 seconds.
Question No 33
A man is 24 years older than his son. In two years, his age will be twice the age of his son. What is the present age of his son?
Select the correct answer
Solution!
Let the present age of the son = x years
Then present age the man = (x+24) years
Given that in 2 years, man's age will be twice the age of his son
(x+24) +2 = 2(x+2)
x = 22.
Let the present age of the son = x years
Then present age the man = (x+24) years
Given that in 2 years, man's age will be twice the age of his son
(x+24) +2 = 2(x+2)
x = 22.
Question No 34
If M x N means M is the daughter of N; M + N means M is the father of N; M % N means M is the mother of N and M - N means M is the brother of N then P % Q + R - T x K indicates which relation of P to K?
Select the correct answer
Solution!
P % Q = P is the mother of Q
Q + R = Q is the father of R
R - T = R is the brother of T
Hence, Q is the father of T
T x K = T is the daughter of K
Hence, Q is the husband of K.
Therefore, P is the mother-in-law of K..
P % Q = P is the mother of Q
Q + R = Q is the father of R
R - T = R is the brother of T
Hence, Q is the father of T
T x K = T is the daughter of K
Hence, Q is the husband of K.
Therefore, P is the mother-in-law of K..
Question No 36
10 women can complete a work in 7 days and 10 children take 14 days to complete the work.How many days will 5 women and 10 children take to complete the work?
Select the correct answer
Solution!
1 woman's 1 day's work =1/70
1 child's 1 day's work =1/140
(5 women + 10 children)'s 1 day's work = (5/70 + 10/140) = (1/14 + 1/14) = 1/7
Hence, 5 women and 10 children will complete the work in 7 days..
1 woman's 1 day's work =1/70
1 child's 1 day's work =1/140
(5 women + 10 children)'s 1 day's work = (5/70 + 10/140) = (1/14 + 1/14) = 1/7
Hence, 5 women and 10 children will complete the work in 7 days..
Question No 39
A 300 metre long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds.What is the length of the platform?
Select the correct answer
Solution!
Speed = (300/18)m/s
= 50/3m/s
Let the length of the platform be x metres
Then, (x+300)/39 = 50/3
3(x + 300) = 1950
Hence, x = 350 m.
Speed = (300/18)m/s
= 50/3m/s
Let the length of the platform be x metres
Then, (x+300)/39 = 50/3
3(x + 300) = 1950
Hence, x = 350 m.
Question No 40
Introducing Sonia, Aamir says, "She is the wife of only nephew of only brother of my mother." How Sonia is related to Aamir?
Select the correct answer
Solution!
Brother of mother means maternal uncle.
Hence only nephew of Aamir's maternal uncle means Aamir himself.
Therefore Sonia is the wife of Aamir..
Brother of mother means maternal uncle.
Hence only nephew of Aamir's maternal uncle means Aamir himself.
Therefore Sonia is the wife of Aamir..
Question No 43
A father is 3 years older than 3 times the age of his son. If the sum of their ages is 31 years, how old was father 3 years ago?
Select the correct answer
Solution!
Let present age of son is x and present age of father is y.
Given that
y = 3x+3 ...(1)
and
x+y = 31
x = 31-y
Put value of x in equation(1)
y = 3(31-y)+3
y = 93-3y+3
4y = 96
y = 24
Three years ago
y = 24-3
y = 21
Hence father was 21 years old 3 years ago..
Let present age of son is x and present age of father is y.
Given that
y = 3x+3 ...(1)
and
x+y = 31
x = 31-y
Put value of x in equation(1)
y = 3(31-y)+3
y = 93-3y+3
4y = 96
y = 24
Three years ago
y = 24-3
y = 21
Hence father was 21 years old 3 years ago..
Question No 46
A can do a work in 15 days and B in 20 days.If they work on it together for 4 days,then the fraction of the work that is left is
Select the correct answer
Solution!
A's 1 day's work = 1/15
B's 1 day's work = 1/20
(A + B)'s 1 day's work = (1/15 + 1/20) = 7/60
(A + B)'s 4 day's work = (7/60 * 4) = 7/15
Therefore, Remaining work = (1 - 7/15) = 8/15.
A's 1 day's work = 1/15
B's 1 day's work = 1/20
(A + B)'s 1 day's work = (1/15 + 1/20) = 7/60
(A + B)'s 4 day's work = (7/60 * 4) = 7/15
Therefore, Remaining work = (1 - 7/15) = 8/15.
Question No 48
A and B can do a job together in 7 days. A is 7/4 times as efficient as B.The same job can be done by A alone in
Select the correct answer
Solution!
(A's 1 day's work) / (B's 1 day's work) = 7/4
Let A's and B's 1 day's work be 7x and 4x respectively.
Then,
7x + 4x = 1/7
11x = 1/7
x = 1/77
Hence, A's 1 day's work = (1/77 * 7) = 1/11.
(A's 1 day's work) / (B's 1 day's work) = 7/4
Let A's and B's 1 day's work be 7x and 4x respectively.
Then,
7x + 4x = 1/7
11x = 1/7
x = 1/77
Hence, A's 1 day's work = (1/77 * 7) = 1/11.
Question No 51
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, what was the son's age five years back?
Select the correct answer
Solution!
Let the son's present age be x years.
Then
(38 - x) = x
2x = 38
x = 38/2 = 19
Son's age 5 years back = 19-5 = 14 years.
Let the son's present age be x years.
Then
(38 - x) = x
2x = 38
x = 38/2 = 19
Son's age 5 years back = 19-5 = 14 years.
Question No 53
Ali's swimming speed in still water is 18 km/h and speed of water is 6 km/h. How long will it take him to go downstream 72km?
Select the correct answer
Solution!
Ali's swimming speed in still water = u = 18 Km/h
Speed of water = v = 6 Km/h
Total speed down the stream = 18+6 = 24 Km/h
Distance to cover = 72 Km
time = ?
time = distance/speed = time = 72/24 = 3 hours..
Ali's swimming speed in still water = u = 18 Km/h
Speed of water = v = 6 Km/h
Total speed down the stream = 18+6 = 24 Km/h
Distance to cover = 72 Km
time = ?
time = distance/speed = time = 72/24 = 3 hours..
Question No 56
How many times do the hands of a clock coincide in a day?
Select the correct answer
Solution!
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).
The hands overlap about every 65 minutes, not every 60 minutes. So, the hands coincide 22 times in a day..
The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock).
The hands overlap about every 65 minutes, not every 60 minutes. So, the hands coincide 22 times in a day..
Question No 57
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Select the correct answer
Solution!
Speed downstream = (5 + 1) kmph = 6 kmph
Speed upstream = (5 - 1) kmph = 4 kmph
Let the required distance be x km.
Then,
x/6 + x/4 = 1
2x + 3x = 12
5x = 12
Hence, x = 2.4 km.
Speed downstream = (5 + 1) kmph = 6 kmph
Speed upstream = (5 - 1) kmph = 4 kmph
Let the required distance be x km.
Then,
x/6 + x/4 = 1
2x + 3x = 12
5x = 12
Hence, x = 2.4 km.
Question No 60
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was?
Select the correct answer
Solution!
Let the son's present age be x years. Then, (38 - x) = x
2x = 38
x = 19
Hence, Son's age 5 years back (19 - 5) = 14 years..
Let the son's present age be x years. Then, (38 - x) = x
2x = 38
x = 19
Hence, Son's age 5 years back (19 - 5) = 14 years..