RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12500 after a year?
A.3630
B.3637
C.3630
D.3750
Answer: D.3750
Explanation: 6300:4200:10500
3:2:5
3/10 * 12500 = 3750
Answer: D
Question: Mudit's age 30 years hence will be thrice his age four years ago. Find Mudit's present age?
A.12
B.19
C.27
D.21
Answer: D.21
Explanation: Explanation:
Let Mudit's present age be 'm' years.
m + 30 = 3(m - 4)
=> 2m = 42 => m = 21 years.
Answer:D
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 24,500. What was Simran's share in the profit ?
A.10,529
B.10,512
C.10,110
D.10,500
Answer: D.10,500
Explanation: The ratio of their investments:
50000x36 : 80000x30 = 3 : 4
Simran's share of profit = (24500x3/7) = Rs.10,500.
Answer: D
Question: The probability that a man will be alive for 10more yrs is 1/4 & the probability that his wife will alive for 10 more yrs is 1/3. The probability that none of them will be alive for 10 more yrs, is
A.1/2
B.1
C.3/2
D.3/5
Answer: A.1/2
Explanation: Sol. Required probability = Pg.) x P(B) = (1— D x(1 —I) =: x 1=1/2
Ans.(A)
Question: If a number x is in octal form and having zero as unit place then if we change that number x in decimal form then what is the probability that number x having zero as unit place?
A.11/64
B.11/69
C.11/66
D.11/64
Answer: A.11/64
Explanation: example (8)10=(10)8(8)10=(10)8, (16)10=(20)8(16)10=(20)8, (24)10=(30)8(24)10=(30)8, (32)10=(40)8(32)10=(40)8, (40)10=(50)8(40)10=(50)8, . . .
So out of five numbers end with zero in octal form, only one (50)8=(40)10(50)8=(40)10 has zero in decimal format. So the required probability is 1/5
My initial thinking:
Let the number be "ab0" in octal form. Remember here a, b < 8. So total possibilities are 64.
If we convert the given number into decimal format, then (ab0)8 = 64a + 8b.
We will find for how many values of 64a + 8b ends in zero.
64a + 8b = 60a + (4a + 8b)
For (0,0), (1, 2), (1, 7), (2, 4), (3, 1), (3, 6), (4, 3), (5, 5), (6, 2), (6, 7), (7, 4), (0, 0) the above expression gives unit digit 0.
So required probability = 11/64
(Imp: Still I am not comfortable with the solution I have written as it is not specified whether the given number is 3 digit or not. Just learn how I tried to solve it. )
Answer:A
Question: A wheel rotates 10 times every minute and moves 30 cm during each rotation. How many metres does
the wheel move in one hour?
A.6 metre
B.18 metre
C.180 metre
D.1800 metre
Answer: C.180 metre
Explanation: Expl : Number of times wheel moves in 1 hour = 10 * 60 = 600
:. Distance moves = (600 *30) cm = 18000 cm
In metres = 180 metre
Answer: C
Question: A is a working partner and B is a sleeping partner in the business. A puts in Rs.15000 and B Rs.25000, A receives 10% of the profit for managing the business the rest being divided in proportion of their capitals. Out of a total profit of Rs.9600, money received by A is?
A.2726
B.1827
C.1199
D.4200
Answer: D.4200
Explanation: Explanation:
15:25 => 3:5
9600*10/100 = 960
9600 - 960 = 8640
8640*3/8 = 3240 + 960
= 4200
Answer:D
Question: 15 litres of mixture contains 20% alcohol and the rest water. If 2litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
A.16.67%
B.23%
C.18.3%
D.17.64%
Answer: D.17.64%
Explanation: Alcohol in the 15litres of mix. = 20% of 15litres = (20*15/100) = 3litres
water in it = 15-3 = 12litres
new quantity of mix. = 15+2 = 17 litres
Quantity of alcohol in it = 3litres
Percentage of alcohol in new mix. = 3*100/17 = 17.64%
Answer is D
Question: The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 30%. By approximately what percent would the output now have to be decreased in order to restore the original output?
A.20%
B.24%
C.30%
D.32%
Answer: C.30%
Explanation: The original output increases by 10% and then 30%.
Total % change = a + b + ab/100
Total % change = 10 + 30 + 10*30/100 = 43%
Now, you want to change it to 0, so,
0 = 43 + x + 43x/100
x = -43(100)/143 = 30% approximately
Answer is C
Question: What is the product of all the possible values of x if x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0?
A.–29
B.–12
C.12
D.29
Answer: B.–12
Explanation: x^2(x + 2) + 7x(x + 2) + 6(x + 2) = 0
=> (x+2)(x^2 + 7x + 6) = 0
=>(x+2)(x+1)(x+6)=0
=> x= -1 or -2 or -6
product =-12
answer option -12
ANSWER:B
Question: A jogger running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 metres long train running at 45 kmph in the same direction . in how much time will the train pass the jogger ?
A.18 seconds
B.26 seconds
C.36 seconds
D.16 seconds
Answer: C.36 seconds
Explanation: Total Distance(d) = 240+120 = 360 meter
Relative speed (s) = 45 - 9 = 36 Kmph = 36*5/18 = 10mps
d = s* t
360 = 10*t
t = 36 seconds
ANSWER:C
Question: The side of a square is increased by 15% then how much % does its area increases?
A.52.65
B.56.25
C.50.75
D.32.25
Answer: D.32.25
Explanation: a = 100 a2 = 10000
a = 115 a2 = 13225
----------------
10000 --------- 3225
100 -------? => 32.25 %
ANSWER: D
Question: set s contains the following numbers 10, 14, 19, 27, 36, 49, 67, 70,94. It was found that Mark had inadvertently interchanged the digits of one of the numbers. Steve, in charge of statistics, rectified this error, and as a result mean and median were changed and the shift in mean was of 5.
Whats the number that was incorrectly noted?
A.36
B.49
C.94
D.27
Answer: D.27
Explanation: Firstly the NEW median will be 27 or 49...
secondly the change in SUM will be 9*5 = 45, so the difference in number and in reversed order will be 45...
and the reversed NUMBER and actual number should be on either side of the MEDIAN 36..
lets see the choices on these points..
A. 36... reverse = 63 but 63−36≠4563−36≠45.... eliminate
B. 49... reverse = 94, and 94-49 = 45, BUT both 49 and 94 lie on the SAME side of 36, so no effect on MEDIAN... ELIMINATE
C. 94... SAME as B.. eliminate
D. 27.... reverse = 72.. 72-27 = 45.. yes and 27 is lesser than 36 and 72 is >36 so median will shift to 49... CORRECT
E. 41.... reverse 14, but 41−14≠4541−14≠45.. eliminate
ANSWER:D
Question: Let C be defined as the sum of all prime numbers between 0 and 28. What is C/3
A.155
B.100/3
C.61
D.47
Answer: B.100/3
Explanation: Prime numbers between 0 and 30 - 2 , 3 , 5 , 7, 11 , 13 , 17 , 19 , 23
Sum,C = 100
C/3 = 11/3
Answer B
Question: A salesman's income consists of a commission and a base salary of $350 per week. Over the past 5 weeks, his weekly income totals have been $406, $413, $420, $436 and $495. What must his average (arithmetic mean) commission be per week over the next two weeks so that his average weekly income is $500 over the 7-week period?
A.$315
B.$245
C.$365
D.$715
Answer: A.$315
Explanation: Total weekly income over 5 weeks=$406+$413+$420+$436+$495=$2170
For avg weekly income to be $500 over 7 weeks, we need total weekly income over 7 weeks=$3500
Now, $3500-$2170=$1330
From this, we subtract base salary for 2 weeks i.e $350*2=$700
Therefore, commission=$1330-$700=$730 for 2 weeks
Avg weekly commission=$315
Answer A
Question: Tanks P and B are each in the shape of a right circular cylinder. The interior of tank P has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank P is what percent of the capacity of tank B?
A.75%
B.80%
C.100%
D.120%
Answer: B.80%
Explanation: B.
For P, r=8/2pi. Its capacity = (4pi)^2 * 10= 160pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
P/B = 160pi/200pi = 0.8
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
A.91.5 cm
B.91.8 cm
C.99.5 cm
D.91.6 cm
Answer: A.91.5 cm
Explanation: Perimeter of the sector
= length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42
= 91.5 cm
Answer: A
Question: Chris wants to pay back his debt to the bank. He has already paid back 60% of the initial debt. His family offered to help by paying 33% of the initial debt, so now he only needs an additional $105 in order to pay off the debt. What was the initial amount of the debt Chris owed to the bank?
A.$1,500
B.$2,000
C.$2,500
D.$3,000
Answer: A.$1,500
Explanation: Answer
Chris already has both 60% and 33% of the debt:
=60%+ 33% = 93%
The remaining amount that he will need to pay is equal to:
=100%-93%=7%
We know that this additional amount is $105; this allows us to find the initial total amount of his debt:
7%=$105
$105/7=$105/0.07= $1,500
answer is A.
Question: The length of a rectangular garden is 2 feet longer than 3 times its width. If the perimeter of the garden is 100 feet, find the length of the garden.
A.42
B.38
C.28
D.57
Answer: B.38
Explanation: Let L and W be the length and width of the garden. The statement "the length of a rectangular garden is 2 feet longer than 3 times its width" may be formulated by
L = 2 + 3 W
The formula for the perimeter is given by
P = 2 L + 2 W
Substitute P and L in the above equation by 100 and 2 + 3 W respectively to obtain
100 = 2(2 + 3 W) + 2 W
Solve for W and L
W = 12 and L = 2 + 3 W = 38.
Check that the perimeter of the rectangular garden is 100
P = 2 L + 2 W = 76 + 24 = 100
correct answer B
Question: Worker A takes 8 hours to do a job. Worker B takes 10 hours to do a job. How long should it take both A and B, working together to do same job.
A.4/9
B.2 4/9
C.3 4/9
D.4 4/9
Answer: D.4 4/9
Explanation: Explanation:
In this type of questions, first we need to calculate 1 hours work, then their collective work as,
A's 1 hour work is 1/8
B's 1 hour work is 1/10
(A+B)'s 1 hour work = 1/8 + 1/10
= 9/40
So both will finish the work in 40/9 hours
=
4 4/9
Option D
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 47, the how old is B?
A.7
B.9
C.18
D.11
Answer: C.18
Explanation: Explanation:
Let C's age be x years. Then, B's age = 2x years. A's age = (2x + 2) years.
(2x + 2) + 2x + x = 47
⇒ 5x = 45
⇒ x = 9.
Hence, B's age = 2x = 18 years.
Answer: C
Question: Train T leaves New York at 7:00 am traveling to Boston at 80mph. Train B leaves Boston at 7:45 am traveling to New York at 70 mph on a parallel track. If the distance between New York and Boston is 210 miles, at what time will the two trains pass each other?
A.8:15 am
B.8:45 am
C.9:00 am
D.9:30 am
Answer: B.8:45 am
Explanation: train T will cover 60 kms in 45 min at 7:45, the time when train B starts...
distance left to cover is 210-60=150..
combined speed=80+70=150..
so the trains meet in 1 hour i.e. 7:45 + 1 hr=8:45
B
Question: How many seconds will a train 150 meters long take to cross a bridge 200 meters long if the speed of the train is 54 kmph?
A.17 sec
B.21 sec
C.23.3 sec
D.27.5 sec
Answer: C.23.3 sec
Explanation: D = 150 + 200 = 350
S = 54 * 5/18 = 15 mps
T = 350/15 = 23.3 sec
C) 23.3 sec
Question: Amit and Ravi invested capitals in the ratio 5:4. At the end of 8 months Amit withdrew and they got equal profits. Find for how long Ravi invested his money?
A.11 months
B.6 months
C.10 months
D.12 months
Answer: C.10 months
Explanation: 8:5=4:x
That is 8*5=4*x
2*5=x
X=10 months
ANSWER:C
Question: Mike took a taxi to the airport and paid $2.50 to start plus $0.25 per mile. Annie took a different route to the airport and paid $2.50 plus $5.00 in bridge toll fees plus $0.25 per mile. If each was charged exactly the same amount, and Annie's ride was 26 miles, how many miles was Mike's ride?
A.20
B.30
C.36
D.46
Answer: D.46
Explanation: The cost of Annie's ride was 2.5+5+(0.25*26) = $14
Let x be the distance of Mike's ride.
The cost of Mike's ride is 2.5+(0.25*x) = 14
0.25*x = 11.5
x = 46 miles
The answer is D.
Question: Evaluate: 10111 - 10*2*5 = ?
A.10101
B.10110
C.11100
D.11001
Answer: A.10101
Explanation: According to order of operations, 10?2?5 (division and multiplication) is done first from left to right
10/2=5* 2 = 10
Hence
10111 - 10*2*5 = 10111 - 10 = 10101
correct answer A
Question: Two pipes can fill a tank in 18 minutes and 30 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
A.1/15
B.1/16
C.1/11
D.1/10
Answer: A.1/15
Explanation: Part of the filled by all the three pipes in one minute
= 1/18 + 1/30 - 1/45 = 1/15
So, the tank becomes full in 15 minutes.
Answer:A
Question: Find the average of the first 20 natural numbers?
A.18.5
B.10.0
C.10.4
D.10.5
Answer: D.10.5
Explanation: Average of the first 'n' natural numbers = (n + 1)/2
We get (20 + 1)/2 = 10.5.Answer: D
Question: What will come in place of the question mark (?) in the following equation?
25(7.5) × 5(2.5) ÷ 125(1.5) = 5?
A.16
B.17.5
C.8.5
D.?=13
Answer: D.?=13
Explanation: 25(7.5) × 5(2.5) ÷ 125(1.5) = 5?
or, 5(2 × 7.5) × 5(2.5) ÷ 5(3 × 1.5) = 5?
or 5(15) × 5(2.5) × 1⁄54.5 = 5?
or, 5(13)= 5? or, ? = 13
Answer D
Question: Two men can fill the tank in 5hr and 4hr respectively, while the third empty it in 20hr. If all pipes are opened simultaneously, then the tank will be filled in
A.2
B.2.5
C.3
D.3.5
Answer: B.2.5
Explanation: Work done by all the men working together in 1 hour.
1/5+1/4−1/20=8/20
Hence, tank will be filled in 20/8=2.5 hour
B
Question: If z is three times larger than n , and if 2n+3 is 20% of 25, what is the value of ?
A.1
B.2
C.3
D.6
Answer: C.3
Explanation: Then the wordings of question are misleading. Moreover, it'd also be a bad way to convey z=4n, if it really wanted to convey so.
From other questions that I have seen, proper wordings could be:
If z is three times as large as n
OR simply,
If z is three times n.C
Question: 3/5 of all married couples have more than one child. 1/2 of all married couples have more than 3 children. What fraction of all married couples have 2 or 3 children?
A.1/5
B.1/10
C.7/20
D.3/5
Answer: B.1/10
Explanation: Plug in simple numbers. Take 100 couples for example.
3/5 of 100 couples have more than one child = 60 couples.
1/2 of 100 couples have more than 3 kids = 50 couples.
This implies that 50 couples are a subset of 60 couples and the complement of 60 couples within those 100 couples, which equals 40 couples have either one or no kids at all.
We need to find couples that have 2 or 3 kids, so essentially, it is 60 - 50 = 10. Fraction will be 10/100 = 1/10.
Option B
Question: The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is
A.720
B.180
C.75
D.65
Answer: C.75
Explanation: Explanation:
The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.
ANSWER IS C
Question: An electric motor makes 4,800 revolutions per minutes. How many degrees does it rotate in one second?
A.18.000 d/sec
B.28.800 d/sec
C.38.000 d/sec
D.26.000 d/sec
Answer: B.28.800 d/sec
Explanation: 4800 revolutions / minute
= 4800*360 degrees / 60 seconds
= 28,800 degrees / second
B
Question: On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
A.0 Remainder
B.1 Remainder
C.2 Remainder
D.4 Remainder
Answer: D.4 Remainder
Explanation: EXPLANATION
Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
x = 5k + 3
x2 = (5k + 3)2
= (25k2 + 30k + 9)
= 5(5k2 + 6k + 1) + 4
On dividing x2 by 5, we get 4 as remainder.
Remainder = 4
Answer D
Question: In how many ways a committee, consisting of 5 men and 6 women can be formed from 8men and 10 women?
A.10000
B.11760
C.12450
D.12666
Answer: B.11760
Explanation: Required number of ways = 8C5 * 10C6
= 8C3 * 10C4
= (8*7*6/3*2*1)*(10*9*8*7/4*3*2*1)
= 11760
Answer is B
Question: Five A-list actresses are vying for the three leading roles in the new film, "Catfight in Denmark." The actresses are Julia Robards, Merly Strep, Sally Fieldstone, Lauren Bake-all, and Hallie Strawberry. Assuming that no actresses has any advantage in getting any role, what is the probability that Julia and Hallie will star in the film together?
A.3/10
B.3/125
C.6/10
D.3/5
Answer: A.3/10
Explanation: Pick Hallie and Julia. Now you can pick the third actress in 3 ways so total number of ways of picking 3 actresses (including Hallie and Julia) = 3
Total number of ways of picking any 3 actresses out of 5 = 5*4*3/3! = 10
Probability that both Hallie and Julia will be picked = 3/10
Ans:A
Question: In the faculty of Reverse-Engineering, 240 second year students study numeric methods, 423 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total?
A.515.
B.545.
C.661.
D.644.
Answer: C.661.
Explanation: Answer is C :661
Solution : Total number of students studying both are 423 + 240 - 134 = 529 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 529, so 100% is approx. 661.
Question: In 1990 the budgets for projects Q and V were $700,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ?
A. 1992
B. 1993
C. 1994
D. 1995
Answer: A. 1992
Explanation: Let the no of years it takes is x.
700+30x = 780-10x --> 40x = 80 and x=2.
Thus, it happens in 1992.
A.
Question: Jean drew a gumball at random from a jar of pink and blue gumballs. Since the gumball she selected was blue and she wanted a pink one, she replaced it and drew another. The second gumball also happened to be blue and she replaced it as well. If the probability of her drawing the two blue gumballs was 25/36, what is the probability that the next one she draws will be pink?
A.1/6
B.4/7
C.3/7
D.16/49
Answer: A.1/6
Explanation: The probability of drawing a pink gumball both times is the same. The probability that she drew two blue gumballs = 25/36 = (5/6) * (5/6)
Therefore probability that the next one she draws is pink =1/6
Option (A)
Question: In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together?
A.720
B.790
C.800
D.820
Answer: A.720
Explanation: Option 'A'
Question: Given the two equations 7r + 2s = 43 and 4r - 3s = 8, by how much does r exceed s?
A.3
B.1
C.5
D.6
Answer: B.1
Explanation: Solve by Simultaneous Equations.
My Answer is B.
r=5
s=4
Question: If 3 workers collect 48 kg of cotton in 4 days, how many kg of cotton will 9 workers collect in 2 days?
A.87 kg
B.67 kg
C.72 kg
D.87 kg
Answer: C.72 kg
Explanation: (3 * 4)/48 = (9 * 2)/ x
x = 72 kg
Answer: C
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 10 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A.22
B.98
C.48
D.88
Answer: C.48
Explanation: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/10 = 3x => x = 20/3.
So, speed of the faster train = 40/3 = 40/3 * 18/5 = 48 km/hr.
Answer:C
Question: What is the simplified result of following the steps below in order?
(1)	add 5y to 2v
(2)	multiply the sum by 3
(3)	subtract v + y from the product
A.5v + 14y
B.5x + 16y
C.5x + 5y
D.6x + 4y
Answer: A.5v + 14y
Explanation: 3(5Y+2V) -V-Y= 14Y+5V
'A' is the answer
Question: A car started running at a speed of 30 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey?
A.288
B.390
C.287
D.266
Answer: B.390
Explanation: The total distance covered by the car in the first 10 hours
= 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 + 48
= sum of 10 terms in AP whose first term is 30 and last term is 48 = 10/2 [30 + 48]
= 390 km.
Answer: B
Question: Of the 13 employees in a certain department, 1 has an annual salary of 38,000, 2 have an annual salary of 45,700 each, 2 have an annual salary of 42,500 each, 3 have an annual salary of 40,000 each and 5 have an annual salary of 48,500 each. What is the median annual salary for the 13 employees?
A.38,000
B.40,000
C.42,500
D.45,700
Answer: D.45,700
Explanation: Median is just the value in the middle when you arrange all values in the ascending order
In this question, the 7th value would be the median (Since there are 13 employees)
38, 40, 40, 40, 42.5, 42.5,45.7
So, answer is D.
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
A.7.5%
B.8%
C.9.7%
D.8.7%
Answer: B.8%
Explanation: Income of Rs 128 on Investment of Rs 1552
Income of Rs ? on Investment of Rs 96
=(96*128)/1522=8%
ANSWER:B
Question: In 1995, the Johns spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johns cut back their water usage. By how much must the Johns have reduce their 1996 water usage to pay exactly the same amount in 1996 as they paid in 1995?
A.a)	33 1/3 %
B.b)	40 %
C.c) 50 %
D.d)	66 2/3 %
Answer: A.a)	33 1/3 %
Explanation: Let x be the water usage and c be the cost water of Jhons
We have
xc =800, c=800/x
Y(1.5c)=800 where Y is the water usage in 1996
Y= 800/ (1.5*800/x)= 1/1.5x=2/3x
Thus reduction will be x-2/3x=1/3x=A
Question: If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio V of the resistors’ sum of A and C to the resistors’ sum of A and B?
A.2(R1+R2):(R1+2R2)
B.(R1+R2):(R1+2R2)
C.(2R1+R2):(R1+2R2)
D.2(R1+R2):(2R1+R2)
Answer: A.2(R1+R2):(R1+2R2)
Explanation: two resistors A (r1) and B (r2).
total or sum of two resistors appear as
r1r2/r1+r2. It is looks like inversion of sum of rates.
1/r1+1/r2= r1+r2/r1r2.
same way sum of A(r1) and c(2r2)=1/r1+1/2r2
=2r2+r1/r12r2.
inversion rate = r12r2/2r2+r1.
ratio V of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2
=2(r1+r2)/2r2+r1.A
Question: How many seconds will a 220 metre long train take to cross a man running with a speed of 8 km/hr in the direction of the moving train if the speed of the train is 80 km/hr?
A.25
B.30
C.40
D.11
Answer: D.11
Explanation: Explanation :
Speed of train relatively to man = ( 80 - 8)km/hr
= 72 km /hr
= (72 x 5 / 18)m/sec
= 20 m/sec
Time taken to pass the man = (220 / 20)sec = 11 sec.
Answer : D
Question: 4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr?
A.40
B.60
C.80
D.90
Answer: B.60
Explanation: 5|5, 10, 15, 20
2|1, 2, 3, 4
|1, 1, 3, 2
L.C.M of 5, 10, 15, 20 is 60
60 times
B
Question: A man rides at the rate of 30km/hr. But stops 30minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 150 kilometers?
A.5hr
B.7hr 30min
C.8hr 10min
D.7hr 20min
Answer: B.7hr 30min
Explanation: speed of man = 30km/hr
number of rests = (150/25)-1 = 5
time taken for the man = (150/30)+5*(30/60) = 7 hr 30 min
Answer is B
Question: a spider web consists of 3 concurrent lines forming radial support for 20 concentric regular hexagon .the hexagon vertices are 5mm from their immidiate neighbour. if the innermost hexagon has a side length 3mm how many meters is the length of the entire web including the 3 diagonals ?
A.6.1
B.6.3
C.7.2
D.8.2
Answer: B.6.3
Explanation: for perimeter of all hexagon =6*(3+8+13+...........20th term.)
sum will be 6060 mm
and for length of one diagonal find 20th term=98
so total length =6060+294=6354 mm=6.354 m
ANSWER:B
Question: 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 15 persons, working 6 hours a day, complete the work?
A.10
B.13
C.14
D.26
Answer: D.26
Explanation: Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons	15	:	39	:: 12 : x
Working hours/day	6	:	5
15 x 6 x x = 39 x 5 x 12
x =	(39 x 5 x 12)/(15 x 6)
x = 26.
ANSWER:D