mathewhe/aqua_rat huggingface dataset:
Question: Peter invested an amount of Rs. 12,000 at the rate of 10% p.a simple interest and another amount at the rate of 20% p.a. simple interest. The total interest earned at the end of one year on the total amount invested became 14% p.a. Find the total amount invested?
(A) Rs.20,000
(B) Rs.20,028
(C) Rs.20,298
(D) Rs.20,029
(E) Rs.20,291
Rationale: Let the second amount be Rs. x. Then,
(12000 * 10 * 1)/100 + (x * 20 * 1)/100 = [(12000 + x) * 14 * 1] / 100
120000 + 20x = 16800 + 14x
x = 8000
Total investment = 12000 + 8000
=Rs.20,000.
Answer:A
Answer: (A) Rs.20,000
Question: If log 2, log (2x -1) and log (2x + 3) are in A.P, then x is equal to ____
(A) 5/2
(B) log(2)5
(C) log(3)2
(D) 3/2
(E) None of these
Rationale: Explanatory Answer
Because log 2, log (2x -1) and log (2x + 3) are in an AP
2 log (2x - 1) = log 2 + log (2x + 3)
Using the power rule of log, we can write 2 log (2x - 1) = log (2x - 1)2
Therefore, we can write the equation as log (2x - 1)2 = log 2 + log (2x + 3)
Using product rule, we can write the right hand side of the equation as follows:
log 2 + log (2x + 3) = log 2 (2x + 3)
The modified equation after applying the power rule and the product rule of logarthims is log (2x - 1)2 = log 2 (2x + 3)
Removing logarithm on both sides of the equation, we get
(2x - 1)2 = 2 (2x + 3)
Or 22x - 2*2x + 1 = 2 * 2x + 6
Or 22x - 4 * 2x - 5 = 0
Let y = 2x
So, the equation can be written as y2 - 4y - 5 = 0
Factorzing, we get (y - 5)(y + 1) = 0.
So, y = 5 or y = -1
So, 2x = 5 or 2x = -1
2x cannot be negative. S, 2x = 5
If 2x = 5, expressed in terms of a log, it becomes x = log(2)5
Answer B
Answer: (B) log(2)5
Question: How many hours are there in 660 minutes?
(A) 60 hours
(B) 6 hours
(C) 30 hours
(D) 11 hours
(E) 10 hours
Rationale: Solution:
Number of minutes in 1 hour = 60 minutes
So
Just divide 660 by 60
660 Ã· 60 = 11, so there are 11 hours in 660 minutes
Option D
Answer: (D) 11 hours
Question: Amar takes as much time in running 12 meters as a car takes in covering 45 meters. What will be the distance covered by Amar during the time the car covers 1.4 km?
(A) 700 m
(B) 500 m
(C) 373 m
(D) 356 m
(E) 640 m
Rationale: Distance covered by Amar
= 12/45 (1.4km)
= 4/15(1400) = 373 m
Answer: C
Answer: (C) 373 m
Question: How many prime numbers Z exist such that 90 < Z < 106 and n is a factor of 99999919?
(A) 1. Zero
(B) 2. One
(C) 3. Two
(D) 4. Three
(E) 5. More than three
Rationale: I found that considering the constraint..Z is a prime num in between 90 to 106 not inclusive , only 3 numbers (91,97 and 101) are present but those numbers are not the factors of the number mentioned....Therefore, i doubt the answer.C
Answer: (C) 3. Two
Question: The average age 9 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?
(A) 18
(B) 12
(C) 27
(D) 21
(E) 28
Rationale: 9 * 2 = 18 years
ANSWER A
Answer: (A) 18
Question: In a small dairy farm, 40 cows eat 20 bags of grass in 40 days. In how many days one cow will eat one bag of grass?
(A) 40
(B) 80
(C) 60
(D) 50
(E) 90
Rationale: Assume that in a days, one cow will eat one bag of grass.
More cows, less days (Indirect proportion)
More bags, more days (direct proportion)
Hence we can write as (cows)40:1
::x:40
(bags)1:20
⇒40×1×40=1×20×x
⇒x=80
ANSWER:B
Answer: (B) 80
Question: Each year, a cyber café charges its customers a base rate of $25, with an additional $0.30 per visit for the first 50 visits, and $0.10 for every visit after that. How much does the cyber café charge a customer for a year in which 72 visits are made?
(A) 36.6
(B) 42.2
(C) 47.8
(D) 51.1
(E) 53.6
Rationale: Explanation:
The café charges $25 + $0.30(first 50) + $0.10(additional after 50). For 72 visits there are 50 visits with an additional 22 visits.
$25 + $0.30(50) + $0.10(22)
=$25 +$15 + $2.20
=$42.20
Answer is (B).
Answer: (B) 42.2
Question: In a group of 6 boys and 3 girls, four children are to be selected. In how many different ways can they be selected such that at least one girl is included?
(A) 105
(B) 111
(C) 117
(D) 123
(E) 129
Rationale: The total number of ways to choose 4 children is 9C4 = 126
The number of ways to choose only boys is 6C4 = 15
The number of groups which include at least one girl is 111.
The answer is B.
Answer: (B) 111
Question: Find the average increase rate, if increase in the population in the first year is 30% and that in the second year is 40%.
(A) 41
(B) 56
(C) 40
(D) 38
(E) 39
Rationale: Solution: Let 100 be the original population.
1st year's population increased = 30%
So, Population after first year = (100 +30% of 100) = 130. Population in second year increases by 40%, then Population
= (130 +40% of 130) = 182.
The final population become 182 which was originally at 100. It means there is 82% increment in the population in 2 years
So, Average increment = 82/2 = 41%.
Mind Calculation Method:
Increase in population is given by,
100==30%↑==>130==40%↑==> 182.
Hence, average increase = 82/2 = 41%
Answer: Option A
Answer: (A) 41
Question: Torry has submitted 2/5 of his homework assignments, and he received an average grade of 75 for those assignments. If he wishes to receive an average grade of 96 for all his homework assignments, the average grade for Torry's remaining homework assignments must be what percent greater than the average grade for the assignments he has already submitted?
(A) 15%
(B) 20%
(C) 25%
(D) 46 2/3%
(E) 40%
Rationale: 0.4*75 + 0.6x = 96
30 + 0.6x=96
0.6x = 66
x= 110
110/75= 1.4666...
Ans:D
Answer: (D) 46 2/3%
Question: If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?
(A) 30
(B) 34
(C) 38
(D) 40
(E) 42
Rationale: 2:3
2x + 10 : 3x + 10 = 5 : 7
7[2x + 10] = 5[3x + 10]
14x + 70 = 15x + 50
15x - 14x = 70 - 50
x = 20
Then the first number is = 2
2x = 40
D
Answer: (D) 40
Question: We invested a total of $1,000. We invested one part of the money at 4% and the rest of the money at 6%. The total investment with interest at the end of the year was $1,046. How much money did we invest at 4%?
(A) $600
(B) $650
(C) $700
(D) $750
(E) $800
Rationale: Let x be the money invested at 4%.
1.04x+1.06(1000-x)=1046.
0.02x=1060-1046.
0.02x=14.
2x=1400.
x=700.
The answer is C.
Answer: (C) $700
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 3 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
(A) 229
(B) 288
(C) 600
(D) 720
(E) 121
Rationale: D = 30 * 6 = 180
RS = 40 – 30 = 10
T = 180/10 = 18
D = 40 * 18 = 720 km
Answer: D
Answer: (D) 720
Question: If x represents the sum of the interior angles of a regular octagon and y represents the sum of the interior angles of a regular pentagon, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?
(A) Triangle
(B) Square
(C) Rhombus
(D) Trapezoid
(E) Pentagon
Rationale: Sum of angles of octagon = 180*(8-2) = 1080 => using formula sum of angles of polygon = 180*(n-2) where n is the number of sides in a polygon
Sum of angles in Pentagon = 180*(5-2) =540
Difference = 1080 - 540 = 540 => Pentagon
hence (E).
Answer: (E) Pentagon
Question: What is the ratio whose term differ by 40 and the measure of which is 2/7?
(A) 32:23
(B) 16:56
(C) 71:85
(D) 32:39
(E) 41:52
Rationale: Let the ratio be x:(x+40)
Then, x/(x+40) = 2/7
x=16
required ratio = 16:56
Answer is B
Answer: (B) 16:56
Question: Baby Isabel plays with blocks. Each block is 3.9 inches tall. She has a collection of 32 blocks. If she could stack all of the blocks up one on top of the other, how many inches tall would her tower of blocks be?
(A) 67"
(B) 124.8"
(C) 106"
(D) 120"
(E) 151.7"
Rationale: 3.9"*32=124.8". Answer is B.
Answer: (B) 124.8"
Question: When y divided by 288, the remainder is 47. Find the remainder when the same y is divided by 24?
(A) 20
(B) 21
(C) 23
(D) 25
(E) 26
Rationale: 23
Option C
Answer: (C) 23
Question: Find the greatest number that will divide 256, 193 and 210 leaving 6, 18 and 100 as remainders respectively
(A) 19
(B) 25
(C) 23
(D) 20
(E) 26
Rationale: Explanation:
Answer will be HCF of (256-6, 193-18, 210-10)
HCF of (250, 175, 200) = 25
Option B
Answer: (B) 25
Question: A bag contains 12 white and 18 black balls. 2balls are drawn in succession. What is the probability that first is white and second is black?
(A) 31/145
(B) 36/145
(C) 21/141
(D) 23/121
(E) 25/145
Rationale: The probability that first ball is white:
=12C130C1=12C130C1
=1230=1230
=25=25
Since, the ball is not replaced; hence the number of balls left in bag is 29.
Hence, the probability the second ball is black:
=18C129C1=18C129C1
=1829=1829
Required probability,
=(25)×(1829)=(25)×(1829)
=36/145
B
Answer: (B) 36/145
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 11 1/0
(B) 11 1/4
(C) 11 1/2
(D) 11 1/1
(E) 11 1/9
Rationale: 3/12 + x/15 = 1
x= 11 1/4
Answer:B
Answer: (B) 11 1/4
Question: A train speeds past a pole in 10 seconds and a platform 150 m long in 25 seconds. Its length is:
(A) 300 m.
(B) 250 m.
(C) 100 m.
(D) 200 m.
(E) 150 m.
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 10=> y = x/10
x + 150 / 25 = x / 10
x = 100 m.
Answer: Option C
Answer: (C) 100 m.
Question: In a Lake, there is a patch of lily pads. Every day, the patch doubles in size. It takes 58 days for the patch to cover the entire lake, how many days would it take the patch to cover half of the lake?
(A) 57
(B) 2^4*3
(C) 24
(D) 38
(E) 47
Rationale: So 57 days
Answer A=57
Answer: (A) 57
Question: Cindy paddles her kayak upstream at a kilometers per hour, and then returns downstream the same distance at n kilometers per hour. How many kilometers upstream did she travel if she spent a total of p hours for the round trip?
(A) mnp
(B) an/p
(C) (a + n)/p
(D) anp/(a + n)
(E) pm/n- pn/m
Rationale: let t1 and t2 be the time taken to row upstream and downstream respectively
now,
t1=distance/speed=d/a
similarly,
t2=d/n (as same distance has to be rowed)
also,
t1+t2=p
therefore,
p=(d/a)+(d/n)
=d(a+n)/an
d=pan/(a+n)=D
Answer: (D) anp/(a + n)
Question: What number comes next in the following series? 4, 13, 40, 121, 364, x
(A) 1093
(B) 1100
(C) 1301
(D) 1400
(E) 1713
Rationale: 44 × 3 + 1 = 1313 × 3 + 1 = 4040 × 3 + 1 = 121121 × 3 + 1 = 364364 × 3 + 1 = 1093 A
Answer: (A) 1093
Question: A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 150 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
(A) 	1.75 hours, 225 miles
(B) 	3 hours, 350 miles
(C) 	4 hours, 450 miles
(D) 	5 hours, 550 miles
(E) 	6 hours, 650 miles
Rationale: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.
Equation 1 - x= 100 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 150 (t-.25) subtracted .25 hrs because it is early or took less time than usual.
Now equating 12 we get 100(t+.5)=150(t-.25)
=> 10t +5 = 15t - 3.75
=> 5t=8.75 => t= 1.75 hrs.
Hence x= 100(1.75+.5) =>100 X 2.25 => 225 miles.
Hence correct answer A
Answer: (A) 	1.75 hours, 225 miles
Question: What is his percentage profit made by Elvis if he purchased 25 dozen belts at Rs. 35 per dozen. He sold 10 dozens at 15% profit and the remaining 15 dozens with 16% profit?
(A) 18%
(B) 12%
(C) 16%
(D) 15%
(E) 19%
Rationale: Explanation :
C.P of 25 dozen = Rs.(35 x 25) = Rs.875
C.P of 10 dozen = Rs. (35 x10) = Rs. 350.
C.P of 15 dozen =Rs. (35 x15) = Rs. 525
profit on 10 dozen at 15% = 15/100*350 = 52.5
profit on 15 remaining dozen at 20% = 20/100*525 = 105
total profit = 52.5 + 105 = 157.5
% profit = ?/100*875 = 157.5
= 18%
Answer : A
Answer: (A) 18%
Question: A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 7 members, then what is the exact number of researchers required?
(A) 23
(B) 20
(C) 21
(D) 22
(E) 19
Rationale: alternatively, we have
7*3-2( because james is included in all the three teams)
=19
E
Answer: (E) 19
Question: A 250 meter long train crosses a platform in 40 seconds while it crosses a signal pole in 20 seconds. What is the length of the platform?
(A) 500
(B) 1000
(C) 350
(D) 250
(E) 20
Rationale: Speed = [250 / 20] m/sec =25/2 m/sec.
Let the length of the platform be x meters.
Then, x + 250 /40 = 25/2
2(x + 250) = 1000 è x = 250m. Answer: D
Answer: (D) 250
Question: If the price of petrol increases by 40, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
(A) 25%
(B) 20%
(C) 16.67%
(D) 28.6%
(E) None of these
Rationale: Explanation :
let us assume before increase the petrol will be Rs. 100.
After increase it will be Rs (100+40) i.e 140.
Now, his consumption should be reduced to :-
=(140−100)/140 ∗ 100.
Hence, the consumption should be reduced to 28.6%.
Answer : D
Answer: (D) 28.6%
Question: Current age of Bruce and Tomy r in the ratio of 5:4 respectively. 3 years hence, the ratio of their ages will become 11:9 respectively. What is Tomy 's present age in years?
(A) 20 years
(B) 21 years
(C) 24 years
(D) 27 years
(E) 30 years
Rationale: Let the present ages of Bruce and Tomy be 5x years and 4x years respectively.
Then,	5x + 3	=	11
4x + 3	9
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x - 44x = 33 - 27
x = 6.
Anand's present age = 4x = 24 years.
C
Answer: (C) 24 years
Question: On increasing the price of T.V. sets by 70%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
(A) 4
(B) 5
(C) 36
(D) 2
(E) 7
Rationale: Explanation:
Let the price be = Rs.100, and number of units sold = 100
Then, sale value = Rs.(100 × 100) = Rs.10000
New sale value = Rs.(170 × 80) = Rs.13600
Increase% = 3600/10000 × 100 = 36%
Answer: C
Answer: (C) 36
Question: How many times digit 7 is used while writing numbers from 1 to 300?
(A) 28
(B) 42
(C) 41
(D) 35
(E) 49
Rationale: in 1 to 100 their are 14 seven's
in 100 to 200 their are 14 seven's
in 200 to 300 their are 14 seven's
so total answer is 42 seven's
CORRECT OPTION :B
Answer: (B) 42
Question: Paul has to secure 50% marks to clear his exam of class 7th.
He got 50 marks and failed by 10 marks.
What is the maximum marks ?
(A) 100
(B) 110
(C) 120
(D) 210
(E) 200
Rationale: C
120
To pass the exam ravish needs 50 + 10 = 60 marks.
=> (60/50) *100 = 120
Answer: (C) 120
Question: A furniture dealer purchased a desk for $240 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk?
(A) $40
(B) $60
(C) $160
(D) $90
(E) $100
Rationale: Purchase price = 240
Selling price = x
240 + 0.4*x = x
0.6*x = 240
x = 400
Profit = 400 - 240 = 160
ANSWER:C
Answer: (C) $160
Question: A man is 30 years older than his son. In three years, his age will be twice the age of his son. The present age of his son is:
(A) 20
(B) 21
(C) 27
(D) 23
(E) 24
Rationale: Let the son's present age be x years. Then, man's present age = (x + 30) years.
(x + 30) + 3 = 2(x + 3)
x + 33 = 2x + 6
x = 27.
Answer:C
Answer: (C) 27
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
(A) 1878
(B) 2890
(C) 2789
(D) 8112
(E) 2789
Rationale: A = 7500(26/25)2
= 8112
Answer:D
Answer: (D) 8112
Question: A train 200m long passes a standing man in 12 seconds. What is the speed of the train?
(A) 30km/hr
(B) 36km/hr
(C) 42km/hr
(D) 60km/hr
(E) 32km/hr
Rationale: Speed of the train = 200/12* 18/5 = 60km/hr
Answer is D
Answer: (D) 60km/hr
Question: How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6?
(A) None
(B) One
(C) Two
(D) Three
(E) Four
Rationale: The possible number N can be written as follow:
N = Multiple of LCM(6,10) + 1st such number
N = 30x + 1
Possible values = 1, 31, 61, 91
Answer : 3 such 2 digit number.
ANSWER:D
Answer: (D) Three
Question: If six persons sit in a row, then the probability that three particular persons are always together is ?
(A) 1/5
(B) 2/8
(C) 1/6
(D) 1/7
(E) 1/2
Rationale: Six persons can be arranged in a row in 6! ways. Treat the three persons to sit together as one unit then there four persons and they can be arranged in 4! ways. Again three persons can be arranged among them selves in 3! ways. Favourable outcomes = 3!4! Required probability
= 3!4!/6!
= 1/5
Answer: C
Answer: (C) 1/6
Question: A can do a piece of work in 14 days which B alone can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total number of days for the work to be completed is
(A) 6 3/5 days
(B) 8 ½ days
(C) 10 1/5 days
(D) 13 ½ days
(E) 7 days
Rationale: Explanation:
B’s 1 day’s work = 1/21
B’s 3 day’s work = 1/21 ×3 = 1/7
The remaining work finished by both of them = 1 – 1/7 = 6/7
Both together can finish it in 14 × 21/35 days = 42/5 days
Their, 1 day’s work = 5/42
Therefore, the No. of days taken by them together to finish 6/7 work
= 6/7/5/42 = 6/7 × 42/5 = 36/5 = 7 1/5 days
Therefore, the total No. of days for the work to be completed = 3 + 7 1/5 = 10 1/5 days.
Answer: Option C
Answer: (C) 10 1/5 days
Question: The ratio of two quantities is 5 to 6. If each of the quantities are doubled, what is the ratio of these 2 new quantities?
(A) 5:6
(B) 10:12
(C) 20:24
(D) 5:12
(E) It cannot be determined from the information given
Rationale: If both sides of a ratio are multiplied by the same number there is no change in the ratio.
5:6 means 5x:6x...
So when you double, 5(1): 6(1) becomes 5(2): 6(2)..
So if the Xs are equal the ratio does not change..
ANSWER:A
Answer: (A) 5:6
Question: A question paper has 2parts, A & B, each containing 10 questions. If a student has to choose 8 from part A &5 from part B, in how many ways can he choose the questions?
(A) 1100
(B) 1130
(C) 1135
(D) 1138
(E) 1140
Rationale: There 10 questions in part A out of which 8 question can be chosen as = 10C8.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 10C5.
Hence, total number of ways,
=10C8*10C5
=[10!/(2!8!)]*[10!/(5!*5)]
= {10*9/2}*{10*9*8*7*6/(5*4*3*2*1)}
= 1140.
E
Answer: (E) 1140
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:D will be?
(A) 1 : 2
(B) 2 : 3
(C) 3 : 5
(D) 3 : 7
(E) 4 : 7
Rationale: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : D = 3 : 6 or, 1 : 2
A
Answer: (A) 1 : 2
Question: What should be the least number to be added to the 11002 number to make it divisible by 11?
(A) 12
(B) 9
(C) 18
(D) 77
(E) 26
Rationale: Answer : 9
Option : B
Answer: (B) 9
Question: If a is divisible by 5!, then a/4 must be
I. an odd integer
II. a multiple of 3
III. a multiple of 10
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) II and III only
Rationale: If a is divisible by 5! then a must be of the form 120*k when k is an integer 1, 2, 3
then a can be 120, 240, 360, 480....
a/4= 30, 60, 90, 120.....
from this we can say a/4 satisfies E.
ANSWER:E
Answer: (E) II and III only
Question: The average weight of 24 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) 48.975
(B) 42.255
(C) 50
(D) 51.255
(E) 52.253
Rationale: Explanation:
Average weight of 24 boys = 50.25
Total weight of 24 boys = 50.25 × 24
Average weight of remaining 8 boys = 45.15
Total weight of remaining 8 boys = 45.15 × 8
Total weight of all boys in the class = (50.25 × 24)+ (45.15 × 8)
Total boys = 24 + 8 = 32
Average weight of all the boys = (50.25×24)+(45.15×8)/32
=48.975
Answer: Option A
Answer: (A) 48.975
Question: x, a, z, and b are single digit positive integers. x = a/3. z = b/3. (10a + b) – (10x + z) could NOT equal
(A) 33
(B) 22
(C) 54
(D) 78
(E) 110
Rationale: 1) firstly we are not given that all are different integers..
2) since each is a positive single digit integer and x=a/3... Z=b/3
so in (10a + b) – (10x + z) ..
10a+b can be
33,66,99,132..
10x+z can be
11,12,21,22..
ans A
Answer: (A) 33
Question: A certain sum of money at simple interest amounted Rs.880 in 10 years at 3% per annum, find the sum?
(A) 672.92
(B) 673.92
(C) 674.92
(D) 675.92
(E) 676.92
Rationale: 880 = P [1 + (10*3)/100]
P = 676.92
Answer: E
Answer: (E) 676.92
Question: The ages of 2 boys differ by 16 yrs. 6 yrs ago, the elder one was 3 times as old as the younger one. What are their present ages of the elder boy?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: Let present age of the elder person =x and
present age of the younger person =x−16
(x−6)=3(x−16−6)⇒x−6=3x−66⇒2x=60⇒x=602=30
C
Answer: (C) 30
Question: A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 20 seconds. What is the length of the train in meters?
(A) 400 meters
(B) 1111 meters
(C) 1777 meters
(D) 200 meters
(E) None of these
Rationale: Train overtakes a bike means that we are talking about total length of the train. (train's head is close to bike when it started and its tail crosses the bike when it overtakes the bike)
Relative speed= 100-64= 36Km/h = 36000 m/h
time= 20 seconds
Distance= speed*time
36000* 20/3600= 200 meters.
D is the answer.
Answer: (D) 200 meters
Question: A car covers a distance of 624 km in 2 3/5 hours. Find its speed?
(A) 104 kmph
(B) 194 kmph
(C) 109 kmph
(D) 174 kmph
(E) 240 kmph
Rationale: 624/2 3/5
=240 kmph
Answer:E
Answer: (E) 240 kmph
Question: By selling 90 pens, a trader gains the cost of 15 pens. Find his gain percentage?
(A) 16.66%
(B) 17.66%
(C) 18.66%
(D) 19.66%
(E) 20.66%
Rationale: Let the CP of each pen be Rs. 1.
CP of 90 pens = Rs. 90
Profit = Cost of 15 pens = Rs. 15
Profit% = 15/90 * 100 = 16.66%
Answer:A
Answer: (A) 16.66%
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 7 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/18 hours
(B) 37/13 hours
(C) 80/13 hours
(D) 20/9 hours
(E) 30/43 hours
Rationale: Speed downstream = 20 + 7 = 27 kmph.
Time required to cover 60 km downstream
= d/s = 60/27
= 20/9 hours.
Answer: D
Answer: (D) 20/9 hours
Question: In a can, there is a mixture of milk and water in the ratio 4:3. If the can is filled with an additional 10 liters of milk, the can would be full and the ratio of milk and water would become 5:2. Find the capacity of the can?
(A) 24
(B) 26
(C) 28
(D) 30
(E) 32
Rationale: Let C be the capacity of the can.
(4/7)*(C-10)+10=(5/7)*C
4C-40+70=5C
C=30
The answer is D.
Answer: (D) 30
Question: The effective annual rate of interest corresponding to a nominal rate of 10% per annum payable half-yearly is?
(A) 10.06%
(B) 10.25%
(C) 10.35%
(D) 16.09%
(E) 16.19%
Rationale: Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 5/100)2] = Rs. 110.25 Effective rate = (110.25 - 100) = 10.25%
ANSWER:B
Answer: (B) 10.25%
Question: A does half as much work as B in three-fourth of the time. If together they take 18 days to complete the work, how much time shall B take to do it
(A) 40days
(B) 35days
(C) 30days
(D) 25days
(E) 10days
Rationale: Explanation:
Suppose B takes x dáys to do the work.
As per question A will take
2∗3 /4∗x=3x /2days
(A+B)s 1 days work= 1/18
1/x + 2/3x = 1/18 or x = 30 days
Option C
Answer: (C) 30days
Question: In 150 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:
(A) 20 m
(B) 25 m
(C) 22.5 m
(D) 9 m
(E) 30 m
Rationale: Distance covered by B in 9 sec. =	150/45 x 9	m = 30 m.
A beats B by 30 metres.
Answer: Option E
Answer: (E) 30 m