divelab/Sys2Bench huggingface dataset:
Question: Set A contains all the even numbers between 10 and 50 inclusive. Set B contains all the even numbers between 110 and 150 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
Options:
A)2100
B)2550
C)5050
D)6275
E)11325
Rationale: Set A contains 10, 12,14 , 16 ... 50
Set B contains 110 , 112 , 114 ... 150
Number of terms in each set = 21
Difference between corresponding terms in set A and B = 100
Difference between Sum of set B and set A = 100*21 = 2100
Answer A
Answer: A
Question: A bag contains 6 green balls and 8 white balls. If two balls are drawn simultaneously, what is the probability that both balls are the same colour?
Options:
A)5/14
B)8/21
C)12/21
D)43/91
E)47/91
Rationale: The total number of ways to draw two balls is 14C2 = 91
The number of ways to draw two green balls is 6C2 = 15
The number of ways to draw two white balls is 8C2 = 28
P(two balls of the same colour) = 43/91
The answer is D.
Answer: D
Question: A’s speed is 20/16 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
Options:
A)1/17
B)3/17
C)1/10
D)4/20
E)3/10
Rationale: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 20 meters, B covers 16 meters in that time. So if the race is 20 meters long, when A reaches the finish line, B would be 4 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 4 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 20 meters) would be the same as the time required by B (to cover 16 meters) to reach the finish line.
So B should get a head start of 4/20th of the race.
Answer (D)
Answer: D
Question: What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular octagon?
Options:
A)1/4
B)1/3
C)1/2
D)2/5
E)7/8
Rationale: From any vertex, there are two vertices on sides, which do not make a diagonal but a side.
So the remaining n-3 vertices make diagonals.
There are 2 of these diagonals which are the shortest.
The probability of choosing one of the shortest diagonals is 2/5.
The answer is D.
Answer: D
Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Rs. 2.40 per hour for regular work and Rs. 3.20 per hours for overtime. If he earns Rs. 432 in 4 weeks, then how many hours does he work for ?
Options:
A)223
B)175
C)297
D)267
E)911
Rationale: Explanation:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 x 8 x 4) = 160.
{\color{Blue} \therefore } 160 x 2.40 + x x 3.20 = 432
=> 3.20x = 432 - 384 = 48
=> x = 15.
Hence, total hours of work = (160 + 15) = 175.
Answer: B) 175
Answer: B
Question: A boy has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)90
B)110
C)140
D)130
E)120
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
A
Answer: A
Question: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: C.P. of 6 toffees = Rs. 1
S.P. of 6 toffees = 120% of Rs. 1 = Rs 6/5
For Rs. 6/5 Toffees Sold 6
For Rs. 1, toffees sold = 6x (5/6)= 5
answer :C
Answer: C
Question: Find the area of the quadrilateral of one of its diagonals is 22 cm and its off sets 9 cm and 6 cm?
Options:
A)188 cm2
B)165 cm2
C)168 cm2
D)198 cm2
E)987 cm2
Rationale: 1/2 * 22(9 + 6)
= 165 cm2
Answer: B
Answer: B
Question: The cross-section of a tunnel is a trapezium in shape. If the tunnel is 15 m wide at the top and 5 m wide at the bottom and the area of cross-section is 400 sq m, the depth of tunnel is?
Options:
A)200 m
B)600 m
C)400 m
D)800 m
E)900 m
Rationale: 1/2 * d (15 + 5) = 400
d = 400
ANSWER:C
Answer: C
Question: The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum.
Options:
A)17008
B)17000
C)170028
D)171776
E)170892
Rationale: The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000
Answer: B
Answer: B
Question: Working together, Jose and Jane can complete an assigned task in 30 days. However, if Jose worked alone and complete half the work and then Jane takes over the task and completes the second half of the task, the task will be completed in 45 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose
Options:
A)90 days
B)30 days
C)60 days
D)65 days
E)36 days
Rationale: Assume:
Jose does 1 job in x days, so Jose does 1/x job in a day
Jane does 1 job in y days, so Jane does 1/y job in a day
Together, they does (x+y)/xy job in a day. This is equals to 1/20. So
(x+y)/xy = 1/30
30(x+y) = xy
Next, we're told 1 job takes 45 days to complete if Jose and Jane each does half the work. So since Jose does 1 job in x days, he wil need x/2 days to do half the job. Jane similarly will need y/2 days to do the other half.
x/2 + y/2 = 45
x+y = 90
So
xy = 30 *90 =2700
The answer choices are:
90 days
30 days
60 days
65 days
36 days
From the answer choices, So I'll go for 90 days for Jose and 30 days for Jane.
Answer : A
Answer: A
Question: The sum of the ages of Latha and Geetha is 60years. Also 5 years ago, the Latha's age was 5 times the age of the Geetha. What is the age of the Geetha?
Options:
A)13years
B)15yeas
C)20years
D)18years
E)22years
Rationale: Let the age of the Geetha be x years
The age of the Latha is 60-x years
5 years ago 5(x-5) = 60-x-5
x = 13 approximately
Geetha's age = 13years
Answer is B
Answer: B
Question: The speed at which a man can row a boat in still water is 150 kmph. If he rows downstream, where the speed of current is 48 kmph, what time will he take to cover 390 metres?
Options:
A)10
B)11
C)12
D)13
E)14
Rationale: Speed of the boat downstream = 150 + 48 = 198 kmph
= 198 * 5/18 = 30 m/s
Hence time taken to cover 390 m = 390/30 = 13 seconds. Answer: D
Answer: D
Question: The 15 homes in a new development are each to be sold for one of three different prices so that the developer receives an average (arithmetic mean) of $200,000 per home. If 4 of the homes are to be sold for $170,000 each and 5 are to be sold for $200,000 each, what will be the selling price of each of the remaining 16 homes?
Options:
A)$200,000
B)$210,000
C)$215,000
D)$207,500
E)$230,000
Rationale: IMO the answer has to be D.
5 houses are being sold for 200,000. 4 houses are being sold for $30,000 less, resulting in a loss of $120,000. To make the average selling price intact i.e. $200,000, the remaining 16 houses must be sold at such a profit that it compensates for the loss of 120,000. Hence 16x=120,000.
x=7500.
The 16 houses are sold at $7,500 profit or at $207,500. (ANSWER D)
Answer: D
Question: Simple interest on a certain amount is 9/16 of the principal. If the numbers representing the rate of interest in percent and time in years be equal, then time, for which the principal is lent out, is :
Options:
A)6 1/2
B)7 1/2
C)8
D)9 1/2
E)None
Rationale: Sol.
Let sum = x. Then, S.I. = 9/16 x.
Let rate = R% and time = R years.
∴ [x * R * R / 100] = 9x / 16 ⇔ R² = 900/16
⇔ R = 30/4 = 7 1/2
Hence, time = 7 1/2 years.
Answer B
Answer: B
Question: What is the area of an equilateral triangle whose one side length is 70?
Options:
A)825√3
B)925√3
C)1025√3
D)1125√3
E)1225√3
Rationale: -> The area of an equilateral triangle with one side length of a is √3a2/4. Thus, √3(70^2)/4=1225√3 and the answer is E.
Answer: E
Question: A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at time t = 0, the find the total number of live bacteria just after 10 seconds :
Options:
A)3 10 /2
B)(3)10 - (2)10
C)243 *(35 -1)
D)(3)10 -(2)5
E)None of these
Rationale: Solution: Total number of bacteria after 10 seconds,
= (3)10 - (3)5
= (3)5 *(3)(5 -1)
= 243 *(3)(5 -1)
Since, just after 10 seconds all the bacterias (i.e. 35 ) are dead after living 5 seconds each.
Answer: Option C
Answer: C
Question: What should come in place of the question mark (?) in the following number series?
11 16 23 32 43 ?
Options:
A)55
B)56
C)57
D)58
E)59
Rationale: Explanation:
The difference is 5,7,9,11.
It increases by every consecutive odd number.
Answer: E
Answer: E
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.65 less, he could have gained 25%. What is the cost price?
Options:
A)325
B)375
C)278
D)267
E)288
Rationale: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
65 ----- ? => 325
Answer:A
Answer: A
Question: How many numbers from 10 to 50 are exactly divisible by 3?
Options:
A)13
B)15
C)16
D)17
E)18
Rationale: 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45,48.
13 Numbers.
10/3 = 3 and 50/3 = 16 ==> 16 - 3 = 13. Therefore 13 digits
A)
Answer: A
Question: The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:
Options:
A)1.2 km
B)2.4 km
C)3.2 km
D)3.6 km
E)4.6 km
Rationale: Speed downstream = (15 + 3) kmph = 18 kmph.
Distance travelled = 18 x 12/60	km = 3.6 km.
ANSWER:D
Answer: D
Question: The average of first 40 prime numbers is?
Options:
A)15.41
B)16.41
C)15.61
D)15
E)16.91
Rationale: Explanation:
Average = (2+3+5+7+11+13+17+19+23+29+31+37)/12= 197/12= 16.41(Approx)
Answer is B
Answer: B
Question: Aishwarya’s mom was 38 years of age at the time of her birth, while her mom was 34 years old when her 4 years younger sister was born. The variance between the parents ages is :
Options:
A)6 years
B)11 years
C)10years
D)12 years
E)8 years
Rationale: E
8 years
Mom’s age when Aishwarya’s sister was born = 34 years.
Dad’s age when Aishwarya’s sister was born = (38 + 4) years = 42 years.
Needed Variance = (42 – 34) years = 8 years.
Answer is E
Answer: E
Question: A thief steals at a car at 2.00 p.m. and drives it at 60 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
Options:
A)1 p.m
B)3 p.m
C)4 p.m
D)4.30 p.m
E)6 p.m
Rationale: D
4.30 p.m
Suppose the thief is overtaken x hrs after 2.00 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
60x = 75(x - 1/2) => x = 5/2 hrs.
So, the thief is overtaken at 4.30 p.m.
Answer: D
Question: If TIER is written as 7163 and BRAIN is written as 23415, how is RENT coded ?
Options:
A)7536
B)7653
C)3657
D)3765
E)None of these
Rationale: Explanation:
Given :
Letter : T I E R B A N
Code : 7 1 6 3 2 4 5
Thus, the code for RENT is 3657.
ANSWER C
Answer: C
Question: How much time will it take for an amount of Rs. 900 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options:
A)2 years
B)3 years
C)1 year
D)4 years
E)5years
Rationale: Solution:
P = Rs.900
SI = Rs.81
T = ?
R = 4.5%
T= 100×SI/PR=100×81/900×4.5=2 years
Answer : Option A
Answer: A
Question: One side of a rectangular field is 14 m and one of its diagonal is 17 m. Find the area of the field.
Options:
A)134.4
B)120
C)150
D)180
E)None
Rationale: Solution
Other side = √(17)2 - (14)2
= √289 - 196
= √93
= 9.6 m.
∴ Area = (14 x 9.6)m2 = 134.4 m2.
Answer A
Answer: A
Question: 337.62+8.591+34.4=?
Options:
A)370.611
B)380.511
C)380.611
D)426.97
E)None of them
Rationale: 337.62
8.591
34.4
----------
380.611
Answer is C
Answer: C
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 40 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
Options:
A)a. 43
B)b. 45
C)c. 55
D)d. 68
E)e. 60
Rationale: 40 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (40 * 12.5 * 100) / (2.5 * 200)
thus, X = 100
Thus, more men needed to finish the task = 100-40=60
hence Answer is E
Answer: E
Question: In the next Cricket World Cup T-20, Team W has decided to score 200 runs only through 4s and 6s. In how many ways can the Team W score these 200 runs?
Options:
A)13
B)15
C)16
D)17
E)18
Rationale: Team W can score a maximum of 50 fours and a minimum of 2 fours with an interval or spacing of 3 units to accommodate the 6's.
So the number of fours scored forms an AP 2, 5, 8, ... 50 with a common difference of 3.
Number of ways of scoring 200 only through 4's and 6's = (50 - 2)/3 + 1 = 17
Answer: D
Alternate solution: 4x + 6y = 200 --> 2x + 3y = 100
x = (100 - 3y)/2 --> 100 - 3y should be even. This is possible when 3y is even.
There are 17 even multiples of 3 between 0 and 100.
Answer: D
Answer: D
Question: Suresh borrowed some money at the rate of 4% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of 11 years is Rs.8160, how much money did he borrow?
Options:
A)s.8500
B)s.6000
C)s.8500
D)s.9000
E)s.7000
Rationale: using the formula S.I=P*T*R/100
(x*4*3/100)+(x*9*5/100)+(x*13*3/100)=8160
x=8500
i.e money borrowed is Rs.8500
ANSWER:C
Answer: C
Question: Convert the 11/36 m/s into kilometers per hour?
Options:
A)1.7
B)1.5
C)1.3
D)1.1
E)1.2
Rationale: 11/36 m/s = 11/36 * 18/5 = 11/10
= 1.1 kmph.
Answer: D
Answer: D
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
Options:
A)area=3
B)4
C)5
D)6
E)7
Rationale: S = (1 + 2 + 3) /2 = 3
=> No triangle exists
Answer: A
Answer: A
Question: The cost of registration at a professional association meeting was $50 per person; a lunch for registrants only was available for an additional $22 per person. If the number of registrants who paid for lunch was 30 more than the number who did not, and if receipts for registration and lunch totaled $75,360, how many people paid just for registration at the meeting?
Options:
A)700
B)800
C)600
D)1,500
E)1,800
Rationale: Hope this might be useful to you.
Let the number of people who have opted only to register = x
Now since the registration cost is 50$ per person, the total amount sums to = 50x $
As per the information given in the question, the number of registrants who paid for lunch was 30 more than the number who did not. That means, total number of people who registered and paid for lunch = 30 + x.
For the people who registered for lunch the cost is 50 $ (for the event registration) + 22 $ (for lunch) = 72 $.
Total amount in this case sums to = 72(30 + x) = 2160 + 72x
Now, total amount received was 75360.
Thus, from the above data,
50x + 2160 + 72x = 75360
122x = 75360 - 2160
122x = 73200
x = 600.
Hence the correct Ans is C
Answer: C
Question: You have been given a physical balance and 5 weights of 45, 42, 37, 36 and 67 kgs. Keeping weights on one pan and object on the other, what is the maximum you can weigh less than 157 kgs.
Options:
A)160
B)151
C)154
D)153
E)152
Rationale: 45+42+67 = 154
Answer: C
Answer: C
Question: Three numbers are in the ratio 4 : 5 : 6 and their average is 42 . The largest number is:
Options:
A)28
B)32
C)36
D)50.4
E)45
Rationale: Explanation:
Let the numbers be 4x, 5x and 6x. Therefore,
(4x+5x+6x)/3 = 42
15x = 126
x = 8.4
Largest number = 6x = 50.4.
ANSWER D
Answer: D
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
Options:
A)20 m
B)60 m
C)40 m
D)80 m
E)90 m
Rationale: 1/2 * d (10 + 6) = 640
d = 80
ANSWER:D
Answer: D
Question: In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder. The dividend is?
Options:
A)80
B)86
C)92
D)94
E)96
Rationale: Divisor = (6 * 3) + 2 = 20
5 * Quotient = 20
Quotient = 4.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 4) + 6 = 86
B)
Answer: B
Question: If n = 2×3×5×7×11×13, then which of the following statements must be true?
I. n2 is divisible by 600
II. n + 19 is divisible by 19
III. is even n+4 / 2 = even
IV . n is Divisible by 35
Options:
A)none and IV only
B)b- II only
C)III only
D)I and III only
E)e None
Rationale: 2×3×5×7×11×13= 2310
I. not divisible by 600
II 2310+19=2329 not divisible by 19
III. 2310+4/2= odd
iv. divisible by 35
A
Answer: A
Question: 700 students took the test on English and Maths. 35% students failed in english and 45% failed in maths. 40% of those who passed in maths also passed in english, then how many students failed in both ?
Options:
A)162
B)138
C)60
D)38
E)14
Rationale: Passed in english = 65%
Passed in maths = 55%
Passed in both = 40% of 55% = 2/5 * (55%) = 22%
Passed in (English + Maths - Both + Neither) = 100%
65 + 55 - 22 + Neither = 100
Neither = 100 - 98 = 2% = 0.02 * 700 = 14
Answer: E
Answer: E
Question: A group of 16 people plan to rent a van and agree to share equally the total cost of the rental, which is E dollars. If n of the people decide not to participate at the last minute, by how many dollars will each remaining person's share of the total cost increase?
Options:
A) E/(12 - n)
B) nE / [16(16-n)]
C) E/[12(12-n)]
D) (12 - n)/E
E) (12-n)E/(12n)
Rationale: total cost =E
no of people willing to participate initially =16
initial cost for each =E/16
when n people decided not to participate
Cost for each =E/16-n
B
Answer: B
Question: Mangala completes a piece of work in 10 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?
Options:
A)8 days
B)10 days
C)11 days
D)12 days
E)14 days
Rationale: 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 = 10 × 40/50 = 8 days
A)
Answer: A
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
Options:
A)27
B)29
C)17
D)10
E)86
Rationale: Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer:D
Answer: D
Question: The side of a square has the length of 5. What is the area of the region shaded?
Options:
A)48-8π
B)48-6 π
C)24+6π
D)16-5π
E)64-8π
Rationale: The area of a square whose side is 5 – (the area of a square whose side is 4 + the area of the semi-circle whose side is 4) = the area of the region shaded
The correct answer is D.
Answer: D
Question: x - y = 4
2x = 2y + 8
The system of equations above has how many solutions?
Options:
A) None
B) Exactly one
C) Exactly two
D) Exactly three
E) Infinitely many
Rationale: x-y=4 ---------------1
2x=2y+8 ---------------2
Divide equation 2 by 2:
2x/2=(2y+8)/2
x=y+4
x-y=3----------------3
Equation 1 and 3 are equal and thus have infinitely many solutions:
x-y=4
x=8, y=4
x=6, y=2
x=7, y=3
Ans:E
Answer: E
Question: A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both spade. Find the probability of the lost card being a spade.
Options:
A)10/50
B)10/53
C)11/50
D)11/53
E)12/53
Rationale: total cards:52
drawn cards(spade):2
now, actual present total cards=total cards-drawn cards=52-2=50
total spade=spade-drawn cards(spade)=13-2=11
so,probability=11/50
ANSWER:C
Answer: C
Question: Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 15 percent during the third year. What is the value of the account today?
Options:
A)$10,350
B)$9817.50
C)$10,500
D)$11,500
E)$12,705
Rationale: Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.85 = 10,395
Answer B is correct.
Answer: B
Question: Integer d is the product of the integers a,b, and c and 1<a<b<c. If the remainder when 233 is divided by d is 79, what is the value of a+c?
Options:
A)7
B)9
C)13
D)14
E)18
Rationale: 79 is the remainder, therefore the number(a*b*c) or multiple of the number we need is 79 less than 233
Hence 233- 79 = 154
Therefore, 154 is either a number we want or it is a multiple of the number we want
But the largest factor of 154 is 77 because 77 * 2 =154
But 77 is less than 79 hence it can not be a number
Thus 154 is the number we want
a*b*c= 154
now factorize 154 =1*2*7*11 all are prime
Also we know 1<a<b<c
thus a = 2 and c = 11
therefore a+c= 2+11= 13
ANSWER:C
Answer: C
Question: If 2/X - 2 = 3/X - 3, then X =
Options:
A)-3/2
B)2/3
C)-1
D)1
E)3/2
Rationale: We're given the equation 2/X - 2 = 3/X - 3. We're asked for the value of X.
The common-denominator of these 4 numbers is X, so we need to multiply both sides of the equation by X, giving us...
2X/X - 2X = 3X/X - 3X
We can then eliminate that denominator, which gives us....
2 - 2X = 3 - 3X
1 = X
D
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 6 sec. What is the length of the train?
Options:
A)535 m
B)100 m
C)186 m
D)168 m
E)150 m
Rationale: Speed = 60 * 5/18
= 50/3 m/sec
Length of the train
= speed * time
= 50/3 * 6
= 100 m
Answer:B
Answer: B
Question: The edges of a cuboid are 4 cm, 5 cm and 6 cm. Find the volume of the cuboid?
Options:
A)120
B)388
C)278
D)298
E)271
Rationale: 4*5*6 = 120
Answer: A
Answer: A
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 metres and they cross each other in 12 seconds, then the speed of each train (in km/hr) is:
Options:
A)30
B)36
C)40
D)45
E)50
Rationale: Speed => x
two trains = 2x
2x = 120+120/12==>2x=20
x=10
speed = 10 m/sec = 10*18/5=36
ANSWER B
Answer: B
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
Options:
A)6 min
B)7 min
C)9 min
D)4 min
E)2 min
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute
= (1/6 - 1/10)
= 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) '
= 6 min.
So, the tank will be emptied in 6 min.
Answer:A
Answer: A
Question: The speed of a boat in still water is 30 kmph. What is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time?
Options:
A)11 kmph
B)10 kmph
C)12 kmph
D)16 kmph
E)15 kmph
Rationale: X = the speed of the stream
(30 + X) / (30 - X) = 2/1
30+ X = 60 - 2X
3X = 30
X = 10 km/hour
If the speed of the stream is 10km/hour, then the 'downstream' speed of the boat is 30+10= 40km/hour and the 'upstream' speed of the boat is 30-10 = 20km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x40 = 80km downstream and 2x20 = 40 km/hour upstream.
Answer : B
Answer: B
Question: A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)3:5
B)3:4
C)3:8
D)3:9
E)3:1
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer:B
Answer: B