RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A train 540 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
A.41 sec
B.42 sec
C.43 sec
D.48 sec
Answer: D.48 sec
Explanation: D
48 sec
D = 540 + 180 = 720
S = 54 * 5/18 = 15 mps
T = 720/15 = 48 sec
Question: If the average (arithmetic mean) of a list of numbers is 12 and the standard deviation of that list of numbers is 1.3, then which of the following numbers is more than two standard deviations from the mean?
I. 14.3
II. 12.3
III. 9.2
A.I only
B.I and II only
C.II only
D.III only
Answer: D.III only
Explanation: Mean = 12
SD = 1.3
2 SD above mean = 12+2*1.3 = 14.6
2 SD below mean = 12-2*1.3 = 9.4
12.3 and 14.3 lies in the range of 2SD from mean
Answer: Option D
Question: What is the ratio R of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
A.1/4
B.3/8
C.1/2
D.3/5
Answer: D.3/5
Explanation: Let X be the side of the cube. Therefore X^2*6= surface area.
the rectangle is the same other than length is 2X. The width and height are the same as the cube. 2*W*H+2*W*L+2*H*L= 2X^2+4X^2+4X^2= 10X^2.
6X^2/10X^2 = 3/5= R.
Answer = D
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
A.22
B.32
C.44
D.66
Answer: B.32
Explanation: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32 .Answer: B
Question: Plane leaves from Chelsea every 30 minutes from West Ham airport. Air hostess told Frank Lampard that the plane had left 25 minutes ago and the next plane for Chelsea will leave at 7:00 p.m.
At what time air hostess convey this information to Frank Lampard?
A.5:35 p.m
B.6:55 p.m
C.7:35 p.m
D.8:55 p.m
Answer: B.6:55 p.m
Explanation: Explanation:
Time of Frank Lampard last missed plane = 7:00 p.m - 30 min = 6:30 p.m
As this information has been given to Frank Lampard 25 minutes after the plane has already left, the air hostess gave the information at 6:30 p.m + 25 min = 6:55 p.m
Answer B
Question: The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the numbers is 77,find the other.
A.99
B.88
C.77
D.66
Answer: A.99
Explanation: Other number = 11 X 693/77 = 99
Answer is A.
Question: Three models (F, G, and H) of cars are distributed among three showrooms. The number of cars in each showrooms must be equal and each model must be represented by at least one car in every showroom. There are 19 cars of Model F, 17 cars of Model G, and 15 cars of Model H. What is the maximum number of cars of model F in any showroom ?
A.17
B.16
C.15
D.14
Answer: C.15
Explanation: The total number of cars is 51. So each showroom has 17 cars(since the number of cars in each showrooms should be equal 51/3=17).
Moreover that the number of model F is maximum means that the numbers of model G and H should be minimum. Since each model must be represented by at least one car in every showroom that minimum number should be 1.
So Maximum number of model F is 17-2= 15.
The answer is (C)
Question: In a question on division with zero remainder, a candidate took 20 as divisor instead of 10. The quotient obtained by him was 35. The correct quotient is?
A.A)70
B.B)24
C.C)28
D.D)29
Answer: A.A)70
Explanation: Number = (35 * 20) = 700
Correct quotient = 700/10 = 70
A)
Question: The 46th digit after the decimal in the decimal expansion of 11996 is
A.0
B.1
C.4
D.6
Answer: C.4
Explanation: Let dj denote the jth digit of 1/1996 after the decimal. In other words, we write
1/1996=0.d1d2d3....The problem is to determine d46. Observe that
(*)
10in45*1/1996=d1d2d3...d45d46d47...
We compute 1045 modulo 1996. Since 1996 5 = (2000 - 4) 5 = 104 -20, we get
that 104* 20 (mod 1996). Since 1996 4 = (2000- 4) 4 = 8000 - 16, we obtain
1012*(104)3 *203 * 8000*6 (mod 1996). Continuing in this manner, we get 1036 *
(1012)3* 16*212 * 4096 * 104 (mod 1996), 1044* 1036 104 104 *104 20 20 *
2080 20*84 20 * 1680 (mod 1996), and 1045 * 1044 10* 16800* 8 (1996 +
4) + 800 * 832 (mod 1996). This means that the remainder when we divide 1045 by 1996
is 832. If q denotes the quotient, we deduce that
1045/1996= q +832/1996= q.4168...
where the digits after the decimal are computed by long division. We are only interested
in the first of these, the digit 4 since it follows from () that this digit must be d46.
correct answer C
Question: A type W machine can complete a job in 5 hours and a type B machine can complete the job in 7 hours. How many hours will it take 2 type W machines and 3 type B machines working together and independently to complete the job?
A.1/5
B.29/35
C.5/6
D.35/29
Answer: D.35/29
Explanation: now D should be the answer.
W need 5 hours to complete
and B needs 7 hours to compete
so 2W + 3B will complete 2/5 + 3/7 or 29/35 portion of the job in 1 hour
so the whole job will take 35/29 hours....=D
Question: A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?
A.12 days
B.9 days
C.6 days
D.5 days
Answer: C.6 days
Explanation: Sol. (A + B)'s 1 day's work = (1/4). A's 1 day's work = (1/12)
B's 1 day's work =((1/4)-(1/12))=(1/6)
Hence, B alone can complete the work in 6 days.
Ans: C
Question: One year ago, the ratio of Gaurav' and Sachin's age was 6 : 7 respectively Four years hence , this raio would become 7 : 8. How old is Sachin ?
A.34 years
B.36 years
C.37 years
D.38 years
Answer: B.36 years
Explanation: Explanation :
Sol Let Gaurav's and Sachins ages one year ago be 6xand7x6xand7x 7ears respectively . Then
Gaurav's age 4 years hence = (6x+1) +4=(6x+5)(6x+1) +4=(6x+5) years
Sachin's age 4 years hence = (7x+1)+4=(7x+5)(7x+1)+4=(7x+5) years.
6X+5 / 7X+5 =7/8
â‡” 8(6x+5)= 7(7x+5)
â‡” 48x+40=49x+35
â‡” x=5
Hence , Schin's present age = (7x+1)(7x+1) = 36 years.
ANSWER IS B
Question: Marge has E candies, where E is an integer such that 20 <E< 50. If Marge divides the candies equally among 5 children, she will have 2 candies remaining. If she divides the candies among 6 children, she will have 1 candy remaining. How many candies will remain if she divides the candies among 7 children?
A. 0
B. 1
C. 2
D. 3
Answer: C. 2
Explanation: If Marge divides the candies equally among 5 children, she will have 2 candies remaining.
This tells us that the candies are of 5x + 2 type and so 22, 27, 32, 37, 42, or 47
If she divides the candies among 6 children, she will have 1 candy remaining.
this tells us it is if 6x+1 type and so 25, 31, 37, 43, or 49
ONLY 37 is common, so candies are 37 in number..
if 37 is divided in 7 kids, remainder E= 2
C
Question: Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5seconds after he sees it strike the tree. How far is the man from the wood chopper?
A.2420 ft
B.2810 ft
C.1800 ft
D.1820 ft
Answer: A.2420 ft
Explanation: Explanation:
Speed of the sound = 1100 ft/s
Time = 11/5 second
Distance = Speed × Time = 1100 ×11/5 = 220 × 11= 2420 ft
Answer: Option A
Question: Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is
A.1/7
B.1/9
C.1/6
D.1/4
Answer: B.1/9
Explanation: Explanation:
One person can select one house out of 3= \inline {\color{Black}3C_{1}} ways =3.
Hence, three persons can select one house out of 3 in 3 x 3 x 3 =9.
Therefore, probability that all thre apply for the same house is 1/9
Answer: B) 1/9
Question: A dog breeder currently has 9 breeding dogs. 6 of the dogs have exactly 1 littermate, and 3 of the dogs have exactly 2 littermates. If 2 dogs are selected at random, what is the probability E that both selected dogs are NOT littermates?
A.1/6
B.2/9
C.5/6
D.7/9
Answer: C.5/6
Explanation: We have three pairs of dogs for the 6 with exactly one littermate, and one triplet, with each having exactly two littermates.
So, in fact there are two types of dogs: those with one littermate - say A, and the others with two littermates - B.
Work with probabilities:
Choosing two dogs, we can have either one dog of type B or none (we cannot have two dogs both of type B).
The probability of choosing one dog of type B and one of type A is 3/9 * 6/8 * 2 = 1/2 (the factor of 2 for the two possibilities BA and AB).
The probability E of choosing two dogs of type A which are not littermates is 6/9 * 4/8 = 1/3 (choose one A, then another A which isn't the previous one's littermate).
The required probability is 1/2 + 1/3 = 5/6.
Find the probability for the complementary event: choose AA or BB.
Probability of choosing two dogs of type A who are littermates is 6/9 * 1/8 = 1/12.
Probability of choosing two dogs of type B (who necessarily are littermates) is 3/9 * 2/8 = 1/12.
Again, we obtain 1 - (1/12 + 1/12) = 5/6.
Answer: C
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 6 minutes the first is turned off. How many more minutes will it take for the cistern to fill after the first pipe is turned off?
A.1
B.1.5
C.2
D.2.5
Answer: B.1.5
Explanation: Let x be the total time it takes for the cistern to fill.
6/12 + x/15 = 1
x/15 = 1/2
x = 7.5
After the first pipe is turned off, it takes 1.5 more minutes to fill the cistern.
The answer is B.
Question: Two friends C and D leave point C and point D simultaneously and travel towards Point D and Point C on the same route at their respective constant speeds. They meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively. How long will D take to cover the entire journey between Point D and point C?
A.90
B.80
C.75
D.60
Answer: A.90
Explanation: Let x per minute be the speed of C and y per minute be the speed of D.
After meeting at a point, C travels for 32 mins and D travels for 50 mins. So distance covered by each of them post point of crossing
C= 32x and D=50y
The distance covered by C and D before they cross each would be distance covered by D and C post crossing respectively.
Therefore distance covered by D before he meets C= 32x
Time taken by D cover 32x distance= 32x/y mins
Therefore total time taken by D= 32x/y + 50 mins ................. I
We need to find value of x in terms of y to arrive at final answer.
Total distance= 32x+50y
Combined speed of C and D= x+y
Therefore time taken before C and D meet en-route= (32x+50y)/(x+y)
Time taken by D reach destination after meeting C= 50 mins
Total travel time for D= [(32x+50y)/(x+y)]+50 mins ...................II
Equate I and II
32x/y+50= [(32x+50y)/(x+y)]+50
(32x+50y)/y=(82x+100y)/(x+y)
32x^2+50xy+32xy+50y^2=82xy+100y^2
32x^2+82xy-82xy+50y^2-100y^2=0
32x^2-50y^2=0
32x^2=50y^2
16x^2=25y^2
Taking square root.. (since x and y denote speed, square root can't be negative)
4x=5y
y=4x/5 ............ III
substitute in I
=32x/(4x/5) + 50
=32x*5/4x + 50
=40+50
=90 mins
A
Question: 1/2+[(2/3*3/8)+4]-8/16=
A.29/16
B.19/16
C.15/16
D.17/4
Answer: D.17/4
Explanation: 1/2+[(2/3*3/8)+4]-8/16=
1/2+[(1/4)+4]-8/16=
1/2+[17/4]-9/16=
8/16 + 68/16 - 8/16 = 68/16=17/4
D
Question: if there is one larger cube with volume 1000 and no. of smaller cubes with volume 8.then how many small cubes are required to make a larger cube with volume of 600?
A.5
B.10
C.125
D.100
Answer: C.125
Explanation: the ratio between larger and smaller is
a13:a23=1000:8
a1:a2=10:2
then length of cube is 10 and 2
so make a cube with length 10, we have to 5 small cubes each in length, breadth and height. so total 125 cubes are required.
then the answer is C
Question: Anil purchased 30 kg of wheat at the rate of Rs. 22 per kg and 20 kg of wheat at the rate of Rs. 24 per kg. He mixed the two. Approximately at what rate per kg should he sell the mixture to make 25% profit?
A.Rs. 28
B.Rs. 29
C.Rs. 26
D.Rs. 282
Answer: A.Rs. 28
Explanation: Explanation:
Total quantity of mixture = 30 + 20 = 50 kg.
By earning a profit of 25% on the total cost, the selling price of the mixture is
125/100 * (660 + 480 = 1140) = Rs. 1425
Selling price per kg = Total selling price / Total of mixture
= 1425 / 50
= Rs. 28.5
ANSWER: A
Question: A football player scores 2 goals in his fifth match thus increasing his average goals score by 0.1. The total number of goals in his 5 matches would be
A.4
B.6
C.8
D.10
Answer: C.8
Explanation: While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...
From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.
Here, I'll start with Answer C = 8 goals
If....
Total goals = 8 goals
5th game = 2 goals
1st 4 games = 6 goals
Avg. for 1st 4 games = 6/4 = 1.5 goal/game
Avg. for all 5 games = 8/5 = 1.6 goals/game
This is an EXACT MATCH for what we're told in the prompt, so Answer C MUST be the answer.
Question: Raju is 10 years elder to Sita. 10 years from now Raju would be twice as old as sita was before 10 years. How old would be Sita after 12 years.
A.42 years
B.46 years
C.50 years
D.52 years
Answer: D.52 years
Explanation: If R and S are their present ages, then
R=S+10
and
R+10= 2*(S-10)
solving these eqns, we get
R=50 and S=40
At present, Sita is 40 years old.
After 12 years, Sita will be 52 years old.
ANSWER:D
Question: A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is?
A.4:6
B.4:9
C.4:3
D.4:1
Answer: C.4:3
Explanation: 12:9
= 4:3
Answer: C
Question: (1/31)+(1/32)+……+(1/61)+(1/62) is including in which of the following ranges?
A.2
B.1/2~ 1
C.1
D.1~2
Answer: B.1/2~ 1
Explanation: Number of terms in the given series = 32.
The lowest term is 1/62 , the largest being 1/31.
Thus, the sum of the given series will be more than
1/62 + 1/62.....1/64 (32 times)
---> 32*(1/62) = 32/62
less than 1/31 + 1/32...... 1/31 (32 times)
---> 32*(1/3) = 32/31 = 1 (approx)
B
Question: Two goods trains each 625 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
A.22 sec
B.88 sec
C.60 sec
D.18 sec
Answer: C.60 sec
Explanation: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 625 + 625 = 1250 m.
Required time = 1250 * 6/125 = 60 sec.
Answer:C
Question: n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
A.3
B.2
C.1
D.0
Answer: B.2
Explanation: Explanation:
Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
Answer: B
Question: A and B together can do a piece of work in 6 days and A alone can do it in 11 days. In how many days can B alone can do it?
A.12 days
B.15 days
C.66/5 days
D.21 days
Answer: C.66/5 days
Explanation: Explanation:
A and B can do work 1/6 in 1 day
A alone can do 1/11 work in 1 day
B alone can do (1/6 -1/11) =5/66 work in 1 day
=> complete work can be done in 66/5 days by B
Answer: Option C
Question: A vendor bought bananas at 6 for a rupee. How many for a rupee must he sell to gain 20%?
A.2
B.4
C.7
D.5
Answer: D.5
Explanation: CP of 6 bananas = 1
Gain = 20%
SP of 6 bananas=1×120/100=12/10
⇒The number of bananas he should sell for Rs.1 for a gain of 20%=10/12∗6=10/2=5
ANSWER:D
Question: How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits H equal to 28?
A.14
B.24
C.28
D.48
Answer: D.48
Explanation: First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.
So you have two solutions. Each can be rearranged in 4!=24 ways. So H=24+24=48.D
Question: If a 10% deposit amounting to $110 has been paid toward buying a brand new TV, how much remains to be paid?
A.$880
B.$990
C.$1000
D.$1100
Answer: B.$990
Explanation: Explanation:
Let's start with what the total price of the TV would be. If 10% is equal to $110 then 100% equals $x. We just have to multiply $110 by 10 to get total amount=$1100. Out of this amount we then need to deduct the amount already paid which was $110 so we have $1100-$110=$990
Answer: Option B
Question: In a class of 52 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?
A.30
B.10
C.18
D.28
Answer: A.30
Explanation: Total=English+German-Both+Neither --> 52=English+22-12+0 --> English=42 --> Only English=English-Both=42-12=30
Answer: A.
Question: How much is 80% of 40 is greater than 4/5 of 25?
A.229
B.87
C.26
D.12
Answer: D.12
Explanation: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D
Question: A man whose bowling average is 12.4, takes 4 wickets for 26 runs and there by decreases his average by 0.4. the number of wickets taken by him before his last match is?
A.53
B.54
C.55
D.56
Answer: C.55
Explanation: 12.4*x+26=(4+x)12
solve equation x=55
ANSWER:C
Question: There are 408 boys and 240 girls in a school which are to be divided into equal sections of either boys or girls alone. Find the total number of sections thus formed.
A.27
B.32
C.35
D.30
Answer: A.27
Explanation: Explanation:
HCF (408, 240) = 24
The number of boys or girls that can be placed in a section = 24.
Thus the total number of sections is given by
408/24+240/24 =17+10 = 27
Answer: A
Question: If a man buys 10 lollipops for $90 and sold them for $6 dollars determine his loss.
A.50
B.60
C.70
D.20
Answer: D.20
Explanation: Cost of 10 lollipops = $80
Sold each lollipop for $6
So he sold 10 lollipops for $(10 × 6) = $60
Loss = $(80 – 60) = $20
answer :D
Therefore, loss = $ 20.
Question: The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is :
A.6000
B.7000
C.8888
D.9000
Answer: D.9000
Explanation: Explanation:
Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.
Cost of cheapest item = 3x = Rs. 9000. Answer: D
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
A.1.99 km
B.2.88 km
C.4.49 km
D.2.99 km
Answer: B.2.88 km
Explanation: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer: B
Question: A runs times as fast as B. If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it at the same time?
A.200
B.378
C.277
D.298
Answer: A.200
Explanation: Explanation:
Ratio of the speeds of A and B =5 : 1 = 5 :3
Thus, in race of 5 m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
80 m will be gained by A in race of \inline \fn_jvn {\color{Black} \left ( \frac{5}{2}\times 80 \right )} m =200m
\inline \fn_jvn {\color{Black} \therefore }Winning post is 200 m away from the starting point.
Answer: A) 200 m
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
A.20
B.21
C.22
D.23
Answer: B.21
Explanation: Explanation:
WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer: B
Question: What is the value of 10^8- 6^4?
A.9,99,98,623
B.9,99,98,704
C.9,99,98,800
D.9,99,99,521
Answer: B.9,99,98,704
Explanation: As 10^n will always have last digit as 0 AND 6^n will always as last digit 6.. hence difference of such sum should always be ending with 4 and there is only on option ..
Answer B
Question: Which of the following is a parallelogram?
A.130,50,130,50(angle in deg)
B.120,30,130,20(angle in deg)
C.95,95,95,95(angle in deg)
D.a & c
Answer: A.130,50,130,50(angle in deg)
Explanation: sum of adjacent angles is 180 degrees.
ANSWER:A
Question: Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H
A.153
B.150
C.137
D.132
Answer: D.132
Explanation: let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
D satisfies
3x/ 2 = 132
=> x = 88
Verify. 88 + 44 = 132
Answer is D
Question: What is the next term in the below series.
1/5 , 1/2 , 1/3 , 2/5 ,1, 2/3, 3/5, 1 1/2 ,1, 4/5,?
A.1/5
B.0
C.2
D.2/5
Answer: C.2
Explanation: 1/5 2/5 3/5 4/5
1/2 1 1 1/2 ?
1/3 2/3 1 4/3
ans :2
ANSWER:C
Question: The price of an item changed from $120 to $100. Then later the price decreased again from $100 to $80. Which of the two decreases was larger in percentage term?
A.10%
B.20%
C.30%
D.40%
Answer: B.20%
Explanation: First decrease in percent
part / whole = (120 - 100) / 120 = 0.17 = 17%
Second decrease in percent
part / whole = (100 - 80) / 100 = 0.20 = 20%
The second decrease was larger in percent term. The part were the same in both cases but the whole was smaller in the second decrease.
Answer B
Question: The distance traveled by eagle in one year approximately 150,000,000 miles.The distance traveled by eagle in 50 years?
A.10<8>
B.10<16>
C.10<4>
D.10<12>
Answer: A.10<8>
Explanation: The distance traveled by eagle in one year = 150,000,000 miles.
The distance traveled by eagle in 50 years = 150,000,000 miles * 50 years = 7,500,000,000 miles
(ie) 75*10<8> exponent Answer : A
Question: A committee of 5 people is to be selected from 8 people. How many different committees are possible?
A.28
B.40
C.56
D.168
Answer: C.56
Explanation: Because the order does not matter in selecting 5 people for the committee, this is a combination question.
The number of ways to select 5 people from 8 = 8C5 = 8!/5!*3! = 56. Hence C.
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5
B.3
C.4
D.5
Answer: A.2.5
Explanation: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
Answer: Option A
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
A.3m
B.5m
C.8m
D.2m
Answer: D.2m
Explanation: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:D
Question: A water tank is three-fifths full. Pipe A can fill a tank in 15 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: The combined rate of filling/emptying the tank = 1/15 - 1/6 = -1/10
Since the rate is negative, the tank will be emptied.
A full tank would take 10 minutes to empty.
Since the tank is only three-fifths full, the time is (3/5) * 10 = 6 minutes
The answer is C.
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 30 kms. what was the total distance traveled in 12 hours?
A.252 kms
B.152 kms
C.492 kms
D.752 kms
Answer: C.492 kms
Explanation: Explanation:
Total distance travelled in 12 hours =(30+32+34+.....upto 12 terms)
This is an A.P with first term, a=30, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 30+{12-1) x 2]
= 6(82)
= 492 kms.
Answer: C