RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Alcohol cost 3.50 per litre and kerosene oil cost 2.50 per litre. In what proportion these should be mixed so that the resulting mixture may be 2.75 per litre?
A.2 : 5
B.1 : 3
C.4 : 7
D.2 : 3
Answer: B.1 : 3
Explanation: ∴ Required ratio = 0.25⁄0.75 = 1⁄3 i.e, 1 : 3
Answer B
Question: A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?
A.34
B.36
C.32
D.30
Answer: B.36
Explanation: Distance to be covered = 240+ 120 = 360 m
Relative speed = 36 km/hr = 36×10/36 = 10 m/s
Time = distance/speed = 360/10 = 36 seconds
Answer is B.
Question: A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
A.200
B.250
C.400
D.500
Answer: C.400
Explanation: C's 1 day's work =	1	- 1	+	1 =	1	-	7	=	1	.
3	6	8	3	24	24
A's wages : B's wages : C's wages =	1	:	1	:	1	= 4 : 3 : 1.
6	8	24
C's share (for 3 days) = Rs. 3 x	1	x 3200 = Rs. 400.
24
Answer is C
Question: A car covers a distance of 930 km in 6 hours. Find its speed?
A.104 kmph
B.289 kmph
C.288 kmph
D.155 kmph
Answer: D.155 kmph
Explanation: 930/6
= 155 kmph
Answer: D
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
A.22
B.89
C.77
D.66
Answer: B.89
Explanation: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec.
Answer:B
Question: A man sells an article at 7% loss. Had he sold it for Rs. 105/- more he could have gained 8%. what is the cost price of the article
A.Rs. 522/-
B.Rs. 622/-
C.Rs. 700/-
D.Rs. 600/-
Answer: C.Rs. 700/-
Explanation: Explanation:
Short cut method:
Loss =====> 7 %
Profit ====> 8 %
~
----------------
15 % ---------> 105
100 % --------> Rs.700/-
Answer: Option C
Question: If each edge of cube increased by 10%, the percentage increase in surface area is:
A.33.1
B.33.5
C.33.7
D.33.2
Answer: A.33.1
Explanation: 100 × (110)/100 × (110)/100 × (110)/100 => 1331/100 = 33.1%
Answer is A.
Question: The arithmetic mean of set A is zero. If B = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of A consisting of all those elements in A which are more than two but less than three standard deviations away from the arithmetic mean of A, what could be equal to the standard deviation of A?
A.0.54
B.0.77
C.0.82
D.0.97
Answer: B.0.77
Explanation: This is a fairly straightforward question that can be solved quickly by just applying the options
We are provided with Mean, m= 0
and B = {-2.22; -1.96; -1.68; 1.62; 1.94; 2.16} is the subset of A
B consists of all those elements in A that are more than 2 but less than 3 ADs away from the arithmetic mean of A
If an element is 1 AD away from the mean, we can write it as either m + AD or m - AD
Similarly, if an element is 2 ADs away from the mean, we can write it as either m + 2*AD or m - 2*AD
So, if these elements lie within 2 and 3 ADs of mean, m=0
we can find which one of these values of AD satisfies each value within B
Only AD = 0.77 does
Answer : B
Question: A horse chases a pony 3 hours after the pony runs. Horse takes 4 hours to reach the pony. If the average speed of the horse is 35 kmph, what s the average speed of the pony?
A.20kmph
B.22kmph
C.24kmph
D.26kmph
Answer: A.20kmph
Explanation: pony take 7 hours and horse take 4 hours...then Distance chased by them is 35*4.so speed of pony is (35*4)/7=20kmph.
ANSWER:A
Question: A and B go around a circular track of length 300 m on a cycle at speeds of 34 kmph and 50 kmph. After how much time will they meet for the first time at the starting point?
A.120 sec
B.60 sec
C.186 sec
D.167 sec
Answer: B.60 sec
Explanation: Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 300/ (36 * 5/18) , 300/ (54 * 5 /18) }
= LCM (30, 20)
=60 sec.
Answer:B
Question: If n is a natural numbe, then(n3 - n)is always divisible by
A.8
B.6
C.12
D.9
Answer: B.6
Explanation: Explanation:
Clearly, 223 is a prime number.
441 is divisible by 9.
357 is divisible by 3.
153 is divisible by 17.
Answer: Option B
Question: Hardy and Robert start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lanes at uniform speeds, but Hardy is faster than Robert. They 1st pass at a point 18.5m from the deep end and having completed one length each 1 is allowed to rest on the edge for exactly 45 sec. After setting off on the return length, the swimmers pass for the 2nd time just 10.5m from the shallow end. How long is the pool?
A.50
B.45
C.35
D.30
Answer: B.45
Explanation: let x=length of pool
at first meeting, combined distance=x
at second meeting, combined distance=3x
if andy swims 18.5 m of x, then he will swim 3*18.5=55.5 m of 3x
andy's total distance to second meeting=x+10.5 m
x+10.5=55.5 m
x=45 m
B
Question: Donald Trump took a flight in his private jet from New York City to Los Angeles for an election rally and returned back to New York City an hour later with the same weather conditions. If the 2700 mile flight to Los Angeles took 6 hours and the flight back to New York City took 5 hrs, what was the speed of the wind in mph?
A.30 mph
B.35 mph
C.40 mph
D.45 mph
Answer: D.45 mph
Explanation: Explanation:
Change the times into minutes first.
Speed from NYC to Los Angeles: (2700/360) X 60 = 450 mph
Speed from Los Angeles to NYC: (2700/300) X 60 = 540 mph
Wind speed: 1/2 (540 - 450) = 90/2 = 45 mph
Answer: Option D
Question: In a division, a student took 72 as divisor instead of 36. his answer was 24 . The correct answer is-
A.42
B.32
C.48
D.28
Answer: C.48
Explanation: X/72 = 24.
X = 24 *72.
So correct answer would be,
(24 *72) /36 = 48.
ANSWER : C
Question: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity Q of the pool?
A.9000 cubic meters
B.10500 cubic meters
C.11750 cubic meters
D.12000 cubic meters
Answer: D.12000 cubic meters
Explanation: D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
Question: If the length of a rectangle is halved and its breadth is tripled, what is the percentage change in its area?
A.30
B.40
C.50
D.60
Answer: C.50
Explanation: Length is halved.
i.e., length is decreased by 50%
Breadth is tripled
i.e., breadth is increased by 200%
Formula for Change in area is:
=(-x+y-xy/100)%
=(−50+200−50×200/100)%=50%
i.e., area is increased by 50%
Answer is C.
Question: If x is the smallest positive integer such that 4,536 multiplied by x is the square of an integer, then x must be
A.12
B.21
C.16
D.17
Answer: B.21
Explanation: 4536= 6*6*3*3*7*3, so we need one 7 and one 3 to make it a square of a number. so 7*3= 21
Ans: B
Question: An article was sold after a discount of 20% and there was a gain of 20%. If the profit made on it was Rs. 6 less than the discount offered on it, find its selling price?
A.72
B.62
C.26
D.20
Answer: A.72
Explanation: Let CP = Rs. 100x
SP = Rs. 120x
MP = 120x/80 * 100 = Rs. 150x
D = Rs. 150x - Rs. 120x = Rs. 30x
D - P = 30x - 20x = Rs. 6, 10x = Rs. 6
120x = 120/10 * 6 = Rs. 72
Answer:A
Question: The G.C.D. of 1.08, 0.33 and 0.9 is:
A.0.03
B.0.9
C.0.18
D.0.108
Answer: A.0.03
Explanation: EXPLANATION
Given numbers are 1.08, 0.33 and 0.90. H.C.F. of 108, 33 and 90 is 3,
H.C.F. of given numbers = 0.03.
Answer A
Question: In city A, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. There is a park that runs from 5th Ave to 7th Ave and from 3rd Rd to 5th Rd, as pictured. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 8th Ave in the shortest possible time without walking through the park, how many different routes could he take?
Is there any formula to find out directly??
A.6
B.66
C.72
D.126
Answer: B.66
Explanation: Center of the park is much important in this problem.
To pass through the park one must have to pass through this point and further to destination.
Ans = Total possible paths to destination(TPPD) - paths passing through the park (PPTP)
All possible paths covering min distance are permutation of pattern RRRRRUUUU R-> One step right / U-> One step up
Thus
TPPD = 9!/(5!x4!) = 126 (direct formula of permutation applied)
I have calculated PPTD in two steps first find all paths from origin to center of park:
1. Possible moves RRRUU total permutations 5!/(3!x2!) = 10
2. From park center to destination, in moves RRUU, total permutations as 4!/(2!x2!)=6.
Thus PPTD= 10 X 6 = 60
Ans = 126 -60 = 66
ANSWER:B
Question: The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%?
A.25% loss
B.16 2/8% loss
C.16 3/3% loss
D.36 2/3% loss
Answer: A.25% loss
Explanation: 15 CP = 20 SP
20 --- 5 CP loss
100 --- ? => 25% loss
Answer:A
Question: 32.42 + 508.622 + 32.32 = ?
A.573.362
B.522.243
C.572.233
D.622.443
Answer: A.573.362
Explanation: Explanation :
32.42 + 508.622 + 32.32 = 573.362. Answer : Option A
Question: If 360 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is :
A.50
B.60
C.40
D.18
Answer: B.60
Explanation: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24
:. The smallest part = (360 *4/24) = 60
ANSWER:B
Question: Last Sunday a certain store sold copies of Newspaper A for $1.00 each and copies of Newspaper B for $1.25 each, and the store sold no other newspapers that day. If r percent of the store's revenues from newspapers sales was from Newspaper A and if k percent of the newspapers that the store sold were copies of Newspaper A, which of the following expresses r in terms of k?
A.100p / (125 - p)
B.150p / (250 - p)
C.300p / (375 - p)
D.400k / (500 - k)
Answer: D.400k / (500 - k)
Explanation: I have just started with qunats section .. I solved this by making two equations and got the answer ... However it was long way of doing it ...
I got the answer as : 100k /(125 - .25 k)...
Multiply this equation by 4 and you get D as the answer ,...
Question: What will come in place of (a) in the following expression?
a - 796.21 + 498.05 = 215.50 – 400.01
A.88.65
B.313.65
C.300.12
D.313.56
Answer: B.313.65
Explanation: Explanation:
a - 796.21 + 498.05 = 215.50 - 400.01
a = 313.65
ANSWER: B
Question: A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 30min will be.
A.80 km/h
B.55 km/h
C.40 km/h
D.70 km/h
Answer: A.80 km/h
Explanation: Time=50/60 hr=5/6hr
Speed=48mph
distance=S*T=48*5/6=40km
time=30/60hr=1/2hr
New speed = 40* 2/1 kmph= 80kmph
Answer : A
Question: A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part folded along one set of sides and the same is 38 cm when folded along the other set of sides. What is the area of the paper ?
A.140 cm
B.240 cm2
C.560 cm2
D.None of these
Answer: A.140 cm
Explanation: Solution
When folded along breadth, we have : 2(l/2 +b) = 34 or l + 2b = 34
When folded along length, we have : 2(l/2 +b) = 38 or 2l + b = 38
Solving (i) and (ii), we get : l = 14 and b = 10.
∴ Area of the paper = (1410) cm2 = 140 cm2 Answer A
Question: A man being asked how much he gave for his watch, replied; If you multiply the price by 4, and to the product add 70, and from this sum subtract 50, the remainder will be equal to 220 dollars.
A.40
B.50
C.60
D.70
Answer: B.50
Explanation: Solution
Let the price of the watch be represented by x
This price is to be multiplied by 4, which makes 4x
To the product, 70 is to be added, making 4x + 70
From this, 50 is to be subtracted, making 4x + 70 - 50
Here we have a number of the conditions, expressed in algebraic terms; but have as yet no equation. We must observe then, that by the last condition of the problem, the preceding terms are said to be equal to 220.
We have, therefore, this equation 4x + 70 - 50 = 220
Which reduced gives x = 50.
Here the value of x is found to be 50 dollars, which is the price of the watch.
Answer B
Question: John, Karen, and Luke collected cans of vegetables for a food drive. The number of cans that John collected was 1/3 the number of cans that Karen collected and 1/4 the number of cans that Luke collected. The number of cans that Karen collected was what fraction of the total number of cans that John, Karen, and Luke collected?
A. 1/4
B. 1/3
C. 2/5
D. 1/2
Answer: A. 1/4
Explanation: John = (1/3)Karen --> Karen = 3(John)
John = 1/4(Luke) --> Luke = 4(John)
Total = 12(John)
Karen/Total = 3/12 = 1/4
Answer: A
Question: Which of the following expressions CANNOT be equal to 0 when x^2 + 7x = -12 ?
A.x^2 + 2x − 8
B.x^2 − 4x + 3
C.x^2 − 4x − 21
D.x^2 + 2x − 3
Answer: B.x^2 − 4x + 3
Explanation: x^2 +7x = -12
x^2 + 7x 12 = 0
x=-3 or x= -4
All other choices result in a possibility of 0 when you plug in -3 or -4 for x except
x^2 − 4x + 3
Answer is B
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:6. What is the number of 25 paisa coins?
A.228
B.236
C.120
D.988
Answer: C.120
Explanation: 4x 5x 6x
100 50 25
400x + 350x + 150x = 16000
x = 20
6x = 120
Answer:C
Question: Two trains are traveling on parallel tracks in the same direction. The faster train travels at 150 miles per hour, while the slower train travels at 100 miles per hour. At 2 o’clock the faster train is 10 miles behind the slower one. How far apart are the two trains at 5 o'clock?
A.60 miles
B.80 miles
C.90 miles
D.140 miles
Answer: D.140 miles
Explanation: Answer = D. 140 miles
Relational speed = 150 - 100 = 50 miles per hour
In 3 hours, difference = 50 * 3 = 150 miles
Fast train trailing 10 miles, so effective difference = 150 - 10 = 140 miles
Question: If a, b and c are even integers, which of the following could be the value of a^2 + b^2 + c^2?
A.a)28
B.b)26
C.c)12
D.d)10
Answer: C.c)12
Explanation: a, b and c are even integers which means that, supposing that x, y and z are integers, then a=2x, b=2y and c=2z
Therefore we have: a^2+b^2+c^2=2^2*x^2+2^2*y+2^2*z=4x^2+4y^2+4z^2=4(x^2+y^2+z^2).
Which means that the total a^2+b^2+c^2 must be divisible by 4.
The only choice which is divisible by 4 is: C)
12=2^2+2^2+2^2
Answer: C.
Question: At what price must an article costing Rs.100 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
A.131.58
B.62.0
C.62.6
D.62.1
Answer: A.131.58
Explanation: CP = 100
SP = 100*(125/100) = 125
MP*(95/100) = 125
MP = 131.58
Answer: A
Question: Sheela deposits Rs. 2500 in bank savings account. If this is 25% of her monthly income. What is her monthly income in?
A.10000
B.20000
C.25000
D.22235
Answer: A.10000
Explanation: Explanation :
25% of income = Rs. 2500
100% of income = 2500 X 100/25 = Rs. 10000
Answer : A
Question: The sum of three numbers is 196. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8,then the second number is :
A.60
B.30
C.38
D.48
Answer: A.60
Explanation: A : B = 2 : 3 = 2 × 5 : 3 × 5 = 10 : 15
and B : C = 5 : 8 = 5 × 3 : 8 × 3 = 15 : 24
Therefore, A : B : C = 10 : 15 : 24
∴ A : B : C = 10 : 15 : 24
Let the number be 10x, 15x and 24x.
Then, 10x + 15x + 24x = 196
or 49x = 196 or x = 4
⇒ Second number = 15x = 15 × 4 = 60
Answer A
Question: A train travels from New York to Chicago, a distance of approximately 270 miles, at an average rate of 30 miles per hour and arrives in Chicago at 6:00 in evening, Chicago time. At what hour in the morning, New York time, did the train depart for Chicago? (Note : Chicago time is one hour earlier than New York time)
A.3:00
B.4:00
C.10:00
D.6:00
Answer: C.10:00
Explanation: 6:00 in evening in Chicago = 7:00 in evening in New York. So, the train was in Chicago 7:00 in the evening, New York time.
The trip took T=D/R=270/30=9 hours. Therefore, the train depart from New York at 7:00 - 9 hours = 10:00 in the morning, New York time.
Answer: C.
Question: Seats for Maths, Physics and Biology are in the ratio of 7 : 7 : 8 respectively. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the respective ratio of increased seats?
A.14 : 15 : 20
B.6 : 7 : 8
C.6 : 8 : 9
D.Cannot be determined
Answer: A.14 : 15 : 20
Explanation: Reqd ratio 7 Ã— 140â„100 : 7 Ã— 150â„100 : 8 Ã— 175â„100
= 7 Ã— 140 : 7 Ã— 150 : 8 Ã— 175 = 14 : 15 : 20
Answer A
Question: A man rows his boat 120 km downstream and 92 km upstream, taking 4 hours each time. Find the speed of the stream?
A.6 kmph
B.4 kmph
C.2 kmph
D.8 kmph
Answer: B.4 kmph
Explanation: Speed downstream = d/t = 120/(4) = 30 kmph
Speed upstream = d/t = 92/(4) = 23 kmph
The speed of the stream = (30 - 23)/2 = 4 kmph
Answer:B
Question: Find the odd man out
4, 15, 40, 121, 364, 1093, 3280
A.4
B.15
C.121
D.364
Answer: B.15
Explanation: 1*3+1 = 4
4*3+1 = 13
13*3+1 = 40
40*3+1 = 121
121*3+1 = 364
364*3+1 = 1093
1093*3+1= 3280
ANSWER:B
Question: The dimensions of an open box are 52, 40 and 29 cms. Its thickness is 2 cms. If 1 cm3 of metal used in the box weighs 0.5 gms, the weight of the box is?
A.8.56 kg
B.7.76 kg
C.7.756 kg
D.6.832 kg
Answer: D.6.832 kg
Explanation: 52 * 40 * 29 = 60320
48 * 36 * 27 = 46650
------------
13664
13664 * 1/2 = 6832 => 6.832 kg
ANSWER:D
Question: A couple married in 1980 had two children, one in 1982 and the other in 1984. Their combined ages will equal the years of the marriage in?
A.1986
B.1985
C.1987
D.1988
Answer: A.1986
Explanation: Sum of year = 1+9+8+0 =(18) 1+8 = 9
1+9+8+2 =(20) 2+0 = 2
1+9+8+4 = (13) 1+3 = 4
Now 9+2+4= (15) 1+5= 6
Nd option A 1+9+8+6 = 24(2+4)= 6
ANSWER:A
Question: If A:B = 1/4: 1/3 B:C = 1/2:1/3 then A:B:C?
A.9:6:6
B.9:12:8
C.9:6:2
D.9:6:4
Answer: B.9:12:8
Explanation: A:B = 1/4:1/3 = 3:4
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:12:8
Answer:B:
Question: Find the odd man out
1, 2, 5, 14, 41,126
A.2
B.126
C.124
D.41
Answer: B.126
Explanation: 1*3-1 =2
2*3-1 = 5
5*3-1 = 14
14*3-1 = 41
41*3 -1 = 122
ANSWER:B
Question: For every X, the action [X] is defined: [X] is the greatest integer less than or equal to X. What is the value of [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.6?
A.12.6.
B.14.4.
C.15.8.
D.16.2.
Answer: C.15.8.
Explanation: [6.5] x [2/3] + [2] x 7.2 + [8.4] - 6.6
= 6*0 + 2*7.2 + 8 - 6.6
= 0 +14.4 +1.4
15.8
Answer C
Question: A hall is 24 meters long and 12 meters wide. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, what is the volume of the hall (in cubic meters)?
A.1896
B.1912
C.2108
D.2304
Answer: D.2304
Explanation: 2HL + 2HW = 2LW
H = LW / (L+W)
Volume = LWH = (LW)^2 / (L+W) = 2304
The answer is D.
Question: 5^x +25* 4^-x = 10 What is the value of x?
A.-1
B.-1/2
C.0
D.1
Answer: D.1
Explanation: let 5^x = t
t+ 25*1/t =10
t^2 -10t +25 =0
(t-5)^2=0
t-5=0
t=5
5^x=5
x=1
Ans: D
Question: The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
A.27
B.29
C.31
D.34
Answer: A.27
Explanation: The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
A
Question: Anu can do a work in 6 days and Binu alone in 9 days. Anu and Binu undertook to do it for Rs.5100. With help of Minu, they completed the work in 3 days. How much is to be paid to Minu and Anu?
A.s.750, Rs.2250
B.s.2000, Rs.750
C.s.750, Rs.2000
D.s.850, Rs.2550
Answer: D.s.850, Rs.2550
Explanation: Minuâ€™s one dayâ€™s work = 1/3 - 1/6 + 1/9= 1/3 - 5/18 = 1/18
Anuâ€™s wages: Binuâ€™s wages: Minuâ€™s wages = 1/6 : 1/9 : 1/18 = 6: 4: 2
Minuâ€™s share = Rs.5100* 2/12 = Rs.850
Anuâ€™s share = Rs.5100* 6 /12 = Rs.2550
ANSWER:D
Question: In the following sequence: [x, y, z, 5, 7, 16, 28] each number is equal to the sum of the three numbers preceding it. What is 5x-2y?
A.19
B.16
C.17
D.18
Answer: A.19
Explanation: lets start from z, as per the question stem
z + 5 + 7 = 16
-->> z= 4
similarly, y + 4 + 5 = 7
--> y = -2
similarly,, x + -2 + 4 = 5
--> x = 3
hence , 5x-2y =5* 3-2*-2 = 15+4 =19
ANSWER:A
Question: The value of a machine depreciates at 20% per annum. If its present value is Rs. 1,50,000, at what price should it be sold after two years such that a profit of Rs. 29,000 is made?
A.Rs. 1,10,000
B.Rs. 1,20,000
C.Rs. 1,25,000
D.Rs. 1,21,000
Answer: C.Rs. 1,25,000
Explanation: The value of the machine after two years = 0.8 * 0.8 * 1,50,000 = Rs. 96,000
SP such that a profit of Rs. 24,000 is made = 96,000 + 24,000 = Rs. 1,25,000
ANSWER:C
Question: A train 90 m long is running with a speed of 54 km per hour. In what time will it pass a telegraph post?
A.11 s
B.10 s
C.6 s
D.12 s
Answer: C.6 s
Explanation: We know from the formula Time = Distance/ Speed
Thus, Time = 90/ 54 x 5/18
or, Time = 6 sec.
ANSWER:C
Question: Out of a classroom of 6 boys and 5 girls, the teacher randomly chooses a president for the student board, a vice president, and a secretary. What is the probability that only girls will be selected for all three positions?
A.2/33
B.4/33
C.2/165
D.4/165
Answer: A.2/33
Explanation: The number of ways to choose three people is 11C3=165.
The number of ways to choose three girls is 5C3=10.
P(only girls are chosen)=10/165=2/33
The answer is A.
Question: A Cistern is filled by pipe A in 6 hrs and the full Cistern can be leaked out by an exhaust pipe B in 10 hrs. If both the pipes are opened in what time the Cistern is full?
A.15 hrs
B.16 hrs
C.17 hrs
D.14 hrs
Answer: A.15 hrs
Explanation: Pipe A can fill 1/6 of the cistern in 1 hour.
Pipe B can empty 1/10 of the cistern in 1 hour
Both Pipe A and B together can effectively fill
1/6−1/10=2/30=1/15 of the cistern in 1 hour
i.e, the cistern will be full in 15 hrs.
ANSWER:A
Question: What is the sum of the following series? -64, -66, -68, ..... , -100
A.-1458
B.-1558
C.-1568
D.-1664
Answer: B.-1558
Explanation: Step by step solution
The sequence is -64, -66, -68, ..... -100.
The given set of numbers are in an arithmetic progression.
Key Data: First term is -64. The common difference is -2. The last term is -100.
Sum of the first n terms of an AP = n/2[2a1+(n−1)d]
To compute the sum, we know the first term a1 = -64 and the common difference d = -2.
We do not know the number of terms n. Let us first compute the number of terms and then find the sum of the terms.
Step to compute number of terms of the sequence
an = a1 + (n - 1)d
-100 = -64 + (n - 1)(-2)
Therefore, n = 19.
Sum Sn = 19/2[2(−64)+(19−1)(−2)]
Sn = 19/2[−128−36]
Sn = 19 * (-82) = -1558
The correct answer is Choice B.
Question: A cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 10 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?
A.4.3 hrs
B.8.9 hrs
C.2.9 hrs
D.7.2 hrs
Answer: A.4.3 hrs
Explanation: Net part filled in 1 hour = (1/3 - 1/10)
= 7/30
The cistern will be filled in 30/7 hrs i.e., 4.3 hrs.
Answer:A
Question: The ratio of two numbers is 3 : 4 and their H.C.F. is 5. Their L.C.M. is
A.48
B.22
C.56
D.60
Answer: D.60
Explanation: Explanation:
Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 5.
So, the numbers 15 and 20.
L.C.M. of 15 and 20 = 60.
Answer: Option D
Question: If 2x^2 + y^2 = 2xy, then (x + y)^2 =
A.x^2
B.3x^2+2y^2
C.4xy
D.2y^2
Answer: B.3x^2+2y^2
Explanation: (x+y)^2 = x^2 + y^2 + 2xy = x^2 + y^2+ 2x^2+y^2 = 3x^2+2y^2
Correct option : B
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 50 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
A.36
B.2^4*3
C.24
D.49
Answer: D.49
Explanation: Working backward from the day it's covered:
day 50: fully covered
day 49: half covered
So 49 days
ANSWER:D