RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
A.5
B.6
C.7
D.9
Answer: B.6
Explanation: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55 = 6 sec.
Answer: B
Question: Irin, Ingrid and Nell bake chocolate chip cookies in the ratio of 9.18: 5.17: 2.05. If altogether they baked a batch of 148 cookies, what percent of the cookies did Nell bake?
A.0.125%
B.1.25%
C.12.5%
D.125%
Answer: C.12.5%
Explanation: 9.18x+5.17x+2.05x = 16.4x = 148 cookies
x= 148/16.4 = 9 (approx)
So, tell baked 9*2.05 cookies or 19 cookies (approx)
% share = 19/148 = 12.5 approx
Hence, answer is C.
Question: On adding four times the age of Chris Hemsworth four years from now to five times his age five years from now, we will get ten times his current age.
How old is Chris right now?
A.38 years
B.24 years
C.40 years
D.41 years
Answer: D.41 years
Explanation: D
41 years.
If the current age of Dakota is x
4(x+4) + 4(x+5) = 10x
Thus x=41 years
Question: If a, b, c are integers; a² + b² = 45 and b² + c² = 40, then the values of a, b and c respectively are :
A.2, 6, 3
B.3, 2, 6
C.5, 4, 3
D.4,5,3
Answer: B.3, 2, 6
Explanation: a² + b² = 45 ….(1) and b² + c² = 40
Subtracting, we get: a² - c² = 5 => (a + c) (a – c) = 5.
(a + c) = 5 and (a – c) = 1.
Solving we get: a = 3, c = 2. Putting c = 2 in (ii), we get b = 6.
ANSWER:B
Question: in a powder mix two varieties of powders costing Rs. 15 and Rs. 20 per kg respectively so as toget a mixture worth Rs. 16.50 kg?
A.1:3
B.2:5
C.7 : 3
D.7:5
Answer: C.7 : 3
Explanation: By the rule of alligation:
Cost of 1 kg pulses of 1st kindCost of 1 kg pulses of 2nd kind
Rs. 15	Mean Price
Rs. 16.50	Rs. 20
3.50	1.50
Required rate = 3.50 : 1.50 = 7 : 3
C
Question: A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. The quantity of whisky replaced is:
A.1/3
B.2/3
C.2/5
D.3/5
Answer: B.2/3
Explanation: Explanation:
By the rule of alligation, we have:
So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2
Required quantity replaced =2/3.
ANSWER IS B
Question: Find the odd man out. 1050, 510, 242, 108, 46, 16, 3
A.46
B.106
C.510
D.108
Answer: D.108
Explanation: Explanation :
1050
(1050 - 30)/2 = 510
(510 - 26)/2 = 242
(242 - 22)/2 = 110
(110 - 18)/2 = 46
(46- 14)/2 = 16
(16- 10)/2 = 3
Hence, 110 should have come in place of 108. Answer : Option D
Question: Mangala completes a piece of work in 20 days, Raju completes the same work in 40 days. If both of them work together, then the number of days required to complete the work is
A.4 days
B.6 days
C.13.33 days
D.10 days
Answer: C.13.33 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 20 × 40/60 = 13.33 days.
Answer : C
Question: From the set of numbers {p, t, u, v, w, x, y, z}, how many different combinations can we have without the t in them? Ex:. (x,y), (x), (w,z,y,x), etc... and note that (x,y)=(y,x)
A.32
B.63
C.64
D.127
Answer: D.127
Explanation: Any letter (p, u, v, w, x, y, z) can be included or not.
Thus there are 2^7 combinations - 1 empty combination = 127 combinations
The answer is D.
Question: How much 60% of 50 is greater than 40% of 30?
A.18
B.99
C.77
D.66
Answer: A.18
Explanation: (60/100) * 50 – (40/100) * 30
30 - 12 = 18ch 60% of 50 is greater than 40% of 30?
Answer:A
Question: In a Private Company 20 Nos. staffs are employed. In a Festival season their Boss give festival allowance to all. He says his accountant to calculate for 30 days @ 100. Also he says balance payment will give to driver and cleaning staff and to be adjust from petty cash. He had given Rs.65000/- to the accountant. How much amount will taken from Petty cash?
A.A)1000
B.B)3000
C.C)3500
D.D)2500
Answer: A.A)1000
Explanation: For 20 staffs: 300*100*20 = 60000
for driver and cleaning staff: 300*100*2 =6000
From petty Cash : 1000
Answer is 1000 Answer is A
Question: How many triangles can be formed by joining vertices of a hexagon?
A.20
B.30
C.40
D.60
Answer: A.20
Explanation: One triangle is formed by selecting group of three vertices from 6 vertices of a hexagon.This can be done in 6C3 ways. ie) 6!/3!x3!=20 ways. Ans : A
Question: A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 104. What was the number he chose?
A.123
B.121
C.277
D.267
Answer: B.121
Explanation: Let xx be the number he chose, then
2â‹…xâˆ’138=104 2â‹…xâˆ’138=104
x=121
Answer:B
Question: What is the next number of the following sequence
8, 24, 12, 36, 18, 54 (...)
A.30
B.32
C.34
D.36
Answer: B.32
Explanation: The series is
4*4=16
16/2=8
8*4=32
32/2=16
16*4=64
64/2=32
ANSWER: B
Question: What is the total number of W integers between 100 and 200 that are divisible by 3?
A. 33
B. 32
C. 31
D. 30
Answer: A. 33
Explanation: yes there is a different way of arriving at that answer ....
u can also use arithmetic progression to get the answer
since the first term to be divisble by 3 is 102 ..take that as A .. the starting no
and since 198 is the last digit to be divisible by 3 take that as N ...
since the difference is 3 take that as D
no u have to find what term is 198 take that as nth term
the formula for that is N = A + (n-1) * d
198 = 102 +(n-1) * 3
from this u get n =33
Question: An old man distributed all the gold coins he had to his two sons into two different numbers such that the difference between the squares of the two numbers is 81 times the difference between the two numbers. How many coins did the old man have?
A. 24
B. 26
C. 30
D. 81
Answer: D. 81
Explanation: Let the number of coins one son got be x and the number of coins another got be y. Total = x + y.
x^2 - y^2 = 81(x - y) --> x + y = 81.
Answer: D.
Question: Which of the following is equal to the cube of a non-integer?
A.-64
B.-1
C.8
D.9
Answer: D.9
Explanation: A. -64 -> cube of -4
B. -1 -> cube of -1
C. 8 -> cube of 2
D. 9
E. 27 -> cube of 3
All other options are cubes of integers except 9. 9 will be the cube of a number slightly greater than 2 since the cube of 2 is 8.
Answer (D)
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
A.15
B.66
C.77
D.52
Answer: A.15
Explanation: 90 * 10/60 = 15 kmph
Answer:A
Question: The fourth proportional to 5, 8, 15 is:
A.15
B.5
C.24
D.8
Answer: C.24
Explanation: Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
= 5x = (8 x 15)
x = (8 x 15)/5= 24.
Answer is C.
Question: If the tens digit of positive integer x is 4 and the tens digit of positive integer y is 4, how many possible values of the tens digit of 2(x+y) can there be?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: We only need to consider the tens and ones digits of x and y, and the last two digits can be represented as 40 + p and 40 + q respectively.
2(40+p+40+q)= 160 + 2(p + q)
2(p+q) can range from 0 up to a maximum value of 36 when p=q=9.
Then the tens and ones digits of 2(x+y) can range from 60 up to 96.
There can be 4 possibilities for the tens digit.
The answer is C.
Question: Sophia finished 23 of a book. She calculated that she finished 90 more pages than she has yet to read. How long is her book?
A.180
B.200
C.250
D.270
Answer: D.270
Explanation: Let x be the total number of pages in the book, then she finished 23⋅x pages.
Then she has x−23⋅x=13⋅x pages left.
23⋅x−13⋅x=90
13⋅x=90
x=270.
So answer is D.
Question: There are 10 people in a room. If each person shakes hands with exactly 3 other people, what is the total number of handshakes?
A.15
B.30
C.45
D.60
Answer: A.15
Explanation: 4 people: shrive 555, cranky, karishma and Mr X
We have to shake hands in this group such that each person shakes hands with 3 people.
So shrive555 starts:
shrive555 - craky : 1 handshake but 2 hands were shaken. shrive 555's and cranky's
shrive 555 - karishma : 1 handshake but 2 hands were shaken. shrive 555's and karishma's
shrive 555 - Mr X : 1 handshake but 2 hands were shaken. shrive 555's and Mr X's
Now shrive 555 has shaken hands with 3 people. There were 3 handshakes. But 6 hands were shaken.
Now, when all 4 of us shake hands with 3 people, each person's hand will be shaken 3 times. i.e. in all 12 hands will be shaken. But they will add up to only 6 handshakes.
The other 3 handshakes will be:
cranky - karishma
cranky - Mr X
karishma - Mr X
So all of us have shaken hands with exactly 3 people.
Similarly when there are 10 people, each person shakes his hand 3 times. So in all 30. But 2 of these hands combined to make one handshake. So we will get only 15 total handshakes.
ANSWER:A
Question: A farmer divides his herd of x cows among his 4 sons so that one son gets one half of the herd, the second gets one-fourth, the third gets one-fifth and the fourth gets 7 cows. Then x is equal to
A.100
B.140
C.180
D.160
Answer: B.140
Explanation: no. of cows:: x
1st son: x/2
2nd son: x/4
3rd son: x/5
4th son: 7
(x)+(x/4)+(x/5)+7=x
=> x - (19x/20)=7
=> (20x-19x)/20=7
=> x =140
ANSWER:B
Question: Which of the following is closest to (5!-4!)/(5!+4!)?
A.0.01
B.0.1
C.0.2
D.0.7
Answer: D.0.7
Explanation: (5!-4!)/(5!+4!)
4! (5-1)/4! (5+1)
4/6 = 2/3 =0.7 (approximately)
D is the answer
Question: Given that -1 ≤ v ≤ 1, -2 ≤ u ≤ -0.5, and -2 ≤ z ≤ -0.5 and w = vz/u, then which of the following is necessarily true ?
A.-0.5 ≤ w ≤ -2
B.-4 ≤ w ≤ 4
C.-4 ≤ w ≤ 2
D.-2 ≤ w ≤ -0.5
Answer: B.-4 ≤ w ≤ 4
Explanation: Explanation :
u is always negative. Hence, for us to have a minimum value of vz/u , vz should be positive.
Also for the least value, the numerator has to be the maximum positive value and the denominator has to be the smallest negative value. In other words, vz has to be 2 and u has to be –0.5.
Hence the minimum value of vz/u = 2−0.5 = –4.
For us to get the maximum value, vz has to be the smallest negative value and u has to be the highest negative value.
Thus, vz has to be –2 and u has to be –0.5. Hence the maximum value of vz/u = 2 / -0.5 = 4.
Answer : B
Question: How many six-digit numbers are there such that all six digits are different and the first digit is not zero?
A.472392
B.648421
C.720756
D.729951
Answer: A.472392
Explanation: All six digits are different and first digit is not zero.
So first digit can be filled in 9 ways.
And, second digit can be filled in 9 ways.
And, third digit can be filled in 9 ways.
And, fourth digit can be filled in 9 ways.
And, fifth digit can be filled in 9 ways.
And, sixth digit can be filled in 8 ways.
Total ways = 9*9*9*9*9*8
= 472392
Hence option (A).
Question: Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3?
A.1/11
B.2/13
C.3/10
D.4/15
Answer: C.3/10
Explanation: Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C
Question: You have been given a physical balance and 7 weights of 52, 50, 48, 44, 45, 46 and 78 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 183 kgs.
A.180
B.181
C.182
D.183
Answer: A.180
Explanation: 52+50+78 = 180
Answer: A
Question: In the class of 40 students, 30 speak Hindi and 20 speak English. What is the lowest possible number of students who
speak both the languages?
A.10
B.15
C.20
D.25
Answer: A.10
Explanation: let the student who speaks hindi-x
let the student who speaks english-y
as (xuy)-(xny)=total
30+20-(xny)=40
=10
A)
Question: Find the next number in the Sequence
5, 14, 41, 86, ?
A.146
B.145
C.149
D.143
Answer: C.149
Explanation: +9 =>14
+27 =>41
+45 =>86
+63 =>149
Answer is C
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 33 kmph?
A.210
B.220
C.125
D.240
Answer: C.125
Explanation: distance covered in 1 min=(33*1000)/60=550m
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=550/4.4=125
ANSWER:C
Question: In an election between two candidates, one got 45% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 2000, the number of valid votes that the other candidate got, was:
A.1500
B.4500
C.3270
D.1100
Answer: D.1100
Explanation: Number of valid votes = 80% of 2000= 1600.
Valid votes polled by other candidate = 55% of 2000
=(55/100)X2000 =1100
ANSWER =D
Question: If four coins are tossed, the probability of getting two heads and two tails is
A.3/8
B.3/9
C.3/6
D.3/1
Answer: A.3/8
Explanation: Explanation:
Since four coins are tossed, sample space = 24
Getting two heads and two tails can happen in six ways.
n(E) = six ways
p(E) = 6/24 = 3/8
Answer:A
Question: A can do a job in 30days and B in 40days. If they work on it together for 10 days, then the fraction of the work that is left is?
A.2/11
B.3/13
C.5/12
D.7/10
Answer: C.5/12
Explanation: A's 1 day work = 1/30
B's 1day work = 1/40
A+B 1day work = 1/30 + 1/40 = 7/120
A+B 4days work = 7/120*10 = 7/12
Remaining work = 1 - 7/12 = 5/12
Answer is C
Question: A motor cycle is moving with the speed of 47.52 km/hr and the radius of the wheel of the motorcycle is 21 cms. Calculate the approximate no of revolutions made by the wheel in one minute.
A.400 rpm
B.500 rpm
C.600 rpm
D.700 rpm
Answer: C.600 rpm
Explanation: Given Speed = 47.52 km/h = 47.52 * 1000/60 m/s
= 792 metre/minute
the radius of the wheel of the motorcycle = 21 cm
circumference of the wheels = 2*22/7*21 = 132cm = 1.32 m
Number of revolutions made by the wheel in one minute
= Speed (in metre/minute)/circumference(in m)
= 792/1.32 = 600
So no of revolutions made by the wheel in one minute will be 600
ANSWER:C
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.2700. How much third person will get?
A.2400
B.2429
C.2980
D.1200
Answer: D.1200
Explanation: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 2700 = 1200
Answer:D
Question: A car takes 6 hours to cover a distance of 469 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
A.48 Kmph
B.50 Kmph
C.52 Kmph
D.56 Kmph
Answer: C.52 Kmph
Explanation: Time = 6
Distence = 469
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 469/9 = 52 Kmph
C
Question: when W is divided by 14, the reminder is 0. if W is three lesser than it value and when divided by 5 its remainder is 0. what is the value of W ?
A.14
B.28
C.42
D.45
Answer: B.28
Explanation: W is divided by 14 so that is multiple of 14 as 14,28,42...
W-3 is divided by 5 the remainder is 0 so it is divisible by 5. Consider from option let us take the number is 14 it is divisible by 14 but 14-3 is not divisible by 5 so it is not answers so let us take 2nd option 28 which is divisible by 14 and 28-3=25 is divisible by 5 so ans is B
Question: Sarah signed 1/2 of the Christmas cards, and Richard signed 3/8 of them. If there are 32 cards in
all, how many are left to be signed?
A.6
B.7
C.4
D.9
Answer: C.4
Explanation: 1/2 x 32 = 16 Sarah signed
3/8 x 32 = 12 Richard signed
16 + 12 = 28 are signed
32 - 28 = 4 cards left to be signed
correct answer C
Question: A man buys an article for Rs. 27.50 and sells it for Rs 28.60. Find his gain percent
A.1%
B.2%
C.3%
D.4%
Answer: D.4%
Explanation: Explanation:
So we have C.P. = 27.50
S.P. = 28.60
Gain = 28.60 - 27.50 = Rs. 1.10
Gain%=(GainCost∗100)%=(1.1027.50∗100)%=4%
ANSWER IS D
Question: What is the ratio between perimeters of two squares one having 3 times the diagonal then the other?
A.3: 5
B.3: 9
C.3: 4
D.3: 1
Answer: D.3: 1
Explanation: d = 3d d = d
a√2 = 3d a√2 = d
a = 3d/√2 a = d/√2 => 3: 1
Answer: D
Question: A part-time employee’s hourly wage was increased by 40%. She decided to decrease the number of hours worked per week so that her total income did not change. By approximately what percent should the number of hours worked be decreased?
A.9%
B.15%
C.29%
D.50%
Answer: C.29%
Explanation: Let's plug in somenicenumbers and see what's needed.
Let's say the employee used to make $1/hour and worked 100 hours/week
So, the TOTAL weekly income was $100/week
After the 40% wage increase, the employee makes $1.40/hour
We want the employee's income to remain at $100/week.
So, we want ($1.40/hour)(new # of hours) = $100
Divide both sides by 1.40 to get:
new # of hours = 100/1.40
≈ 71 hours
So, the number of hours decreases from 100 hours to (approximately) 71 hours.
This represents a 29% decrease (approximately) .
Answer : C
Question: A reduction of 15% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
A.s.24
B.s.46
C.s.40
D.s.41
Answer: A.s.24
Explanation: 800*(15/100) = 120 ---- 5
? ---- 1 => Rs.24
Answer: A
Question: Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
A.8 min
B.5 min
C.10 min
D.14 min
Answer: C.10 min
Explanation: Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54 x 60) min = 10 min
Answer : C
Question: In an election, candidate Smith won 52 percent of the total vote in Counties A and B. He won 61 percent of the vote in County A. If the ratio of people who voted in County A to County B is 3: 1, what percent of the vote did candidate Smith win in County B?
A.25%
B.27%
C.34%
D.43%
Answer: A.25%
Explanation: Given voters in ratio 3:1
let A has 300 voters & B has 100 voters
for A 61% voted means 61*300=183 votes
combined for A & B has 400 voters and voted 52% so total votes =208
balance votes=208-183=25
As B has 100 voters so 25 votes means 25% of votes required
Answer: A
Question: How many cubes will have 4 coloured sides and two non-coloured sides ?
A.5
B.4
C.3
D.2
Answer: B.4
Explanation: Only 4 cubes situated at the corners of the cuboid will have 4 coloured and 2 non-coloured sides.
ANSWER B
Question: The average of 2,7,6 and x is 5 and the average of 18,1,6,x and y is 10. What is the value of y?
A.5
B.10
C.20
D.30
Answer: C.20
Explanation: We have : ( 2+7+6+x)/4 = 5 or 15+x =20 or x = 5
Also (18+1+6+x+y)/5 = 10, 25+5+y = 50, y =20
ANSWER:C
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.388
B.277
C.245
D.288
Answer: C.245
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer: C
Question: Jill bought items costing $3.45, $1.99, $6.59, and $12.98. She used a coupon worth $2.50.
If Jill had $50.00 when she went into the store, how much did she have when she left?
A.$17.49
B.$27.49
C.$37.49
D.$57.49
Answer: B.$27.49
Explanation: $3.45 + $1.99 + $6.59 + $12.98 = $25.01
$25.01 - $2.50 = $22.51
$50.00 - $22.51 = $27.49 is money left
correct answer B
Question: A train running at the speed of 60 km/hr crosses a pole in 21 sec. What is the length of the train?
A.535 m
B.178 m
C.186 m
D.350 m
Answer: D.350 m
Explanation: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train
= speed * time
= 50/3 * 21
= 350 m
Answer:D
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
A.42
B.43
C.46
D.47
Answer: A.42
Explanation: A
42
After 10 days : 150 men had food for 35 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
125 : 150 :: 35 : x 125 x x = 150 x 35
x = (150 x 35)/125
x = 42
Question: A man covers a distance on scooter. Had he moved 3kmph faster he would have taken 40 min less. If he had moved 2kmph slower, he would have taken 40min more. The distance is.
A.30 km
B.40 kilometre
C.45 km
D.50 km
Answer: B.40 kilometre
Explanation: Let distance = x m
Usual rate = y kmph
x/y – x/y+3 = 40/60 hr
2y(y+3) = 9x ---------------------------------(1)
x/y-2 – x/y = 40/60 hr y(y-2) = 3x -----------(2)
divide 1 & 2 equations
by solving we get x = 40 km
Answer : B.
Question: After decreasing 90% in the price of an article costs Rs.320. Find the actual cost of an article?
A.2777
B.2987
C.3200
D.9977
Answer: C.3200
Explanation: CP* (10/100) = 320
CP= 32* 100 => CP = 3200
Answer: C
Question: Mr. JACK invested in Fund X and Fund Y. The total amount she invested, in both funds combined, was $100,000. In one year, Fund X paid 33% and Fund Y paid 15%. The interest earned in Fund Y was exactly $500 greater than the interest earned in Fund X. How much did Ms. Tom invest in Fund X?
A.31,041.66
B.45,041.66
C.37,041.78
D.78,041.90
Answer: A.31,041.66
Explanation: X+Y=100,000
0.15Y=0.33A+500
Take away decimals first: 15Y+33X+50,000
Isolate first equation to solve for X (your goal): Y=100,000-Y
Plug in for B:
15(100,000-X)=33X+30,000
1,500,000-15X=33X+10,000
1,490,000=48X
1,490,000/48=X
X=31,041.66=Answer Choice A
Question: David covered a distance of 50 miles on his first trip. On a later trip he traveled 75 miles while going three times as fast. His new time compared with the old time was:
A.twice as much
B.three times as much
C.the same
D.half as much
Answer: D.half as much
Explanation: Let t be the time of the first trip.
On the later trip, David can travel 150 miles in time t.
The trip of 75 miles takes t/2.
The answer is D.
Question: A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?
A.190 metres
B.160 metres
C.200 metres
D.120 metres
Answer: C.200 metres
Explanation: Explanation:
Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 18 s
Distance Covered, d = vt = (400/36)× 18 = 200 m
Distance covered is equal to the length of the train = 200 m
Answer: Option C
Question: From a Group of 8 People, Including George and Nina, 3 people are to be selected at random to work on a certain project. What is the probability that 3 people selected will include George but not Nina
A.5/56
B.9/56
C.15/56
D.21/56
Answer: C.15/56
Explanation: Number of ways of selecting 3 people out of 8 people = 8C3
In the three members George will always be there in the team. At this step we have vacancy for 2 more members and 7 members are available. Lina cannot be there in the team. So 2 members have to be selected and the number of available members = 7 - Lina = 6
Number of ways to form a 3 member team that includes George and excludes Lina = 6C2
Probability = 6C2/8C3 = 15/56
Answer: C
Question: There are 5 bags three of which each contains 5 white and 2 black balls, and remaining 2 bags each contains 1 white and 4 black ball; a white ball has been drawn, find the chance that it came from first group.
A.2/7
B.6/35
C.8/25
D.75/89
Answer: D.75/89
Explanation: Please go through my solution and suggest any mistake.
Chances of selecting a white ball from group 1: 5/7----------------------Chances of selecting a white ball from group 2: 1/5
Thus combined probability of section of white ball from group 1:
3/5 x 5/7 = 3/7
Thus combined probability of section of white ball from group 2:
2/5 x 1/5 = 2/25
Out of these chances, chance of occurrence of first case : (3/7) / (3/7 + 2/25) = 75/89
D
Question: In 1995, the Jims spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Jims cut back their water usage. By how much must the Jims have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
A.a)	33 1/3 %
B.b)	40 %
C.c) 50 %
D.d)	66 2/3 %
Answer: A.a)	33 1/3 %
Explanation: Let x be the water usage and c be the cost water of Jims.
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Question: In 10 years, P will be as old as Q is now. Twenty years ago, Q was twice as old as P was then. How old is P now?
A.30
B.35
C.40
D.45
Answer: A.30
Explanation: Q = P+10
Q-20 = 2(P-20)
P-10 = 2P-40
P = 30
The answer is A.