mathewhe/aqua_rat huggingface dataset:
Question: Two trains of equal lengths take 9 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 10
(B) 11.3
(C) 13
(D) 14
(E) 15
Rationale: Speed of the first train = 120/9 = 13.3 m/sec.
Speed of the second train = 120/15 = 8 m/sec.
Relative speed = 13.3 + 8 = 21.3 m/sec.
Required time = (120 + 120)/21.3 = 11.3 sec.
Answer: Option B
Answer: (B) 11.3
Question: The difference of the squares of two consecutive even integers is divisible by which of the following integers ?
(A) 6
(B) 4
(C) 2
(D) 5
(E) 1
Rationale: Let the two consecutive even integers be 2n and (2n + 2). Then,
(2n + 2)^2 = (2n + 2 + 2n)(2n + 2 - 2n)
= 2(4n + 2)
= 4(2n + 1), which is divisible by 4.
ANSWER B
Answer: (B) 4
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 45 sec. The length of each train is?
(A) 50
(B) 26
(C) 27
(D) 62.5
(E) 21
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/45 = 25/9 => x = 65.5.
Answer: D
Answer: (D) 62.5
Question: A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 126 km downstream.
(A) 4 hours
(B) 5 hours
(C) 6 hours
(D) 7 hours
(E) 8 hours
Rationale: Explanation:
It is very important to check, if the boat speed given is in still water or with water or against water. Because if we neglect it we will not reach on right answer. I just mentioned here because mostly mistakes in this chapter are of this kind only.
Lets see the question now.
Speed downstream = (16 + 5) = 21 kmph
Time = distance/speed = 126/21 = 6 hours
Option C
Answer: (C) 6 hours
Question: Find the principal which yields a simple interest of Rs. 20 and compound interest of Rs. 21 in two years, at the same percent rate per annum?
(A) Rs. 520
(B) Rs. 480
(C) Rs. 420
(D) Rs. 200
(E) Rs. 600
Rationale: Explanation:
SI in 2 years = Rs. 20, SI in 1 year = Rs. 10
CI in 2 years = Rs. 21
% rate per annum = [(CI – SI) / (SI in 1 year)] *100
= [(21 – 20) / 20] * 100
= 5 % p.a.
Let the principal be Rs. X
Time = T = 2 years
% rate = 5% p.a.
SI = (PRT/100)
20 = (X*5*2) / 100
X = Rs. 200
ANSWER: D
Answer: (D) Rs. 200
Question: The ratio of the present age of two brothers is 1:2 and 5 years back, the ratio was 1:3. What will be the ratio of their ages after 5 years?
(A) 3:9
(B) 3:0
(C) ratio 3:5
(D) 3:2
(E) 3:1
Rationale: Let the present ages of the two brothers be x and 2x years respectively.
Then, (x - 5)/(2x - 5) = 1/3
3(x - 5) = (2x - 5) => x = 10
Required ratio = (x + 5) : (2x + 5) = 15 : 25 = 3:5
Answer: C
Answer: (C) ratio 3:5
Question: If the sum of a number and its square is 210, what is the number?
(A) 14
(B) 26
(C) 28
(D) 91
(E) none of these
Rationale: Let the number be x. Then,
x + x2 = 210
(x + 15)(x - 14) = 0
x = 14
ANSWER:A
Answer: (A) 14
Question: The edges of a cuboid are 4 cm, 4 cm and 6 cm. Find the volume of the cuboid?
(A) 90
(B) 60
(C) 96
(D) 80
(E) 72
Rationale: 4*4*6
= 96
Answer: C
Answer: (C) 96
Question: What is the average (arithmetic mean) of all the multiples of ten from 10 to 210 inclusive?
(A) 90
(B) 95
(C) 100
(D) 120
(E) 110
Rationale: 10 and 190 inclusive would mean there are 21 terms.
No need to add up all the terms and further divide by 21 since the terms are evenly spaced in ascending order from 10, 20, 30........210
The middle term is the average which is the tenth term = 120
D is the answer.
Answer: (D) 120
Question: Working together, Jose and Jane can complete an assigned task in 5 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 15 days. How long will Jose take to complete the task if he worked alone? Assume that Jane is more efficient than Jose
(A) 26 days
(B) 15 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 = 1/5
5(x+y) = xy
Next, we're told 1 job takes 15 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 = 15
x+y = 30
So
xy = 150
The answer choices are:
26 days
15 days
60 days
65 days
36 days
From the answer choices, So I'll go for 15 days for Jose and 10 days for Jane.
Answer : B
Answer: (B) 15 days
Question: Which four figure number contains four different digits and meets the following criteria? The first digit is twice the value of the fourth digit and two more than the second digit. The third digit is one more than the first digit and four more than the fourth digit.
(A) 5367
(B) 6473
(C) 3573
(D) 3262
(E) 7364
Rationale: B
6473
Answer: (B) 6473
Question: k = 2^n + 9, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9?
(A) 2^n - 8
(B) 2^n - 2
(C) 2^n+5
(D) 2^n + 4
(E) 2^n
Rationale: Given: k, M and N are integers
If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)
We're told that 9 is a divisor of 2^n + 9
We also know that 9 is a divisor of9.
So, applying the aboverule, 9 is a divisor of 2^n + 9 +9, and 9 is a divisor of 2^n +9 -9 =2^n
E
Answer: (E) 2^n
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
(A) 12, 9
(B) 10, 5
(C) 12, 7
(D) 11, 6
(E) 13, 8
Rationale: Explanation:
x – y = 5
4x – 6y = 6
x = 12 y = 7
ANSWER IS C
Answer: (C) 12, 7
Question: Lakshmi took a loan of Rs. 1500 with simple interest for as many years as the rate of interest. If she paid Rs. 960 as interest at the end of the loan period, what was the rate of interest?
(A) 8
(B) 7
(C) 6
(D) 5
(E) 4
Rationale: Let rate = R% and time = R years.
Then, (1500 * R * R) / 100 = 960
15R2 = 960
R2 = 64 => R = 8
Answer:A
Answer: (A) 8
Question: If Danny scored 86, 75, 52, 87, 85 and 82 marks (out of 100) in English, Social Studies, Art, Music, Biology and French. What are his average marks ?
(A) 77.8
(B) 75.8
(C) 67.8
(D) 87.8
(E) 97.8
Rationale: Explanation:, 75, 52, 87 and 82
Average = (86+ 75 + 52 + 87 + 85 + 82 )/ 6 = 77.8.
Answer: A)77.8
Answer: (A) 77.8
Question: Let the polynomials be:
P1(x)=3x2−7x+3,
P2(x)=−5x2−4x+2,
P1(x)+P2(x)=
(A) 2x2 + 11x - 7
(B) -2x2 - 11x + 5
(C) -2x2 - 11x + 6
(D) 2x2 - 9x + 7
(E) None of these
Rationale: Solution:
P1(x)+P2(x)=(3x2−7x+3)+(−5x2−4x+2)=P1(x)+P2(x)=(3x2−7x+3)+(−5x2−4x+2)=
3x2−7x+3−5x2−4x+2=3x2−7x+3−5x2−4x+2=
−2x2−11x+5
Answer B
Answer: (B) -2x2 - 11x + 5
Question: A salesperson gets a 15% commission on each sale he makes. How many sales of $270 each must he make in order to reach a salary of at least $1000?
(A) 15
(B) 24
(C) 25
(D) 26
(E) 52
Rationale: Soln:-
10% of 270 = 27.
5% of 270 = 13.5.
so,
15 % of 270 = 40.5
total salary required 1000
earning from single sale 40.5
# of sale = 1000/40.5 = 24.62
Approx 25 sale
ANSWER:C
Answer: (C) 25
Question: Aman started a business investing Rs. 70,000. Rakhi 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 among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business ?
(A) 12 : 15 28
(B) 12 : 15 :29
(C) 12 : 15 :99
(D) 12 : 15 :16
(E) 12 : 15 :11
Rationale: Explanation:
Aman : Rakhi : Sagar = (70000 x 36) : (105000 x 30) : (140000 x 24) = 12 : 15 : 16.
Answer: D) 12 : 15 :16
Answer: (D) 12 : 15 :16
Question: A factory has 15 machines of equal efficiency in its factory. The annual manufacturing costs are Rs.42,000 & establishment charges are Rs.12,000. The annual output of the company is Rs.70,000. The annual output and manufacturing costs are directly proportional to the number of machines. The shareholders get 12.512.5 profit, which is directly proportional to the annual output of the company. If 7.147.14 machines remain closed throughout the year, then the % decrease in the amountof profit of the shareholders would be?
(A) 12.5%
(B) 13.5%
(C) 14%
(D) 15%
(E) 16%
Rationale: Option(B) is correct
Original profit
= 70,000−42,000−12,000=16,00070,000−42,000−12,000=16,000
If 7.14%7.14% of 14 i.e. one of the machines closed throughout the year, then change in profit will be:
=1314×[70,000−42,000]=1314×[70,000−42,000]
=14,000=14,000
Thus, decrease in the profit %%
=200016000×100=200016000×100
=12.5%
A
Answer: (A) 12.5%
Question: Sue planted 4 times as many apple seeds as she planted orange seeds. 15 percent of the apple seeds grew into trees, and 10 percent of the orange seeds grew into trees. If a total of 420 apple trees and orange trees grew from the seeds, how many orange seeds did Sue plant?
(A) 540
(B) 600
(C) 660
(D) 720
(E) 760
Rationale: Sue planted 4 times as many apple seeds as she planted orange seeds.
Yes, apple:orange be 4:1 but this translates to Apple = 4*Orange and not 4*Apple = Orange
Let Orange be x
Apple = 4*Orange = 4x
0.15Apple + 0.10Orange = 420
=> 0.15*4x + 0.10*x = 420
=> 0.7x = 420
=> x = 600
So, answer will be B
Answer: (B) 600
Question: The proportion of water to alcohol in Solution A is 5:1 and the proportion of water to alcohol in Solution B is 2:3. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution?
(A) 36.7%
(B) 37.6%
(C) 38.3%
(D) 39.8%
(E) 40.5%
Rationale: Let V be the total volume of the new solution.
Then a volume of V/2 was added from each solution A and B.
The amount of alcohol added to the new solution was:
(1/6)(V/2)+(3/5)(V/2)=V/12+3V/10=23V/60.
The concentration of alcohol is 23/60=38.3%
The answer is C.
Answer: (C) 38.3%
Question: Two trains A and B starting from two points and travelling in opposite directions, reach their destinations 9 hours and 4 hours respectively after meeting each other. If the train A travels at 60kmph, find the rate at which the train B runs.
(A) 40
(B) 60
(C) 120
(D) 90
(E) 100
Rationale: If two objects A and B start simultaneously from opposite points and, after meeting, reach their destinations in ‘a’ and ‘b’ hours respectively (i.e. A takes ‘a hrs’ to travel from the meeting point to his destination and B takes ‘b hrs’ to travel from the meeting point to his destination), then the ratio of their speeds is given by:
Sa/Sb = √(b/a)
i.e. Ratio of speeds is given by the square root of the inverse ratio of time taken.
Sa/Sb = √(4/9) = 2/3
This gives us that the ratio of the speed of A : speed of B as 2:3.
Since speed of A is 60 kmph, speed of B must be 80*(3/2) = 90 kmph
D
Answer: (D) 90
Question: A certain electric-company plan offers customers reduced rates for electricity used between 8 p.m. and 8 a.m. weekdays and 24 hours a day Saturdays and Sundays. Under this plan, the reduced rates C apply to what fraction of a week?
(A)  1/2
(B)  5/8
(C)  9/14
(D)  16/21
(E)  9/10
Rationale: Number of hours between 8 PM to 8 AM = 12
Number of hours with reduced rates = (12*5)+(24*2)
Hours with reduced rates C/Total number of hours in a week = (12*5)+(24*2)/(24*7) = 108/(24*7) = 9/14
Answer: C
Answer: (C)  9/14
Question: Karan started a business investing Rs 29000. After five months, Satish joined with a capital of Rs 18000. If at the end of the year, they earn a profit of Rs. 16970, then what will be the share of Satish in the profit ?
(A) 4512
(B) 4552
(C) 4511
(D) 4529
(E) 4771
Rationale: Now as per question, Karan invested for 12 months and Satish invested for 7 months.
So
Karan:Satish = (29000*12):(18000*7)
= 348:126
= 58:21
Satish Ratio in profit will be
=(16970 )=Rs. 4511
Answer: C
Answer: (C) 4511
Question: The average age of husband, wife and their child 3 years ago was 21 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
(A) 22 years
(B) 40 years
(C) 50 years
(D) 55 years
(E) None
Rationale: Solution
Sum of the present ages of husband, wife and child	= (21x3+3x3) years
= 72 years.
Sum of the present ages of wife and child	= (20x2+5x2) years
= 50 years.
âˆ´ Husband's present age	= (72 - 50) years
= 22 years.
Answer A
Answer: (A) 22 years
Question: What is the least possible product of 4 different integers, each of which has a value between –4 and 10, inclusive?
(A) –5040
(B) –2880
(C) –720
(D) –600
(E) –120
Rationale: Maximize the total product with a -ve sign
so -4 * 10 * 9 * 8 = 720 * -4 = -2880
Answer is B.
Answer: (B) –2880
Question: Jones has 6 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 12 shoes, what is the probability that she will select 2 shoes of the same color?
(A) 2/5
(B) 1/13
(C) 1/9
(D) 1/10
(E) 1/25
Rationale: Can be tackled in this way as well: Probability of selecting any 1 out of 12 shoes = 12/12 = 1
Probability of selecting the next shoe (out of 13 available) having the same color = 1/13 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/13=1/13.
B is the correct answer.
Answer: (B) 1/13
Question: 43 : 34 :: 52 :?
(A) 49
(B) 25
(C) 36
(D) 64
(E) 56
Rationale: Ans 25
Reverse of 52
ANSWER:B
Answer: (B) 25
Question: One fourth of a solution that was 15% salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent salt by weight?
(A) 24%
(B) 34%
(C) 22%
(D) 19%
(E) 8.5%
Rationale: consider total solution to be 100 liters and in this case you'll have: 75*0.15+25*x=100*0.16 --> x=0.19.
Answer: D.
Answer: (D) 19%
Question: There are 38 students in a certain geometry class. If two thirds of the students are boys and three fourths of the boys are under six feet tall, how many boys in the class are under six feet tall?
(A) 6
(B) 12
(C) 19
(D) 24
(E) 27
Rationale: 38*2/3 *3/4= 19
Answer: C
Answer: (C) 19
Question: The sector of a circle has radius of 21 cm and central angle 110o. Find its perimeter?
(A) 91.5
(B) 91.4
(C) 91.7
(D) 82.3
(E) 91.1
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (110/360 * 2 * 22/7 * 21) + 2(21)
= 40.3 + 42 = 82.3 cm
Answer:D
Answer: (D) 82.3
Question: In a test containing 16 questions , contestants get a base core of 20 points for taking the test. 5 points for each correctly answered question and 2 points for each unanswered question.An incorrectly answeredquestion is worth 0 points.Of the following scores which one is not attainable
(A) 96
(B) 97
(C) 94
(D) 95
(E) 93
Rationale: 1. 15 corrected and 1 uncorrected
20+5*15+0=95
2.15 corrected and 1attempted
20+5*15+2=97
3. 14corrected+2attempted
20+14*5+2*2=94
so 96 is not possible
ANSWER:A
Answer: (A) 96
Question: Out of 10 persons working on a project, 7 are graduates. If 3 are selected, what is the probability that there is at least one graduate among them?
(A) 5/7
(B) 119/3
(C) 5/120
(D) 119/120
(E) 5/6
Rationale: P(at least one graduate) = 1 - P(no graduates)
= 1 - 3C₃/¹⁰C₃ = 1 - (1)/(10 * 9 * 8)
= 119/120
Answer: D
Answer: (D) 119/120
Question: In a certain village, 200 litres of water are required per household per month. At this rate, if there are 5 households in the village, how long (in months) will 2000 litres of water last?
(A) 9
(B) 5
(C) 6
(D) 2
(E) 4
Rationale: I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p:
In a certain village,m 200 litres of water are required per household per month. At this rate, if there aren 5 households in the village, how long (in months) willp2000litres of water last?
Water required is 200*5=1000 (m*n)
Water available is 2000 (p)
It will last 2 months (p/m*n)
Ans : D
Answer: (D) 2
Question: What is the place value of 3 in the numeral 3259
(A) 2000
(B) 2500
(C) 2600
(D) 3000
(E) 3100
Rationale: Option 'D'
3 * 1000 = 3000
Answer: (D) 3000
Question: A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?
(A) $5,000 and $1,000
(B) $9,000 and $5,000
(C) $11,000 and $9,000
(D) $15,000 and $5,000
(E) $20,000 and $10,000
Rationale: lets denote cost of Car1 as c1 and cost car2 as c2 respectively.
overall sale resulted in a profit of 5%
=> profit from first sale - loss from second sale still yielded in overall 5% profit
=> (10/100)c1 - (10/100)c2 = (5/100)(c1+c2)
=> c1 = 3c2 ----equation 1
Overall profit = 1000
=>(5/100)(c1+c2) = 1000
=> c1+c2 = 20000------equation 2
from 1 and 2 we can find out values of c1 and c2.
c2=5000
c1 = 15000
Answer is D.
Answer: (D) $15,000 and $5,000
Question: One year ago, the ratio of Gaurav’s and Sachin’s age was 6: 7 respectively.Four years hence, this ratio would become 7: 8. How old is Sachin ?
(A) 27 years
(B) 36 years
(C) 12 years
(D) 41 years
(E) 35 years
Rationale: Let Gaurav's and Sachin's ages one year ago be 6x and 7x years respectively. Then, Gaurav's age
4 years hence = (6x + 1) + 4 = (6x + 5) years.
Sachin's age 4 years hence = (7x + 1) + 4 = (7x + 5) years.
6x+5 = 7
____ _
7x+5 8
8(6x+5) = 7 (7x + 5)
48x + 40 = 49x + 35
x = 5.
Hence, Sachin's present age = (7x + 1) = 36 years
Answer is B.
Answer: (B) 36 years
Question: If 2x+3y+z=55,x-y=4 and y - x + z=12,then what are the values of x , y and z?
(A) 11,8,
(B) 8,11,7
(C) 8,7,11
(D) 11,7,8
(E) 7,11,8
Rationale: The given equations are:
2x+3y+z=55 …(i); x + z - y=4 …(ii); y -x + z =12 …(iii)
Subtracting (ii) from (i), we get: x+4y=51 …(iv)
Subtracting (iii) from (i), we get: 3x+2y=43 …(v)
Multiplying (v) by 2 and subtracting (iv) from it, we get: 5x=35 or x=7.
Putting x=7 in (iv), we get: 4y=44 or y=11.
Putting x=7,y=11 in (i), we get: z=8.
Answer is E.
Answer: (E) 7,11,8
Question: A man sitting in a train which is travelling at 50 kmph observes that a goods train, travelling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed?
(A) 52 kmph.
(B) 62 kmph.
(C) 72 kmph.
(D) 80 kmph.
(E) None
Rationale: Solution
Relative Speed	= (280 / 9)m/sec
= (280/9 x 18/5)
= 112 kmph.
Speed of the train	= (112 - 50)kmph
= 62 kmph.
Answer B
Answer: (B) 62 kmph.
Question: A local bank that has 8 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 8 codes?
(A) 4
(B) 6
(C) 5
(D) 3
(E) 7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Total = 9 Codes. Enough.
Answer: D
Answer: (D) 3
Question: If there are 4 peanuts in a box and Mary puts 4 more peanuts inside, how many peanuts are in the box?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: 4+4=8
correct answer is A)8
Answer: (A) 8
Question: A package contains 8 black and 14 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
(A) 3/5
(B) 7/11
(C) 6/8
(D) 7/9
(E) 1/3
Rationale: Let number of balls = (8+14) = 22.
Number of white balls = 14.
P (drawing a white ball) =	14/22=7/11
B
Answer: (B) 7/11
Question: At what time between 5.30 and 6 will the hands of a clock be at right angles?
(A) (43 + 7/11) min pats 7
(B) (43 + 7/11) min pats 5
(C) (43 + 7/11) min pats 4
(D) (43 + 7/11) min pats 2
(E) (43 + 7/11) min pats 1
Rationale: At 5 o'clock, the hands are 25 min. spaces apart.
To be at right angles and that too between 5.30 and 6, the minute hand has to gain (25 + 15) = 40 min. spaces.
55 min. spaces are gained in 60 min
40 min. spaces are gained in min
Answer: B
Answer: (B) (43 + 7/11) min pats 5
Question: Each customer of a networking company subscribes to one of two plans: Plan A or Plan B. Plan A costs $75 per month and Plan B costs $175 per month per customer. If the company’s average revenue per customer per month is $150, then what percent of the company's revenue comes from customers with Plan A?
(A) 25%
(B) 30%
(C) 37.5%
(D) 56.25%
(E) 75%
Rationale: We can show this algebraically:
If there are A customers with plan A, and B customers with plan B, then the total revenue is $75A + $175B.
Since the average customer pays $150, we know that
$150 = ($75A + $175B) / (A + B)
$150(A + B) = ($75A + $175B)
$150A + $150B = $75A + $175B
$75A = $25B
3A = B.
Since there are 1/3 times as many $75 clients as $175 clients, for every $175 received from Plan B customers, 3($75) = $75 is received from Plan A customers, and the percent of revenue from customers with Plan A is:
$75/($75 + $175)= 30%.
The correct answer is choice (B).
Answer: (B) 30%
Question: The annual budget of a certain college is to be shown on a circle graph. If the size of each sector of the graph is to be proportional to the amount of the budget it represents, how many degrees of the circle should be used to represent an item that is 40 percent of the budget?
(A)  15 °
(B)  144 °
(C)  54 °
(D)  90 °
(E)  150 °
Rationale: 100 percent = 360 degrees
40 percent = 360*40/100 = 144 degrees
Answer is B.
Answer: (B)  144 °
Question: A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
(A) Rs. 4991
(B) Rs. 5991
(C) Rs. 6001
(D) Rs. 6991
(E) Rs. 6992
Rationale: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs. [ (6500 x 6) - 34009 ]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer A
Answer: (A) Rs. 4991
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
(A) 6
(B) 7
(C) 4
(D) 9
(E) 5
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.
Answer: E
Answer: (E) 5
Question: If a company allocates 25 percent of its budget to advertising, 15 percent to capital improvements, and 55 percent to salaries, what fraction of its budget remains for other allocations?
(A) 4/5
(B) 3/5
(C) 3/10
(D) 1/20
(E) 1/40
Rationale: 25 + 15 + 55 = 95% 100 - 95 = 5% to all others
D
Answer: (D) 1/20
Question: A shopkeeper sells 400 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
(A) 12
(B) 27
(C) 29
(D) 50
(E) 21
Rationale: SP per metre = 18000/400 = Rs. 45 Loss per metre = Rs. 5 CP per metre = 45 + 5 = Rs. 50.Answer: D
Answer: (D) 50
Question: From a group of 4 boys and 4 girls, 6 children are to be randomly selected. What is the probability that 3 boys and 3 girls will be selected?
(A) 1/2
(B) 2/3
(C) 3/5
(D) 4/7
(E) 5/9
Rationale: The total number of ways to choose 6 children from 8 is 8C6 = 28
The number of ways to choose 3 boys and 3 girls is 4C3*4C3 = 4*4 = 16
P(3 boys and 3 girls) = 16/28 = 4/7
The answer is D.
Answer: (D) 4/7
Question: A man is walking at a speed of 6 km per hour. After every km he takes rest for 6 minutes. How much time will he take to cover a distance of 12 km.
(A) 3 hr
(B) 5 hr 42 min
(C) 4 hrs. 10 min
(D) 3 hr. 6 min
(E) None of these
Rationale: Explanation:
For 12 km he takes 11 times rest.
11 x 6 = 66 minutes rest
= 1 hr 6 min
For 12 km, 2 hr is required + rest
= 2 + 1 hr 6m = 3 hr. 6 min
Answer: Option D
Answer: (D) 3 hr. 6 min