divelab/Sys2Bench huggingface dataset:
Question: Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?
Options:
A)3 pm
B)2 pm
C)1:00 pm
D)11 am
E)12 am
Rationale: Explanation :
Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the machines were operating.
Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60
Pending work = 1- 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm
Answer : Option C
Answer: C
Question: The distance from City A to City B is 200 miles. While driving from City A to City B, Glen drives at a constant speed of 40 miles per hour. Hannah leaves City A 108 minutes after Glen. What is the minimum constant speed in miles per hour that Hannah must exceed in order to arrive in City B before Glen?
Options:
A)52.5
B)55
C)57.5
D)60
E)62.5
Rationale: The time it takes Glen to drive to City B is 200 / 40 = 5 hours.
Hannah needs to take less than 3.2 hours for the trip.
Hannah needs to exceed a constant speed of 200 / 3.2 = 62.5 miles per hour.
The answer is E.
Answer: E
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
Options:
A)87
B)67
C)23
D)75
E)25
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
Answer: C
Answer: C
Question: The value for A=(0.889 × 55)/9.97 to the nearest tenth is
Options:
A)0.5
B)4.63
C)4.9
D)7.7
E)49.1
Rationale: if we read the Q, we can easily home on to the answer,,
the numerator is clearly between 40 and 50..
denomiator is close to 10..
so A=(0.889 × 55)/9.97 is between 4 and 5..
It may tempt us to solve it since ther are two values between 4 and 5..
but the catch is innearest tenth
4.63 can be called nearest to hundreth and no tenth, so can be eliminated..
4.9 is our answer...
C
Answer: C
Question: The perimeter of a triangle is 32 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)87 cm2
B)28 cm2
C)98 cm2
D)26 cm2
E)40 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 32/2
= 40 cm2
Answer:E
Answer: E
Question: A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 9000 interest. The principal amount borrowed by him was.
Options:
A)Rs 14000
B)Rs 25000
C)Rs 16000
D)Rs 17000
E)None of these
Rationale: Explanation:
S.I.=Pâˆ—Râˆ—T/100
=>P=S.I.âˆ—100/Râˆ—T
=>P=9000âˆ—100/12âˆ—3=Rs25000
Option B
Answer: B
Question: A motor pool has 500 vehicles of which 30 percent are trucks. 20 percent of all the vehicles in the motor pool are diesel, including 15 trucks. What percent of the motor pool is composed of vehicles that are neither trucks nor diesel?
Options:
A)165%
B)90%
C)53%
D)55%
E)10%
Rationale: Trucks = 30% of 500 = 150
Other Vehicles (Excluding Trucks) = 500-150 = 350
Diesel Vehicle = 20% of 500 = 100 (Including 15 Trucks)
Other Diesel Vehicles (Excluding Trucks) = 100-15 = 85
Trucks that are NOT diesel = 150 - 15 = 135
Other Vehicles that are NOT diesel Vehicles = 350-85 = 265
Required % = (265/500)*100 = 53%
Answer: option C
Answer: C
Question: Find the average of all prime numbers between 30 and 50.
Options:
A)30
B)33.6
C)39.8
D)44.9
E)None
Rationale: Sol.
There are five prime numbers between 30 and 50.
They are 31, 37, 41, 43 and 47
∴ Required average = [31 + 37 + 41 + 43 + 47 / 5] = 199/ 5 = 39.8
Answer C
Answer: C
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
Options:
A)4.1%
B)4.04%
C)4.35%
D)5.04%
E)4%
Rationale: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Answer: B
Question: A man can row at 5 kmph in still water. If the velocity of current is 2 kmph and it takes him 1 hour to row to a place and come back, how far is the place?
Options:
A)2.1 km
B)2.9 km
C)3.4 km
D)4.4 km
E)5.6 km
Rationale: Explanation:
Speed in still water = 5 kmph
Speed of the current = 1 kmph
Speed downstream = (5+2) = 7 kmph
Speed upstream = (5-2) = 3 kmph
Let the required distance be x km
Total time taken = 1 hour
â‡’ x/7+x/3=1
â‡’3x+7x=21
â‡’10x=21
â‡’x=2.1 km
Answer: Option A
Answer: A
Question: Johnson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another.
Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?
Options:
A)0.14
B)0.26
C)0.49
D)0.55
E)0.86
Rationale: probability of adams approval = 0.7
baker approval =0.5
corfu approval=0.4
proabability of approval is must adam approval and atleast one approval
= adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+
adam approval*baker not approval*coffu approval( atleast one remaining approval
= 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4
=0.14+0.21+0.14
=0.49
so answer C sufficient
Answer: C
Question: If the odd numbers between 20 to 40 are arranged in a row, what will be the 6th number from the right?
Options:
A)27
B)31
C)33
D)25
E)29
Rationale: 21,23,25,27,29,31,33,35,37,39 these are odd numbers between 20 to 30. The question is 6th number from the right is 29
ANSWER:E
Answer: E
Question: From a pack of cards two cards are drawn one after the other, with replacement. The probability that the first card is a black and the second card is a spade is?
Options:
A)1/16
B)1/8
C)1/13
D)1/26
E)1/52
Rationale: Probability of a black card= 26/52 = 1/12
Probability of a jack = 13/52 = 1/4
Probability of both = P1*P2 = 1/(2*4) = 1/8
Answer is B.
Answer: B
Question: What would be the seventh rung of the following pyramid?
1
11
21
1211
111221
312211
13112221
Options:
A)1113213211
B)1223213211
C)1527321321
D)1112343211
E)1532213211
Rationale: A
1113213211. After the first line, each line describes the previous line as follows:
One 1
2 Ones
One 2, One 1
(and so on...)
Answer: A
Question: Cindy wants to buy dolls for her playhouse. Each doll costs $10. Cindy's mother gives her $30 to spend. How many dolls can Cindy buy with the money her mother gave her?
Options:
A)5
B)10
C)2
D)1
E)3
Rationale: E. 3
Answer: E
Question: Which of the following inequalities is equivalent to 2 + 5x > 17?
Options:
A) x > -2
B) x > 3
C) x > -3
D) x < -3
E) x < 3
Rationale: You can work with the inequality in the same way as you do when you have the equal to sign. You can take terms to the other side by flipping their sign, you can multiply/divide the inequality by the same term on both sides of the equation etc.
The only important thing to note is the following:
When you multiply/divide by a negative number, the sign of the inequality flips.
To illustrate,
2 + 5x > 17
5x > 15 (Correct)
x > 3 (Correct)
the correct option is B
Answer: B
Question: A man has Rs. 560 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)94
C)96
D)105
E)99
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 560
16x = 560
x = 35.
Hence, total number of notes = 3x = 105.
D
Answer: D
Question: I. x2 - x - 42 = 0,
II. y2 - 17y + 72 = 0 to solve both the equations to find the values of x and y?
Options:
A)If x < y
B)If x > y
C)If x ≤ y
D)If x ≥ y
E)If x = y or the relationship between x and y cannot be established.
Rationale: I. x2 - 7x + 6x - 42 = 0
=> (x - 7)(x + 6) = 0 => x = 7, -6
II. y2 - 8y - 9y + 72 = 0
=> (y - 8)(y - 9) = 0 => y = 8, 9
=> x < y
ANSWER:A
Answer: A
Question: 4
x
<
y
<
0
which of the following is greatest?
Options:
A)x+3y
B)2x-y
C)-(5x+y)
D)-x+2y
E)4x+3y
Rationale: Plugging in -1 for both x and y we get
A.x+3y =-4
B. 2x-y=-1
C. -(5x+y)=6
D. -x+2y =-1
E. 4x+3y=-7
Answer: C
Answer: C
Question: Adam borrowed some money at the rate of 6% p.a. for the first two years, at the rate of 9% p.a. for the next three years, and at the rate of 14% p.a. for the period beyond five years. If he pays a total interest of 11,400 at the end of nine years, how much money did he borrow?
Options:
A)10,000
B)12,000
C)14,000
D)16,000
E)None of these
Rationale: Let the sum borrowed be x. Then,
(x×6×21/00)+(x×9×3/100)+(x×14×4/100)= 11400
⇒ (3⁄25x + 27⁄100x + 14⁄25x) = 11400 ⇒ 95⁄100x = 11400
⇒ x = (11400×100/95)= 12000
Hence, sum borrowed = 12,000.
Answer B
Answer: B
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 110 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
Options:
A)28 sec
B)16 sec
C)35 sec
D)18 sec
E)17 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 110 = 350 m.
Time taken = 350/10 = 35 sec.
Answer:C
Answer: C
Question: If 12 persons are seated in a row, the number of ways of selecting 3 persons from them, so that no two of them are seated next to each other is
Options:
A)85
B)100
C)120
D)240
E)None of these
Rationale: The number of ways of selecting 3 persons from 12 people under the given condition :
Number of ways of arranging 3 people among 9 people seated in a row, so that no two of them are consecutive
= Number of ways of choosing 3 places out of the 10[8 in between and 2 extremes]
= 10C3 = 10×9×8/3×2×1=5×3×8=120
Answer C
Answer: C
Question: A is twice as good a workman as B and they took 7 days together to do the work B alone can do it in.
Options:
A)11 days
B)13 days
C)21 days
D)16 days
E)18 days
Rationale: WC = 2:1
2x + x = 1/7
x = 1/21 => 21 days
Answer: C
Answer: C
Question: An ant and a blind spider are on opposite corners of a cube. The ant is stationary and the spider moves at random from one corner to another along the edges only. What is the expected number of turns before the spider reaches the ant?
Options:
A)20
B)43
C)38
D)10
E)55
Rationale: The answer is 10.
If the spider started at a corner diagonally on the same face as the ant the answer would be 9, and if the spider started at an adjacent corner the answer would be 7.
Let x=number of turns to reach ant from starting point.
Let y=number of turns to reach ant from diagonal corner on same face as ant.
Let z=number of turns to reach ant from an adjacent corner to ant.
After one turn the spider will be on a diagonal corner of a common face as the ant. So the mean number of turns from the x position is one more than the mean number from the y position:
E(x)=1+E(y).
Once at a y position there is a 2/3 chance it will then move to a z position, and a 1/3 chance back to an x position:
E(y)=(2/3)*(1+E(z))+(1/3)*(1+E(x)).
If the spider arrives at a z position there is a 1/3 chance it will move to the ant, and a 2/3 chance it will move back to a y position:
E(z)=(1/3)*1+(2/3)*(1+E(y)).
With these three equations and three unknowns it is not difficult to solve for E(x), E(y), and E(z).
correct answer D
Answer: D
Question: Find the value of 72519 x 9999 = m?
Options:
A)345454621
B)565767443
C)457672466
D)725117481
E)665355224
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: D
Question: The average of five numbers is 70. If one number is excluded, the average becomes 72. The excluded number is?
Options:
A)8
B)6
C)58
D)35
E)62
Rationale: Excluded number
= (70 * 5) - (72 * 4)
= 350 - 288 = 62
Answer:E
Answer: E
Question: Convert the 12/36 m/s into kilometers per hour?
Options:
A)3.5 kmph.
B)2.5 kmph.
C)1.2 kmph.
D)1.5 kmph.
E)1.9 kmph.
Rationale: 15/36 m/s = 12/36 * 18/5 = 1 (1/5) = 1.2 kmph.
ANSWER:C
Answer: C
Question: The average age 4 members of a committee are the same as it was 2 years ago, because an old number has been replaced by a younger number. Find how much younger is the new member than the old number?
Options:
A)8 years
B)17 years
C)18 years
D)12 years
E)11 years
Rationale: 4 * 2
= 8
Answer:A
Answer: A
Question: Real-estate salesman Z is selling a house at a 10 percent discount from its retail price. Real-estate salesman X vows to match this price, and then offers an additional 10 percent discount. Real-estate salesman Y decides to average the prices of salesmen Z and X, then offer an additional 10 percent discount. Salesman Y's final price is what fraction of salesman X's final price?
Options:
A)38/6
B)38/5
C)77/81
D)38/7
E)38/10
Rationale: Let the retail price be = x
Selling price of Z = 0.90x
Selling price of X = 0.90*0.90x = 0.81x
Selling price of Y = ((0.90x + 0.81x)/2)*0.90 = 0.86x * 0.90 = 0.77x
0.77x = k * 0.81x
k = 0.77/0.81 = 77/81
Answer: C
Answer: C
Question: 10 play kabadi, 35 play kho kho only, 5 play both gmaes. Then how many in total?
Options:
A)30
B)35
C)38
D)40
E)45
Rationale: 10 play kabadi =>n(A)=10,
5 play both gmaes.=> n(AnB)=5
35 play kho kho only,=>n(B)=n(B only)+n(AnB)=35+5=40
Total => n(AUB)= n(A)+n(B)-n(AnB)
= 10+40-5
= 45
ANSWER:E
Answer: E
Question: If a toy store's revenue in November was 4/5 of its revenue in December and its revenue in January was 1/4 of its revenue in November, then the store's revenue in December was how many times the average (arithmetic mean) of its revenues in November and January?
Options:
A) 1/4
B) 1/2
C) 2/3
D) 2
E) 4
Rationale: Let Dec rev =100
Then Nov rev is 4/5 (100) => 80
Therefore Jan rev = 1/4(Nov rev) = 1/4(80) => 20
Hence Dec rev = x*( Nov rev+Jan rev)/2
100 = x* (80+20)/2
x = 100/50 => 2
Ans) D
Answer: D
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 246 m, what is its area?
Options:
A)2510
B)3650
C)2530
D)2515
E)2520
Rationale: length = breadth +23. Therefore,
4× breadth +2×23=246 m
⇒ breadth =50 m
length =50+23=73 m
Area =73×50=3650 m2
Answer is B.
Answer: B
Question: If a randomly selected non-negative single digit integer is added to {2, 3, 5, 8}. What is the probability that the median of the set will increase but the range still remains the same?
Options:
A)0.2
B)0.3
C)0.4
D)0.5
E)0.6
Rationale: We are selecting from non-negative single digit integers, so from {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. These 10 digits represent the total number of outcomes.
Hence, the total number of outcomes is 10.
We need to find the probability that the median of the set will increase but the range still remains the same.
The median of the set is (3 + 5)/2 = 4, thus the number selected must be 5 or greater.
For the range to remain the same, the number must be between 2 and 8 inclusive.
To satisfy both conditions, the number selected must be 5, 6, 7, or 8.
The probability is 4/10 = 0.4
The answer is C.
Answer: C
Question: There are 12 person among whom 2 are brother. The total no.of ways in which these persons can be seated around a round table so that exactly 1 person sit between the brothers, is equal to?
Options:
A)9!*2!
B)7!*2!
C)6!*1!
D)2!*1!
E)5!*1!
Rationale: Total number of ways = 9!*2!.
A
Answer: A
Question: The C.P of 20 pens is equal to the S.P of 22 pens. Find his gain % or loss%?
Options:
A)6 2/11%
B)7 2/11%
C)9 1/11%
D)8 1/11%
E)10 1/11%
Rationale: 20 CP = 22 SP
22 --- 2 CP loss
100 --- ? => 9 1/11%
Answer: C
Answer: C
Question: A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
Options:
A)36
B)54
C)67
D)76
E)None
Rationale: Sol.
Let the length of the train be x metres.
Then, the train covers x metres in 8 seconds and (x + 180) metres in 20 seconds.
∴ x/8 = x + 180 / 20 ⇔ 20x = 8(x + 180) ⇔ x = 120.
∴ Length of the train = 120 m.
Speed of the train = [120/8]m/sec = m/sec = [15 * 18/5]kmph = 54 kmph.
Answer B
Answer: B
Question: which of the following could be the greatest common factor of positive integers 4 and 8 ?
I) 8 II) 4 III) 2
Options:
A)III only
B)II only
C)I only
D)I,II only
E)II,III only
Rationale: 4=2*2
8=2*2*4
GCF = 2*2 = 4
Answer : B
Answer: B
Question: Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?
Options:
A)82,92
B)63,98
C)83,98
D)60,84
E)63,98
Rationale: (5x-25):(7x-25) = 35:59
x = 12 => 60,84
Answer:D
Answer: D
Question: P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
Options:
A)10
B)5
C)15
D)20
E)25
Rationale: Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1
Ie, the work will be done in 15 days.
Answer is C.
Answer: C
Question: In a School, 69 percent of students Participated in Chess, 74 percent of students Participated in Table Tennis, 84 percent Participated in Carom and 79 percent Participated in shuttle.
Can you find out the percentage of students who Participated in all 4 Competition?
Options:
A)12%
B)10%
C)6%
D)18%
E)19%
Rationale: C
6% of student Participated in all four Competition.
Answer: C
Question: Sam's grade was 60th percentile of the 100 grades for his class. Of the 120 grades from another class, 48 were higher than Sam's, and the rest were lower. If no other grade was the same as Sam's grade, then Sam's grade was what percentile of the grades of the two classes of two classes combined?
Options:
A)51st
B)60th
C)67th
D)72nd
E)92nd
Rationale: 51st/60th/67th/72nd/92nd
Correct option: B
Answer: B
Question: How many numbers amongst the numbers 7 to 41 are there which are exactly divisible by 9 but not by 3?
Options:
A)Nil
B)1
C)2
D)3
E)More than 3
Rationale: 9,18,27,36 are divisible by 9 and 3 also.So there are no numbers exactly divisible by 9 but not by 3
ANSWER:A
Answer: A
Question: A new home buyer pays 4% annual interest on her first mortgage and 9% annual interest on her second mortgage. If she borrowed a total of $300,000, 80% of which was in the first mortgage, what is her approximate monthly interest payment?
Options:
A)$1,250
B)$1,733
C)$3,466
D)$13,333
E)$20,796
Rationale: 0.04x + 0.09y = 300000 [1]
0.04x = 0.80 * 300000 = 240000 [2]
240000 + 0.09y = 300000 --> 0.09y = 60000 [3]
240000 / 12 = 20000 [4]
60000 / 12 = 5000 [5]
Adding [4,5] we get: 25000 [6]
Dividing [6] / 2 to get an average we get 1.25,ANS A
Answer: A
Question: When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ?
Options:
A)339
B)NONE
C)349
D)369
E)379
Rationale: x = 13p + 11 and x = 17q + 9
13p + 11 = 17q + 9
17q - 13p = 2
q =	2 + 13p
17
The least value of p for which q =	2 + 13p	is a whole number is p = 26
17
x = (13 x 26 + 11)
= (338 + 11)
= 349
ANSWER C
Answer: C
Question: A farm has chickens, horses and sheep. There are six times the number of chickens and cows than sheep. If there are more horses than chickens or sheep, and together, horsess and chickens have a total of 100 feet and heads, how many sheep live at the farm?
Options:
A)5
B)4
C)10
D)14
E)17
Rationale: Chicken - ch
horses - H
Sheep -S
ch+H=6S
H> ch and H>s
Each Horse has 4 legs and 1 head
Each chicken has 2 legs and 1 head
So 5h+3ch=100 (sum of legs and head)
There are 2 possible solutions to this equation
h=11 and ch=9 or
h=14 and ch=10
Since from first equation where ch+h=6s
The sum of ch and c should be divisbile by 6. 20 is not so the only possible solution is h=14 and ch=10. So s=4
Answer : B
Answer: B
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Options:
A)77
B)88
C)14
D)12
E)17
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer:C
Answer: C
Question: A fort had provision of food for 180 men for 45 days. After 25 days, 40 men left the fort. The number of days for which the remaining food will last, is:
Options:
A)29	1/5
B)25	3/4
C)42
D)54
E)45
Rationale: we have food for 180 men for 45 days.
After 25 days food left for 180 men for 20 days.
so
180 : 20
now we have 140 men and x days
140 : 180 :: 20 : x
x = (180*20)/140 = 25 3/4 days.
ANSWER:B
Answer: B
Question: A shopkeeper sells some toys at Rs. 250 each. What percent profit does he make? To find the answer, which of the following information given in Statements I and II is/are necessary?
I. Number of toys sold.
II. Cost price of each toy.
Options:
A)Only I is necessary
B)Only II is necessary
C)Both I and II are necessary
D)Either I or II ins necessary
E)None of these
Rationale: EXPLANATION
S.P. = Rs. 250 each.
To find gain percent, we must know the C.P. of each.
answer is (B).
Answer: B
Question: Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.9 sec
B)10.1 sec
C)10.6 sec
D)10.8 sec
E)10.2 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 160 = 300 m.
Required time = 300 * 9/250
= 54/5 = 10.8 sec.
Answer:D
Answer: D
Question: Mr. Yutaro’s class contains 6 boys and 10 girls. If two students are chosen, one at a time, from the class, what is the probability that a boy and a girl are chosen?
Options:
A)9/48
B)9/20
C)1/2
D)27/48
E)13/16
Rationale: Probability of a boy being chosen first, then a girl:
6/16 * 10/15
Probability of a girl being chosen first, then a boy:
10/16 * 6/15
Probability of a boy and a girl being chosen:
(6*10+6*10) / (15*16)
=1/2
Answer:C
Answer: C
Question: David started a business investing Rs. 70,000. Robert joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio amoung David, Robert and Sagar respectively, 3 years after David started the business?
Options:
A)12 : 10 : 16
B)12 : 15 : 16
C)15 : 12 : 16
D)16 : 15 : 12
E)None
Rationale: Sol.
David : Robert : Sagar = (70000 * 36) : (105000 * 30) : (140000 * 24)
= 12 : 15: 16.
Answer B
Answer: B
Question: A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1860 are infected, how manyworkersinhabit the colony?
Options:
A)1500
B)2500
C)2750
D)3000
E)3250
Rationale: From two question we get wo equations:
(1) 0,3s + 0,14w = 1860
(2) s + w = 7000
From (2) we get w=7000-s
In (1) 0,3s + 980-0,14s= 1860
0,16s=880
88000:16= 5500 =s
In (2) 5500 + w = 7000
w= 1500 A
Answer: A
Question: A travel agent offers a vacation plan which costs 'a' dollars for the first day, and a/10 for each additional day. How much does a vacation of b days cost, where b > 1.
Options:
A)(ab+9a)/5
B)(ab+8a)/10
C)(ab+9a)/2
D)(ab+5a)/10
E)(ab+9a)/10
Rationale: Cost = a + (b-1)*a/10 = (10a + (b - 1)*a)/10 = (ab+9a)/10
Answer is E
Answer: E