mathewhe/aqua_rat huggingface dataset:
Question: The cost per pound of green tea and coffee were the same in June. In July, the price of coffee shot up by 100% and that of green tea dropped by 70%. If in July, a mixture containing equal quantities of green tea and coffee costs $3.45 for 3lbs, how much did a pound of green tea cost in July?
(A) $4
(B) $0.3
(C) $1
(D) $3
(E) $1.65
Rationale: Lets assume price of Coffee in June =100x
Price of green Tea in June =100x
Price of Coffee in July = 200x (because of 100% increase in price)
Price of green Tea in July = 30x (because of 70% Decrease in price)
Price of 1.5 pound of Coffee 1.5 pound of green Tea in July will be = 300x + 45x = 345x
As per question
345x= 3.45$
x = 0.01S
So the Price of Tea in July = 30x = 30 x 0.01 = 0.3$/pound
Answer B
Answer: (B) $0.3
Question: The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.
(A) 48
(B) 48.55
(C) 46
(D) 34.5
(E) 50.0
Rationale: Avg weight of 16 boys = 50.25
tot weight of 16 boys = 50.25 * 16
avg weight of remaining 8 boys = 45.15
tot weight of remaining 8 boys=45.15*8
tot weight of remaining 8 boys = 45.15 * 8
tot weight of all boys = 50.25 * 16 + 45.15*18
=24
avg weight=(50.25*16)+(45.15*8)/24=48.55
ANSWER B
Answer: (B) 48.55
Question: Two numbers are in the ratio of 1 : 2. If 5 be added to both, their ratio changes to 3 : 5. The greater number is
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: Let the ratio be X : Y,
Given X/Y = 1/2 ,
(X + 5)/(Y + 5) = 3/5
=> X = 10
And Y = 20
ANSWER:A
Answer: (A) 20
Question: If R=30^65−29^65/3064+2964 then
(A) 0<R≤0.10<R≤0.1
(B) 0.1<R≤0.50.1<R≤0.5
(C) 0.5<R≤1.00.5<R≤1.0
(D) R<1.0
(E) R>1.0
Rationale: This question is based on your understanding of number properties. You don't have to do any calculations actually.
At higher powers, a difference of even 1 in the base creates creates a huge difference in the number. For example, 2^10=10242 but 3^10=59049.
So 30^65 will not be very different from 30^65-29^65
Similarly, 30^64 will not be very different from 30^64+29^64
So the question boils down to approx 30^65/30^64 This will be something less than 30 but certainly greater than 1.
Answer (E)
Answer: (E) R>1.0
Question: If the seventh day of a month is three days earlier than Friday, What day will it be on the nineteenth day of the month?
(A) Saturday
(B) Monday
(C) Sunday
(D) Wednesday
(E) None of these
Rationale: Explanation :
Given that seventh day of a month is three days earlier than Friday
=> Seventh day is Tuesday
=> 14th is Tuesday
=> 19th is Sunday, Answer : Option C
Answer: (C) Sunday
Question: The average of 6 observations is 14. A new observation is included and the new average is decreased by 1. The seventh observation is?
(A) 1
(B) 3
(C) 5
(D) 6
(E) 7
Rationale: Let seventh observation = X.
Then, according to the question we have
=> (84 + X) / 7 = 13
=> X = 7.
Hence, the seventh observation is 7.
ANSWER:E
Answer: (E) 7
Question: Machine A and machine E are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine E. Machine E produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: [Reveal]Spoiler:
TimeE: 660/x
TimeA: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeA
660/100+10 => 660/110 = 6
Answer: (A) 6
Question: A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number?
(A) 100
(B) 919
(C) 102
(D) 200
(E) 234
Rationale: 25 + 25 = 50
25% ------ 50
100% ----- ? => 200
Answer:D
Answer: (D) 200
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 40 as remainder. Find the no. is?
(A) 220044
(B) 145778
(C) 220400
(D) 220014
(E) 220040
Rationale: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220040
E
Answer: (E) 220040
Question: John distributes his pencil among his 4 friends Rose, Mary, Ranjan, and Rohit in the ratio 1/3 : 1/3 :1/4:1/5 . What is the minimum no. of pencils that the person should have?
(A) 45
(B) 67
(C) 70
(D) 77
(E) 98
Rationale: Rakesh : Rahul : Ranjan : Rohit = 1 / 3 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 3,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 3 x 60 ) = 20.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.
Step 3: Total number of pencils are ( 20 x + 20 x + 15 x + 12 x) = 67 x.
For minimum number of pencils x = 1 .
The person should have atleast 67 pencils.
B)
Answer: (B) 67
Question: A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours.
What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
(A) 1 hour
(B) 2 hour
(C) 3 hour
(D) 4 hour
(E) 5 hour
Rationale: In one hour,
Soln 1:
the large inlet tube fills 1 / 3 of the tank;
the small inlet tube fills 1 / 6 of the tank;
the outlet tube empties 1 / 9 of the tank; and therefore
all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank.
Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.
Soln 2:
Let V be the total volume of the tank. From equation (1),
Flow Rate (large inlet tube) = V / 3
Flow Rate (small inlet tube) = V / 6
Flow Rate (outlet tube) = V / 9.
Substituting in equation (2),
Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9).
Using the above result in equation (1),
Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ].
Note that V cancels out on simplifying the above expression.
Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.
Answer: (A) 1 hour
Question: For which of the following values of s is (20+s)/s an integer?
(A) 3
(B) 4
(C) 9
(D) 11
(E) 20
Rationale: This problem has to be solved by checking the options
(20 + s)/s
For this entity to be an integer, 50 + s should be divisible by s
Option A: 23/3 - Not an Integer
Option B: 24/4 - Not an Integer
Option C: 29/9 - Not an integer
Option D: 41/11 - Not an integer
Option E - 40/20 - Integer
Correct Option: E
Answer: (E) 20
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are drawn at random, what is the probability that at least one is green?
(A) 23/35
(B) 23/32
(C) 23/31
(D) 23/30
(E) 63/35
Rationale: Explanation:
Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
Probability that at least one green marble can be picked in the random draw of two marbles = Probability that one is green + Probability that both are green
= (â¶Câ‚ * â¹Câ‚)/Â¹âµCâ‚‚ + â¶Câ‚‚/Â¹âµCâ‚‚
= (6 * 9 * 2)/(15 * 14) + (6 * 5)/(15 * 14) = 36/70 + 1/7
= 46/70 = 23/35
Answer: A
Answer: (A) 23/35
Question: Kamal is 60 years old and Karthi is 80 years old. How many years ago was the ratio of their ages 4 : 6?
(A) 20 yrs
(B) 30 yrs
(C) 25 yrs
(D) 40 yrs
(E) 15 yrs
Rationale: (60-x)/(80-x) = 4/6
6(60-x)=4(80-x)
x = 20
ANSWER A
Answer: (A) 20 yrs
Question: The average of first 9 natural numbers is?
(A) 1.5
(B) 2.5
(C) 3.5
(D) 4.5
(E) 5.5
Rationale: Sum of 10 natural no. = 90/2 = 45
Average = 45/10 = 4.5
ANSWER:D
Answer: (D) 4.5
Question: In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2?
(A) 60
(B) 277
(C) 299
(D) 66
(E) 221
Rationale: 2:1 --- 60
1:2
2:4
---------------
3
3 ----------- 60
3 ----------- ? => 60 liters
Answer:A
Answer: (A) 60
Question: The average age of the mother and her six children is 11 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother
(A) 40
(B) 41
(C) 42
(D) 43
(E) 44
Rationale: Total age of mother and 6 children = avg x n = 11 x (6+1)= 77
If mother is excluded new average is (11 - 5) = 6
so for 6 children = 6 x 6 =36
so mother's age is 77 - 36 =41
Answer: Option B
Answer: (B) 41
Question: In a kilometer race, A beats B by 60 meters or 10 seconds. What time does A take to complete the race?
(A) 199 sec
(B) 156.7 sec
(C) 726 sec
(D) 127 sec
(E) 128 sec
Rationale: Time taken by B run 1000 meters
= (1000 * 10)/60 = 166.7 sec.
Time taken by A = 166.7 - 10
= 156.7 sec.
Answer: B
Answer: (B) 156.7 sec
Question: Increasing the original price of a certain item by 30 percent and then increasing the new price by 30 percent is equivalent to increasing the original price by what percent?
(A) 31.25
(B) 37.5
(C) 50.0
(D) 52.5
(E) 69.0
Rationale: We're told that the original price of an item is increased by 30% and then THAT price is increased by 30%....
IF....
Starting value = $100
+ 30% = 100 + .30(100) = 130
+ 30% = 130 + .30(130) = 130 + 39 = 169
The question asks how the final price relates to the original price. This is essentially about Percentage Change, which means we should use the Percentage Change Formula:
Percentage Change = (New - Old)/Old = Difference/Original
Doing either calculation will yield the same result:
59/100 = 69%
Final Answer:
E
Answer: (E) 69.0
Question: Sachin borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends money to Rahul
at 25/4% p.a. for 2 years. Find the gain of one year by Sachin.
(A) 110.5
(B) 111.5
(C) 112.5
(D) 113.5
(E) None of these
Rationale: Explanation:
Two things need to give attention in this question, First we need to calculate gain for 1 year only.
Gain in 2 year = [(5000×254×2100)−(5000×4×2100)]=(625−400)=225 So gain for 1 year = 2252=112.50
Answer: C
Answer: (C) 112.5
Question: The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years?
(A) 31
(B) 41
(C) 51
(D) 61
(E) 71
Rationale: Solution
Age of the teacher	= (37 x 15 - 36 x 14)
= 51 years.
Answer C
Answer: (C) 51
Question: In a group of 25, 13 can speak Latin, 15 can speak French, and 6 don't speak either. How many of these speak both Latin and French?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 8
Rationale: let no.of persons who speeks booth latin and french = x
so, no.of persons who speeks only latin = 13-x
no.of persons who speeks only french= 15-x
no.of persons who speeks dont speek any lag = 6
therefore (13-x)+(15-x)+x+6=25
34-x=25
x=9
ANSWER:A
Answer: (A) 9
Question: A train traveling at 72 kmph crosses a platform in 34 seconds and a man standing on the platform in 18 seconds. What is the length of the platform in meters?
(A) 240 meters
(B) 320 meters
(C) 420 meters
(D) 600 meters
(E) Cannot be determined
Rationale: Speed of train = 72 * (5/18) = 20 m/s
Lets consider the man as a stationery point on the platform.
Crossing the point gives us the length of the train.
Lt = 20 * 18 = 360 m.
Crossing the platform gives us the length of trainlength of platform.
L(t+p) = 20 * 34 = 680 m.
So, length of platform = 680 - 360 = 320 m
IMO, Answer
B
Answer: (B) 320 meters
Question: Siddharth wants to borrow Rs.4000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
(A) s.21.60
(B) s.21.68
(C) s.21.18
(D) s.14.4
(E) s.21.29
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.4,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 4,000{ [1 + 6/100]2 - 1 - 12/100}
= 4,000 {(1.06)2- 1 - 0.12} = 4,000(1.1236 - 1 - 0.12)
= 4,000 (0.0036) = 4 * 3.6
= Rs.14.4
Answer: D
Answer: (D) s.14.4
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/3 hours to fill the tank. The leak can drain all the water of the tank in?
(A) 4 1/3 hrs
(B) 7 hrs
(C) 8 hrs
(D) 14 hrs
(E) 15 hrs
Rationale: Work done by the tank in 1 hour = (1/2 - 1/3) = 1/14 Leak will empty the tank in 14 hrs.
ANSWER:D
Answer: (D) 14 hrs
Question: Find the smallest number which should be multiplied with 13225 to make it a perfect square.
(A) 25
(B) 5
(C) 1
(D) 23
(E) 6
Rationale: 13225 = 5*5*23*23
Required smallest number = 1
1 is the smallest number which should be multiplied with 13225 to make it a perfect square.
ANSWER:C
Answer: (C) 1
Question: If 36 men can do a piece of work in 20 hours, in how mwny hours will15 men do it?
(A) 22
(B) 48
(C) 60
(D) 88
(E) 72
Rationale: Explanation:
Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
\inline \fn_jvn \therefore 15:36 ::20:x \inline \fn_jvn \Leftrightarrow (15 x X)=(36 x 20) \inline \fn_jvn \Leftrightarrow \inline \fn_jvn x=\frac{36\times 20}{15}=48
Hence, 15 men can do it in 48hours.
Answer: B)48
Answer: (B) 48
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 38 years now, the son's age five years back was?
(A) 14yr
(B) 15yr
(C) 20yr
(D) 25yr
(E) 30yr
Rationale: Let the son's present age be x years
Then, 38-x = x
x = 19
Son's age 5 years back = 19-5 = 14 years
Answer is A
Answer: (A) 14yr
Question: The value of “A” varies in inverse proportion as the square of “B”. If the value of “A” is equal to 40 when “B” is equal to 12. What would be the value of “A” when “B” is equal to 24 ?
(A) 10
(B) 88
(C) 26
(D) 27
(E) 28
Rationale: Explanation:
We have, A α 1/B2
A * B2 = K (constant)
When B = 12, A = 40 …..Given
K = 40 * (12)2 = 5760
Now, B = 24. Hence, A = 5760 / 576 = 10
ANSWER: A
Answer: (A) 10
Question: In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 55 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 9x/80
(B) 13x/20
(C) 80/9x
(D) 20x/13
(E) 80x/11
Rationale: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;
Sales of Japanese tools = 55% of the sales of imported tools = 0.55*{total}/4 = 11/20*{total}/4 = 11*{total}/80.
Since the sales of of Japanese tools was x, then 11*{total}/80 = x --> {total} = 80x/11.
Answer: E.
Answer: (E) 80x/11
Question: what is the smallest integer that is multiple of 5,7,9
(A) A)70
(B) B)315
(C) C)200
(D) D)280
(E) E)140
Rationale: It is the lcm of 5, 7 and 9 which is 315.
The answer is B.
Answer: (B) B)315
Question: What is the difference between the compound interest on Rs.12000 at 28% p.a. for one year when compounded yearly and half yearly?
(A) 399
(B) 383
(C) 235
(D) 288
(E) 133
Rationale: When compounded annually, interest
= 12000[1 + 28/100]1 - 12000 = Rs.3360
When compounded semi-annually, interest
= 12000[1 + 14/100]2 - 12000 = Rs.3595.2
Required difference = 3595.2 - 3360 = Rs.235.2
Answer: C
Answer: (C) 235
Question: Nelson borrowed some money at the rate of 6 p.c.p.a. for the first three years, 9 p.c.p.a. for the next five years and 13 p.c.p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is 8,160, how much money did he borrow?
(A) 12,000
(B) 10,000
(C) 8,000
(D) Data inadequate
(E) None of these
Rationale: Let ‘x’ be the amount borrowed by Nelson
and x×6×3/100+x×9×5/100+x×13×3/100=8160
⇒ 102⁄100x = 8,160
∴ x = 8,160×100102=8000
Answer C
Answer: (C) 8,000
Question: Monica planned her birthday party. She prepared 5 muffins for each of her guests and kept aside two additional muffins in case someone will want extra. After the party, it turned out that one of the guests didn't come but every one of the guests that did come ate six muffins and 4 muffins remained. How many guests did Monica plan on?
(A) 3.
(B) 4.
(C) 5.
(D) 6.
(E) 7.
Rationale: Let x be the number of guests.
Number of muffins prepared = 5x + 2
Number of muffins eaten + Number of muffins remaining = Number of muffins prepared
6(x - 1) + 4 = 5x + 2
6x - 4 = 5x + 2
x = 6
Answer: D
Answer: (D) 6.
Question: The present ages of A,B & C are in the ratio of 5:7:8. 7years ago, the sum oftheir ages was 59. What is the present age of eldest one?
(A) 30
(B) 31
(C) 32
(D) 35
(E) 36
Rationale: Let their present ages be 5x, 7x and 8x.
7 years ago, sum of their ages was 59.
Sum of their present ages = 59 +( 3 x 7) = 80
Sum of their present ages given is 5x + 7x + 8x = 20x
20x = 80 =>x = 80 20
=4
Age of the Eldest one= 8x = 8x 4 = 32 years.
C
Answer: (C) 32
Question: A, B, K start from the same place and travel in the same direction at speeds of 30km/hr, 40km/hr, 60km/hr respectively. B starts six hours after A. If B and K overtake A at the same instant, how many hours after A did K start?
(A) 3
(B) 4.5
(C) 4
(D) d) 12
(E) e) 5
Rationale: The table you made doesn't make sense to me. All three meet at the same point means the distance they cover is the same.
We know their rates are 30, 40 and 60.
Say the time taken by B is T hrs. Then A takes 6+T hrs. And we need to find the time taken by K.
Distance covered by A = Distance covered by B
30*(6+T) = 40*T
T = 18 hrs
Distance covered by B = Distance covered by K
40*T = 60*Time taken by K
Time taken by K = 40*18/60 = 12 hrs
Time taken by A = 6+T = 6+18 = 24 hrs
Time taken by K = 12 hrs
So K starts 24-12 = 12 hrs after A. (ANSWER D)
Answer: (D) d) 12
Question: How long does a train 110 m long traveling at 72 kmph takes to cross a bridge of 170 m in length?
(A) 16.5
(B) 16.0
(C) 16.4
(D) 14
(E) 16.1
Rationale: D = 110 + 170 = 280 m
S = 72 * 5/18 = 20
T = 280 * 1/20 = 14 sec
Answer: D
Answer: (D) 14
Question: As part of her MBA program, Karen applied for three different Spring Break outreach projects, each of which selects its students by a random lottery of its applicants. If the probability of her being accepted to each individual project is 30%, what is the probability that Karen will be accepted to at least one project?
(A) 729/1000
(B) 657/1000
(C) 343/500
(D) 123/250
(E) 17/100
Rationale: Since the probability of Karen's being accepted to each individual project is 30%, the probability of her not being accepted to each project is 70%. The probability that she will be accepted to none is, therefore, (7/10)*(7/10)*(7/10)=343/1000.
P(Karen will be accepted to at least one project) = 1 - (343/1000) = 657/1000.
The answer is B.
Answer: (B) 657/1000
Question: For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 25 percent of the seeds in the first plot germinated and exactly 40 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
(A) 12%
(B) 26%
(C) 29%
(D) 31%
(E) 60%
Rationale: In the first plot 25% of 300 seeds germinated, so 0.25 x 300 = 75 seeds germinated.
In the second plot, 40% of 200 seeds germinated, so 0.4 x 200 = 80 seeds germinated.
Since 75 + 80 = 155 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (155/500) x 100%, or 31%.
Answer: D.
Answer: (D) 31%
Question: Which of the following numbers must be added to 5678 to give a remainder of 35 when divided by 460?
(A) 797
(B) 798
(C) 799
(D) 796
(E) 795
Rationale: 5678 - 35 + (one of the answer option) should be divisible by 460. Only option C satisfies.
Answer:A
Answer: (A) 797
Question: How many multiples of 3 are less than 6500, and also multiples of 7?
(A) 104
(B) 208
(C) 310
(D) 340
(E) 454
Rationale: LCM of 3 & 7 = 21
Tried dividing 6500 by 21
Got quotient 309.5'So C is answer
Answer: (C) 310
Question: If (A-B-C+D = 13) and (A+B-C-D = 5), what is the value of (B-D)^2?
(A) 4.
(B) 8.
(C) 12.
(D) 16
(E) 64
Rationale: A-B-C+D = 13 -- equation 1
A+B-C-D = 5 -- equation 2
Adding 1 and 2 , we get
2A - 2C = 18
=> A-C = 9 -- equation 3
Using equation 3 in 2 , we get
B-D = 5 - 9 = -4
=>(B-D)^2 = 16
Answer D
Answer: (D) 16
Question: What is the sum of all the multiples of 7 between 30 and 100?
(A) 692
(B) 700
(C) 677
(D) 654
(E) 665
Rationale: You first have to know all the multiples of 7 between 30 and 100. They are 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98. If you add all these numbers together, you get 665.
Final Answer:
E
Answer: (E) 665
Question: In how many different number of ways 1 boys and 2 girls can sit on a bench?
(A) 700
(B) 7
(C) 6
(D) 8
(E) 1
Rationale: npn = n!
3p3 = 3 × 2 × 1 = 6
C)
Answer: (C) 6
Question: A bangle was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) Rs.800
(B) Rs.700
(C) Rs.1000
(D) Rs.1100
(E) Rs.1200
Rationale: 90%
104%
--------
14% ---- 140
100% ---- => Rs.1000
C
Answer: (C) Rs.1000
Question: John was thrice as old as Tom 6 yrs back. He will be 5/3 times as old as Tom 6 years hence. How old is Tom today?
(A) 8 years
(B) 10 years
(C) 12 years
(D) 14 years
(E) 15 years
Rationale: Sol. RMBflSk -6 = 3 (Ravi - 6)	...(j)
and Rupesh + 6 = | (Ravi + 6)	...(ii)
Solving both the equations we get,
Ravi = 12 years.
C
Answer: (C) 12 years
Question: The length of rectangle is thrice its breadth and its perimeter is 80 m, find the area of the rectangle?
(A) 300 sq m
(B) 356 sq m
(C) 452 sq m
(D) 428 sq m
(E) 528 sq m
Rationale: 2(3x + x) = 80
l = 30 b = 10
lb = 30 * 10 = 300
ANSWER:A
Answer: (A) 300 sq m
Question: A goods train runs at the speed of 72 km/hr and crosses a 220 m long platform in 26 sec. What is the length of the goods train?
(A) 382
(B) 782
(C) 300
(D) 270
(E) 881
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 26 sec.
Let the length of the train be x meters.
Then, (x + 220)/26 = 20
x = 300 m.
Answer: C
Answer: (C) 300
Question: Cities M and N are 600km apart. Bus A starts from city M towards N at 9AM and bus B starts from city N towards M at the same time. Bus A travels the first one-third of the distance at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmpr. Bus B travels the first one-third of the total time taken at a speed of 40kmph, the second one-third at 50kmph and the third one-third at 60kmph. When and where will the two buses cross each other?
(A) 300 kms from A
(B) 280 kms from A
(C) 305 kms from A
(D) 295 kms from A
(E) 265 kms from A
Rationale: DETAILED SOLUTION
Bus A
Travels 200km @ 40kmph
the next 200km @ 50kmph and
the final 200km @ 60kmph
So, Bus A will be at a distance of 200km from city M after 5 hours, and at a distance of 400km after 9 hours, and reach N after 12 hours and 20 mins
Bus B
Travels at an overall average speed of 50kmph, so will take 12 hours for the entire trip.
So, Bus B will travel
160 kms in the first 4 hours
200 kms in the next 4 hours
and 240 in the final 4 hours
So, both buses cross each other when they are in their middle legs.
After 5 hours, bus A will be at a position 200kms from city M. At the same time, bus B will be at a distance 210kms from city N (4 * 40 + 50).
The distance between them will be 190kms (600 - 200 - 210). Relative speed = Sum of the the two speeds = 50 + 50 = 100 kmph.
Time taken = 190/100 = 1.9 hours. = 1 hour and 54 minutes. So, the two buses will meet after 6 hours and 54 minutes. Bus B will have travelled 210 + 95 = 305 kms. So, the two buses will meet at a point that is 305 kms from City N and 295 kms from city A.
CORRECT ANSWER D
Answer: (D) 295 kms from A
Question: Sum of two numbers is 25. First exceeds by 5 from the other. Then the numbers will be?
(A) 20, 5
(B) 10, 15
(C) 15, 10
(D) 5, 20
(E) 12, 13
Rationale: Explanation:
x + y = 25
x - y =5
x = 15 y = 10
Answer: C
Answer: (C) 15, 10
Question: In how many different ways can the letter of the word 'CONCEALED ' be arranged in such a way that the vowels occupy the odd positions?
(A) 7412
(B) 4596
(C) 5760
(D) 4563
(E) 8521
Rationale: In the given word there 5 letters in that there are 4 vowels and 5 consonants
no of ways of arranging the vowels=4P4=48
no of ways of arranging the consonants=5P5=120
total number of ways 120*48=5760
Answer(C)
Answer: (C) 5760