RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late . Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late. What is the speed T of the train.
A.a) 45
B.b) 33
C.c) 48
D.d) 55
Answer: C.c) 48
Explanation: Let y be the balance distance to be covered and x be the former speed.
A train after traveling for 50km meets with an accident and then proceeds at 3/4 of its former speed and arrives at its destination 35 minutes late
so, y/(3x/4) - y/x = 35/60
4y/3x - y/x = 7/12
y/x(4/3-1)=7/12
y/x*1/3=7/12
y/x=7/4
4y-7x=0 ........ 1
Had the accident occurred 24 km farther, it would have reached the destination only 25 minutes late
so, (y-24)/(3x/4) - (y-24)/x = 25/60
4(y-24)/3x - (y-24)/x = 5/12
(y-24)/x (4/3-1) = 5/12
(y-24)/x *1/3 = 5/12
(y-24)*12 = 3x*5
(y-24)*4 = 5x
4y-5x = 96 ....... 2
eq2 - eq1
2x=96
x=48=T
Ans = C
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 90, what is the value of c âˆ’ a?
A.25
B.90
C.100
D.140
Answer: B.90
Explanation: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=180 --2
subtracting 1 from 2 we have
c-a=90;
ANSWER:B
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
A.5/21
B.5/28
C.5/27
D.5/29
Answer: A.5/21
Explanation: Number of ways of (selecting at least two couples among five people selected) =
As remaining person can be any one among three couples left.
Required probability
= (10 * 6)/252 = 5/21
Answer:A
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
A.270
B.280
C.290
D.300
Answer: A.270
Explanation: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270.
A)
Question: The residents of Town X participated in a survey to determine the number of hours per week each resident spent watching television. The distribution of the results of the survey had a mean of 21 hours and a standard deviation of 7 hours. The number of hours that Pat, a resident of Town X, watched television last week was between 1 and 2 standard deviations below the mean. Which of the following could be the number of hours that Pat watched television last week?
A.30
B.20
C.18
D.12
Answer: D.12
Explanation: Given: mean=21 and SD=7
The number of hours that Pat watched television was between 1 and 2 standard deviations below the mean: 1 SD below the mean ismean-1*SD=14 and 2 SD below the mean ismean-2*SD=7 ,so the number of hours that Pat watched television was between 7 and 14 hours.
Answer: D.
Question: Statement: Unemployment allowance should be given to all unemployed Indian youth above 18 yrs of age.
Assumptions:
1) There are unemployed youth in India who needs monetary support.
2) The government has sufficient funds to provide allowance to all unemployed youth.
A.Only assumption I is implicit
B.Only assumption II is implicit
C.Either I or II is implicit
D.Neither I nor II is implicit
Answer: A.Only assumption I is implicit
Explanation: I directly follows from the statement and so is implicit. Also, the statement is a suggestion and does not tell about a government policy or its position of funds. So, II is not implicit.
A
Question: In a nationwide poll, N people were interviewed. If 1/6 of them answered yes to question 1, and of those, 1/3 answered yes to question 2, which of the following expressions represents the number of people interviewed who did NOT answer yes to both questions?
A.N/9
B.8N/9
C.11N/18
D.17N/18
Answer: D.17N/18
Explanation: The number of people who answered yes to both questions is (1/3)(1/6)N = N/18
The number of people who did not answer yes to both is 1 - N/18 = 17N/18
The answer is D.
Question: Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 40 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
A. 60
B. 80
C. 100
D. 120
Answer: C. 100
Explanation: 30% of the members have passed the test, thus 70% have not passed the test.
We also know that 30+40=70 members have not passed the test, thus 0.7*Total=70 --> Total=100.
Answer: C.
Question: Two persons starting from the same place walk at a rate of 10kmph and 12.5kmph respectively. What time will they take to be 10km apart, if they walk in the same direction?
A.17 hrs
B.4 hrs
C.6 hrs
D.12 hrs
Answer: B.4 hrs
Explanation: The relative speed of the boys = 12.5kmph – 10kmph
= 2.5 kmph
Distance between them is 10 km
Time= 10km / 2.5 kmph = 4 hrs
Answer : B
Question: A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,020 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
A.25
B.30
C.35
D.40
Answer: D.40
Explanation: Day 1
2t+3=21
t=9
Day 2
t+3
9+3=12
9r+12(r+15)=1020
r=40
Answer:D
Question: A man rows his boat 90 km downstream and 72 km upstream, taking 3 hours each time. Find the speed of the stream?
A.6
B.5
C.7
D.3
Answer: D.3
Explanation: Speed downstream = d/t = 90/3 = 30 kmph
Speed upstream = d/t = 72/(3) = 24 kmph
The speed of the stream = (30 - 24)/2 = 3 kmph
Answer:D
Question: If two sides of a triangle have lengths 3 and 6, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19
A.None
B.I only
C.II only
D.II and III only
Answer: C.II only
Explanation: Let x be the length of the third side.
6-3 < x < 6+3
3 < x < 9
12 < perimeter < 18
The answer is C.
Question: Pipe A can fill a tank in 20 hrs and pipe B can fill it in 60 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill quarter of that tank?
A.3 hr 15 mins
B.3 hr 25 mins
C.3 hr 35 mins
D.3 hr 45 mins
Answer: D.3 hr 45 mins
Explanation: Part filled A in 1 hr= (1/20)
Part filled B in 1 hr= (1/60)
Part filled by (A+B) together in 1 hr=(1/20)+(1/60)=1/15
So, The tank will be full in 15 hrs
Time taken to fill Exact quarter tank = (15) * (1/4) = 3.45 hr= 3 hr 45 mins
Answer : D
Question: A shopkeeper loses 15%,if an article is sold for $102. What should be the selling price of the article to gain 20%?
A.$165
B.$174
C.$144
D.$164
Answer: C.$144
Explanation: C
$144
Given that SP = $102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = $120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = $144
Question: If a coin is tossed 5 times what is the probability that it will land either heads 5 times or tails 5 times?
A.1/4
B.1/8
C.1/16
D.1/32
Answer: C.1/16
Explanation: The probability of 5 heads is (1/2)^5 = 1/32
The probability of 5 tails is (1/2)^5 = 1/32
The probability of 5 heads or 5 tails is 1/32 + 1/32 = 1/16
The answer is C.
Question: Out of 10 persons working on a project, 4 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
A.5/5
B.5/3
C.5/2
D.5/6
Answer: D.5/6
Explanation: P(at least one graduate) = 1 - P(no graduates)
= 1 - 6C1/10C3 = 1 - (6 * 5 * 4)/(10 * 9 * 8)
= 5/6
Answer:D
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other?
A.57/7 sec
B.80/7 sec
C.20/7 sec
D.60/7 sec
Answer: B.80/7 sec
Explanation: Explanation:
Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
ANSWER IS B
Question: At 6'o clock clock ticks 6 times. The time between first and
last ticks was 30sec. How much time it takes at 9'o clock.
A.60sec
B.62sec
C.66sec
D.48sec
Answer: D.48sec
Explanation: At 6'0 clock, clock ticks 6 times.
So, there must be 5 intervals between clock ticks.
Time Between first and last ticks = 30sec
So, 1 interval = 30/5 = 6sec
So 6'o clock 5 *6=30sec
7'o clock 6 *6=36sec
8'o clock 7 *6=42sec
9'o clock 8 *6=48sec
So, 48sec at 9'o clock.
ANSWER:D
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 12 minutes is:
A.9
B.5
C.7
D.6
Answer: B.5
Explanation: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(12/60)) km = 5 km.
ANSWER:B
Question: Two kinds of Vodka are mixed in the ratio 2:6 and 6:3 and they are sold fetching the profit 10% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of
A.20%
B.40%
C.18%
D.23%
Answer: A.20%
Explanation: The profit on the first kind of vodka = x%;
The profit on the second kind of vodka = y%.
When they are mixed in the ratio 1:2 (total of 3 parts) the average profit is 10%: (x + 2y)/3 = 10.
When they are mixed in the ratio 2:1 (total of 3 parts) the average profit is 20%: (2x + y)/3 = 20.
Solving gives: x = 30% and y = 0%.
After the individual profit percent on them areincreased by 4/3 and 5/3 times respectively the profit becomes 40% and 0%,on the first and te second kinds of vodka, respectively.
If they are mixed in equal ratio (1:1), then the mixture will fetch the profit of (40 + 0)/2 = 20%.
Answer:A
Question: A number x is 18 times another number y. The percentage that y is less than x is
A.12.5%
B.87.5%
C.80%
D.94.4%
Answer: D.94.4%
Explanation: Say y=1 and x=18.
Then y=1 is less than x=18 by (18-1)/18*100=17/18*100=94.4%.
Answer: D.
Question: A housewife saved Rs. 2.50 in buying an item on sale. If she spent Rs. 25 for the item, approximately how much percent she saved in the transaction ?
A.8
B.9
C.7
D.6
Answer: B.9
Explanation: Explanation:
Actual price = Rs. (25 + 2.50) = Rs. 27.50.
Saving = 2.50
Percentage Saving =
Answer: B) 9
%
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
A.7/20
B.1/2
C.16/19
D.3/5
Answer: A.7/20
Explanation: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
A)
Question: On a certain transatlantic crossing, 25 percent of a ship's passengers held round-trip tickets and also took their cars aboard the ship. If 60 percent of the passengers with round-trip tickets did not take their cars aboard the ship, what percent of the ship's passengers held round-trip tickets?
A.33 1/3%
B.40%
C.50%
D.62.5%
Answer: D.62.5%
Explanation: On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?
Solution: Let total number of passengers be 100
According to Q stem 40% of passengers who had round-trip tics have taken cars - let number of passengers with round trip be X then
40% of X = 25 => X= 62.5.
Answer D
Question: The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?
A.3:4
B.2:3
C.1:3
D.2:1
Answer: D.2:1
Explanation: Solution: Let,
B1 : B2 : B3 = 3x : 4x : 5x
Again,
B1 : B2 : B3 = 5y : 4y : 3y
Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets.
Hence, 5x = 3y
and,
3x : 4x : 5x
→ 9y /5 : 12y /5 : 15y /5 = 9y : 12y : 15y
And,
5y : 4y : 3y → 25y : 20y : 15y
Therefore, Increment in first basket = 16.
Increment in second basket = 8.
Thus, Required ratio = 16 /8 = 2 : 1
Answer: Option D
Question: 225 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
A.10
B.13
C.15
D.16
Answer: A.10
Explanation: 26 trees have 25 gaps between them,
Required distance (225/25) = 10
A
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is:
A.35.55 km/hr
B.36 km/hr
C.71.11 km/hr
D.71 km/hr
Answer: C.71.11 km/hr
Explanation: Total time taken = 160/64 + 160/80 = 9/2 hours
--> Average speed = 320 x 2/9 = 71.11 km/hr.
Answer : C.
Question: What will be 70 percent of a number whose 200 percent is 90 ?
A.144
B.72
C.31.5
D.None of these
Answer: C.31.5
Explanation: Answer
∵ 200% of N = 90
⇒ N = (90 x 100) / 200 = 45
∴ 70% of N = (70 x 45) / 100 = 31.5
Correct Option: C
Question: If the selling price of 50 articles is equal to the cost price of 20 articles, then the loss or gain percent is:
A.45%
B.23%
C.20%
D.60%
Answer: D.60%
Explanation: C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 20.
Loss % = 30/50 * 100 = 60%
ANSWER D
Question: The average of 10 numbers is 20 and the average of 10 other numbers is 25. What is the average of all 20 numbers?
A.22.5
B.21.1
C.2.6
D.7.5
Answer: A.22.5
Explanation: The average of 10 numbers is 20....
The sum of those numbers is (10)(20) = 200.
The average of 10 other numbers is 25....
The sum of those numbers is (10)(25) = 250
The sum of ALL 20 numbers is 200+250 = 450. The average of those numbers is 450/20 = 22.5
Answer is A
Question: The mean of 50 observations was 36. It was found later that an observation 44 was wrongly taken as 23. The corrected new mean is
A.35.22
B.36.12
C.36.22
D.36.42
Answer: D.36.42
Explanation: Solution
Correct sum = (36x50+44-23)
= 1821.
âˆ´ Correct mean = 1821 / 50
= 36.42.
Answer D
Question: How many 4 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a vowel, and each letter can be used only once?
A.20
B.40
C.120
D.60
Answer: B.40
Explanation: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)
Fifth letter can be filled in 1 Ways ( As the question states that the last letter has to be a vowel)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and fourth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 1 ways = 40
Answer B
Question: Simplify: 81 X 81 + 68 X 68-2 x 81 X 68.
A.169
B.159
C.189
D.179
Answer: A.169
Explanation: = (81)^2 + (68)^2 – 2x 81 x 68 = a^2 + b^2 – 2ab,Where a =81,b=68
= (a-b)^2 = (81 –68)^2 = (13)^2 = 169.
Answer is A.
Question: If X,Y is 20%,30% smaller than Z then how much percentage is Y greater than X?
A.12 1/2 %
B.13%
C.13 1/2%
D.14%
Answer: A.12 1/2 %
Explanation: X = 80 %
Y = 70 %
Z = 100 %
X-Y/X × 100 = 10/80 × 100 = 12 1/2 % greater than X
A)
Question: A car covers 4 successive 3 km stretches at speed of 10 kmph, 20 kmph, 30 kmph & 60 kmph resp. Its average speed is
A.20 kmph
B.40 kmph
C.10 kmph
D.60 kmph
Answer: A.20 kmph
Explanation: A
20 kmph
Average speed = total distance / total time
total distance = 4 * 3 = 12 km
total time = 3/10 + 3/20 + 3/30 + 3/60
= 36/60 hr
speed =12/36 * 60 = 20 kmph
Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?
A.40
B.65
C.72
D.76
Answer: D.76
Explanation: Solution
Average after 11 innings = 36.
∴ Required number of runs	= (36x11)-(32x10)
= 396 - 320
= 76.
Answer D
Question: A box contains 4 blue marbles, 3 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are red or yellow?
A.4/35
B.6/35
C.7/35
D.8/35
Answer: C.7/35
Explanation: Given that there are 4 blue marbles, 4 red marbles, 6 green marbles and 2 yellow marbles. Probability that both marbles are red = 4Câ‚‚/Â¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 2/35
Probability that both are yellow = Â²Câ‚‚/Â¹âµCâ‚‚ = (2 * 1)/(15 * 14) = 1/105
Probability that one red and other is yellow = (4Câ‚ * Â²Câ‚)/Â¹âµCâ‚‚ = 8/105
Required probability = 2/35 + 1/105 + 8/105
= 7/35
Answer:C
Question: If n is an integer and 101n^2 is less than or equal to 6400, what is the greatest possible value of n?
A.7
B.8
C.9
D.10
Answer: A.7
Explanation: 101 * n^2 <=6400
n^2 <=6400/101 which will be less than 81 since 6400/100 = 64 which is the square of 9
Next closest value of n where n^2<=64 is 7
Ans A
Question: Sixty five percent of a number is 21 less than four fifth of that number. What is the number
A.140
B.165
C.150
D.142
Answer: A.140
Explanation: Let the number be x.
Then, 4*x/5 –(65% of x) = 21
4x/5 –65x/100 = 21
5 x = 2100
x = 140.
ANSWER A 140
Question: A man's speed with the current is 16km/hr and the speed of the current is 2km/hr. The man's speed against the current is:
A.8 km/hr
B.9 km/hr
C.12 km/hr
D.15 km/hr
Answer: C.12 km/hr
Explanation: Man's rate in still water = (16 - 2) km/hr = 14 km/hr.
Man's rate against the current = (14 - 2) km/hr = 12 km/hr
C
Question: How many bricks, each measuring 125 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
A.1280
B.2400
C.5500
D.7400
Answer: A.1280
Explanation: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (125 x 11.25 x 6) = 1280
ANSWER:A
Question: Of the 200 employees at company X, 50 are full-time, and 150 have worked at company X for at least a year. There are 10 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
A.20
B.30
C.10
D.80
Answer: C.10
Explanation: 200 employees
50 are full-time
150have worked at company X for at least a year
10 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
200-50=150 employees not full time
150-10= 140 employees not full time who worked over a year
150 employees have worked at company X for at least a year-140 employees not full time who worked over a year = 10 full-time employees of company X have worked at the company for at least a year
ans C
Question: A die is thrown twice and the sum of the numbers appearing is observed to be 6.
find the conditional probability that the number 4 has appeared at least once?
A.1/5
B.2/5
C.2/5
D.3/5
Answer: C.2/5
Explanation: Let E be the event that ‘number 4 appears at least once’ and F be
the event
that ‘the sum of the numbers appearing is 6’.
Then, E = {(4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (1,4), (2,4), (3,4),
(5,4), (6,4)}
and F = {(1,5), (2,4), (3,3), (4,2), (5,1)}
We have P(E) = 11/36
and P (F) = 5/36
Also EnF = {(2,4), (4,2)}
Therefore P(EnF) = 2/36
the required probability
P(E|F) = P(EnF)/P(F) = (2/36)/(5/36) = 2/5
C)
Question: A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability X that out of the two, one is white and one is blue?
A.15/56
B.41/56
C.13/28
D.15/28
Answer: D.15/28
Explanation: The required probability X= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8C6 = 15/28.
D is thus the correct answer.
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
A.123400 m
B.145500 m
C.153600 m
D.186400 m
Answer: C.153600 m
Explanation: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Question: In how many ways the letters of the word RAIMBON be arranged?
A.2467
B.2696
C.5040
D.5768
Answer: C.5040
Explanation: Total ways of arranging the letters = 7! = 5040 ways.
C)
Question: A house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $100,000 and $250,000, one of them is $300,000 house, two houses are between $500,000 and 750,000, what is the range of his revenue?
A.800
B.850
C.875
D.880
Answer: C.875
Explanation: (1) 2(100)+300+2(500) = 1500
1500*0.95=1425 (Revenue considering the minimum values with the discount)
(2) 2(250)+300+2(750) = 2300 (Revenue considering the maximum values without the discount)
So, the the revenue range could be = 2300 - 1425 = 875
C
Question: There is 2/5 chance it will rain today.
There is a probability of 1/2 I will find the love of my life today.
What is the probability that it won't rain and that I will find the love of my life today?
A.2/5
B.3/5
C.3/10
D.1/5
Answer: C.3/10
Explanation: the probability that it won't rain today is 3/5.
therefore the probability that it won't rain and that I will find the love of my life today is 3/5*1/2 = 3/10
Answer:C
Question: The price of a T.V. set worth Rs. 60000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
A.22678
B.59000
C.26788
D.19000
Answer: B.59000
Explanation: Money paid in cash = Rs. 1000
Balance payment = (60000 - 1000) = Rs. 59000
Answer: B
Question: The average age of a couple was 24 years. After their 1st and 2nd children (twins) were born, the average age of the family became 13.5 years. The average age of the family just after 3rd child was born was 13.2 years. The average age of the family after 4th child was born was 16 years. The current average age of the family is 19 years. What is the current age of the twin children?
A.14 years
B.15 years
C.11 years
D.12 years
Answer: D.12 years
Explanation: DETAILED SOLUTION
Sum of the ages of the couple = 24 * 2 = 48
After the 1st and 2nd children, sum = 13.5 * 4 = 54
Difference in sum = 54 – 48 = 6 years
Or after 6/ 2 = 3 years, the twin were born to the couple (Ages of children at the time of birth is 0)
After 3rd child, sum = 13.2 * 5 = 66 yrs
Difference = 66 – 54 = 12
Or after 12/4 = 3 yrs, 3rd child was born (Couple + 2 children were already present. So 4)
After 4th child, sum = 16 * 6 = 96 yrs
Difference = 96 – 66 = 30
Or after 30/5 = 6 yrs, 4th child was born
Current sum = 19 * 6 = 114 yrs
Difference 114 – 96 = 18 yrs
Or after 18/6 = 3 yrs
The gap between the children are as follows: 3 yrs, 6 yrs and 3 yrs
Age of eldest ones = 3 + 6 + 3 = 12
Correct Answer: D
Question: A rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14cm. how many times can it go round a cylinder having radius 20 cm?
A.49 rounds
B.42 rounds
C.54 rounds
D.52 rounds
Answer: A.49 rounds
Explanation: Explanation:
Let the required number of rounds be x
More radius, less rounds (Indirect proportion)
Hence we can write as
(radius) 14 : 20 :: x : 70
⇒14×70=20x
⇒14×7=2x
⇒x=7×7=49
Answer: Option A
Question: Two persons starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 8.5km apart, if they walk in the same direction?
A.17 hrs
B.22 hrs
C.25 hrs
D.12 hrs
Answer: A.17 hrs
Explanation: The relative speed of the boys = 5.5kmph – 5kmph
= 0.5 kmph
Distance between them is 8.5 km
Time= 8.5km / 0.5 kmph = 17 hrs
Answer : A
Question: In a deck of cards there are 52 cards numbered from 1 to 13. There are 8 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?
A.1/4.
B.4/17.
C.5/29.
D.5/16.
Answer: D.5/16.
Explanation: 8+12 tens/52+12 total cards=20/64=5/16
D