RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: When the oil from a circular cylinder leaked, the formula for the speed of the leak is V = kh^2, where h was the height of the remaining oil and k was constant. If the height of the cylinder is 4, the speed of the leak is Vâ€™, When the height of the oil remaining is 12, what was the speed of the leak, in terms of Vâ€™?
A.9Vâ€™
B.4Vâ€™
C.Vâ€™/2
D.Vâ€™/4
Answer: A.9Vâ€™
Explanation: When h=4 v=V'
So V' = k.16
Hence k = V'/16
Now when h=12
v=(V'/16).12^2
v=V'.144/16
v=9V'
Ans : A
Question: A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
A.13 days
B.15 days
C.17 days
D.21 days
Answer: B.15 days
Explanation: A's 2 day's work = 1	x 2 =	1	.
20	10
(A + B + C)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.
20	30	60	60	10
Work done in 3 days = 1	+	1 =	1	.
10	10	5
Now,	1	work is done in 3 days.
5
Whole work will be done in (3 x 5) = 15 days.
Option B
Question: Lucy's personal library had 1/20 the capacity as the town library. Lucy decided to donate 1/2 of her book collection to the town library. What fraction of the town library's capacity would Lucy's book donation fill?
A.3/16
B.1/10
C.1/6
D.1/18
Answer: B.1/10
Explanation: Assuming that the town library has space for 100 books, that would mean that Lucy's personal library had 20 books. If Lucy donated a 1/2 of her books, that would mean she donated 10 books. Those 10 books would make 10/100 of the town library's collection. 10/100 simplifies to 1/10. (Answer: B)
Question: Arithmetic mean and standard deviation of a certain normal distribution are 13 and 1.5. What value is exactly 2 standard deviations less than the mean?
A. 10.5
B. 10
C. 11.5
D. 12
Answer: B. 10
Explanation: The value which is exactly two SD below the mean is: mean-2*SD=13-2*1.5=10.
Answer: B.
Question: A train of 50 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
A.6
B.3
C.4
D.4.5
Answer: D.4.5
Explanation: D = 50 * 60 + 1500 = 3000 m
T = 4500/60 * 18/5 = 270 sec = 4.5 mins
Answer:D
Question: A specialized type of sand consists of 40% mineral X by volume and 60% mineral Y by volume. If mineral X weighs 2.5 grams per cubic centimeter and mineral Y weighs 2 grams per cubic centimeter, how many grams does a cubic meter of specialized sand combination weigh? (1 meter = 100 centimeters)
A.5,500,000
B.2,200,000
C.55,000
D.28,000
Answer: B.2,200,000
Explanation: Let the volume be 1 m^3 = 1m * 1m * 1m = 100cm * 100cm * 100cm = 1,000,000 cm^3
By volume
40% is X = 400,000 cm^3
60% is Y = 600,000 cm^3
By weight,
In 1 cm^3, X is 2.5 gms
In 400,000 cm^3 , X = 2.5 * 400,000 = 1,000,000 grams
In 1 cm^3, Y is 2 gms
In 600,000 cm^3, Y = 2 * 600,000 = 1,200,000 gms
Total gms in 1 m^3 = 1,000,000 + 1,200,000 = 2,200,000
ANSWER:B
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
A.299
B.150
C.267
D.551
Answer: B.150
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Question: What percent of a day is 10 hours?
A.12%
B.12.5%
C.13%
D.41.6%
Answer: D.41.6%
Explanation: Explanation :
Solution: required percentage = (10/100 * 24) = 41.6%
Answer : D
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 40 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
A.17 1/8 min
B.17 2/7 min
C.17 1/7 min
D.17 1/6 min
Answer: C.17 1/7 min
Explanation: Explanation:
1/20 + 1/30 - 1/40
= 7/120
120/7
= 17 1/7
Answer:C
Question: A rectangle A has an area of 30 square centimeters. Square B has a perimeter of 16 centimeters. If square B is placed within square A and a random point is chosen within square A, what is the probability the point is not within square B?
A.9/30
B.14/30
C.4/9
D.3/5
Answer: B.14/30
Explanation: I guess it's mean that square B is placed within rectangle A entirely.
Since, the perimeter of B is 16, then its side is 16/4=4 and the area is 4^2=16;
Empty space between the squares is 30-16=14 square centimeters, so if a random point is in this area then it won't be within square B: P=favorable/total=14/30.
Answer: B.
Question: The edge of a cube is 5a cm. Find its surface?
A.24a8
B.150a2
C.24a1
D.24a2
Answer: B.150a2
Explanation: 6a2 = 6 * 5a * 5a = 150a2
Answer:B
Question: If a number between 10 and 40 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?
A.31/41
B.1041
C.7/31
D.27/41
Answer: C.7/31
Explanation: If tens digi is 4 ---> ones digit : 0
If tens digi is 3 ---> ones digit : 0, 1, 2
If tens digi is 2 ---> ones digit : 0, 1
If tens digi is 1 ---> ones digit : 0
So the number of numbers whose tens digit is greater than ones digit is 11.
The total number is 40-10+1=31.
So the probability is 7/31.
The answer is (C).
Question: Two friends A and B leave point A and point B simultaneously and travel towards Point B and Point A on the same route at their respective constant speeds. They meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively. How long will B take to travel the entire journey between Point B and point A?
A.65
B.70
C.90
D.75
Answer: C.90
Explanation: Let x per minute be the speed of A and y per minute be the speed of B.
After meeting at a point, A travels for 32 mins and B travels for 50 mins. So distance covered by each of them post point of crossing
A= 32x and B=50y
The distance covered by A and B before they cross each would be distance covered by B and A post crossing respectively.
Therefore distance covered by B before he meets A= 32x
Time taken by B cover 32x distance= 32x/y mins
Therefore total time taken by B= 32x/y + 50 mins ................. I
We need to find value of x in terms of y to arrive at final answer.
Total distance= 32x+50y
Combined speed of A and B= x+y
Therefore time taken before A and B meet en-route= (32x+50y)/(x+y)
Time taken by B reach destination after meeting A= 50 mins
Total travel time for B= [(32x+50y)/(x+y)]+50 mins ...................II
Equate I and II
32x/y+50= [(32x+50y)/(x+y)]+50
(32x+50y)/y=(82x+100y)/(x+y)
32x^2+50xy+32xy+50y^2=82xy+100y^2
32x^2+82xy-82xy+50y^2-100y^2=0
32x^2-50y^2=0
32x^2=50y^2
16x^2=25y^2
Taking square root.. (since x and y denote speed, square root can't be negative)
4x=5y
y=4x/5 ............ III
substitute in I
=32x/(4x/5) + 50
=32x*5/4x + 50
=40+50
=90 mins
C
Question: The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 24 years. What is the age of the new member ?
A.20 years
B.21 years
C.34 years
D.23 years
Answer: C.34 years
Explanation: The average age of a group of 5 members is 20 years --> the sum of the ages is 5*20=100;
Two years later the sum of the ages of these 5 members would be 100+5*2=110;
Now, say the age of the new member is x years, so the sum of the ages of a new 6 member group is 110+x. Since given that the average age of this group of 6 members is 24 years then: 24*6=110+x --> x=34.
Answer: C.
Question: Three math classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.
What is the average score for all the three classes, taken together?
A.81
B.81.5
C.82
D.84.5
Answer: B.81.5
Explanation: Explanation :
Let the number of students in classes X, Y and Z be a,
b and c respectively. Then
Total of X = 83a
Total of Y = 76b
Total of Z = 85c
And , (83a + 76b) / (a + b) = 79. i.e 4a = 3b.
Also, (76b + 85c) / (b + c) = 81. i.e 4c = 5b.
Hence, b= (4/3)a, c =(5/4)b = (5/4) x (4/3)a = (5/3)a.
Average of X, Y and Z = (83a + 76b + 85c ) / (a + b + c).
=> 83a+76∗(4/3)a+85∗(5/3)a /a+(4/3)a+(5/3)a .
=> 978/12
=> 81.5
Answer : B
Question: How many numbers are there between 20 and 60 which are divisible by 3 and the total of two digits is 9?
A.2
B.3
C.4
D.5
Answer: C.4
Explanation: Since number are
27,36,45,54
ANSWER:C
Question: Mother's age is 65 years. If he is 3 more than twice the age of his son, find the age of his son.
A.32 years
B.31 years
C.16 years
D.18 years
Answer: B.31 years
Explanation: Let Mike's son age be x.
3+ 2 x =65
x = 31
Hence Mike's son age is 31 years
Answer : B
Question: A big container is 30% full with water. If 9 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
A.20 liters
B.40 liters
C.45 liters
D.54 liters
Answer: A.20 liters
Explanation: A big container is 30% full with water and after 9 liters of water is added, the container becomes 75% full. Hence these 9 liters account for 45% of the container, which means that the capacity of it is 9/0.45=20 liters.
OR: if the capacity of the container is x liters then: 0.3x+9=0.75x --> x=20 liters.
Answer: A.
Question: When a person aged 39 is added to a group of n people, the average age increases by 2. When a person aged 15 is added instead, the average age decreases by 1. What is the value of Q?
A. 7
B. 8
C. 9
D. 10
Answer: A. 7
Explanation: A simple and elegant solution.
As addition of 39, shifts mean by 2, and addition of 15, shifts mean by 1 to the other side, we have the mean lying between 3915, and in a ratio of 2:1
39-15 = 24
24 divide by 3 is 8.
Meaning mean of the n terms is 15+8 = 39-16 = 23
Now, from first statement, When a person aged 39 is added to a group of n people, the average age increases by 2.
Q*23 +39 = 25*(Q+1)
Q = 7
Ans. (A)
Question: When tossed, a certain coin has an equal probability of landing on either side. If the coin is tossed 5 times, what is the probability that it will land on the same side each time?
A.1/6
B.1/8
C.1/12
D.1/16
Answer: D.1/16
Explanation: On the first toss, the coin will land on one side or the other.
On the second toss, the probability of landing on the same side is 1/2.
On the third toss, the probability of landing on the same side is 1/2.
On the fourth toss, the probability of landing on the same side is 1/2.
On the fifth toss, the probability of landing on the same side is 1/2.
P(same side all five times)=1/2*1/2*1/2*1/2=1/16.
The answer is D.
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
A.2 : 5
B.2 : 6
C.2 : 0
D.2 : 5
Answer: A.2 : 5
Explanation: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
Answer: A
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
A.140
B.130
C.150
D.170
Answer: C.150
Explanation: Speed=(60x5/8)m/sec = (50/3) m/sec.
Length of the train = (Speed x Time).
Length of the train = (50/3 x 9)m = 150 m.
Answer is C.
Question: Consider the set S = {1, 2, 3, …., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and with 1000 and have at least 3 elements?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: Explanation :
We know that it should be an AP, 1st element is 1, and last element 1000.
a = 1, a + (n-1) d = 1000 ; (n-1) d = 999.
So 999 is the product of (n-1) and d. So, we need to see the factors of 999 to see what all values /how many of those values (n-1) and d can assume.The prime factors are 3, 3, 3, and 37.
(999 = 3 * 3 * 3 * 37). (Other than 1 and 999)
So, we can have
(n - 1) = 3, d = (3 * 3 * 37)
(n - 1) = 3 * 3, d = (3 * 37)
(n - 1) = 3 * 3 * 3, d = (37)
(n - 1) = 37, d = (3 * 3 * 3)
(n - 1) = 37 * 3, d = (3 * 3)
(n - 1) = 37 * 3 * 3, d = (3)
Other than this, we can have 1 and 999 also as factors of 999. If we have n-1 as 1, n is 2. But that means only 2 terms in AP. (Not possible according to the question). If we have n-1 = 999, n = 1000. d = 1. This is possible. So, we have totally, 7 possible combinations.
Answer : D
Question: A, B and C can complete a piece of work in 24,6 and 12 days respectively.Working together, they will complete the same work in:
A.22/9 days
B.23/8 days
C.24/7 days
D.23/8 days
Answer: C.24/7 days
Explanation: Explanation:
(A+B+C)'s 1 day's work =\inline {\color{Black}\left ( \frac{1}{24}+\frac{1}{6}+\frac{1}{12} \right )=\frac{7}{24}}
so, A,B and C together will complete the work in 24/7 days.
Answer: C) 24/7 days
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
A.172
B.267
C.265
D.176
Answer: D.176
Explanation: 25x + 46 = 26(x – 5)
x = 176
Answer:D
Question: An article is sold at a certain price. By selling it at 2/3 of that price one loses 10%. Find the gain percent at original price.
A.15%
B.35%
C.25%
D.50%
Answer: B.35%
Explanation: Let the original S.P be Rs. X. Then new S.P = Rs. 2/3 X, Loss =10%
So C.P = Rs. [100/90*2/3 X ] = 20 X/27.
Now C.P = Rs. 20X/27, S.P =Rs. X, Gain = Rs. [ X -20X/27 ] =Rs.7X/27.
Gain % = [ 7X/27 *27/20X *100 ]% =35%
ANSWER:B
Question: How many litres of water must be added to 16 liters of milk and water containing 10% water to make it 20% water in it?
A.2 litre
B.4 litre
C.6 litre
D.7 litre
Answer: A.2 litre
Explanation: By rule of alligation,
% Concentration
of water in pure water (100)	% Concentration
of water in the given mixture (10)
Mean % concentration
(20)
20 - 10 = 10	100 - 20 = 80
=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8
Here quantity of the mixture = 16 litres
=> Quantity of water : 16 = 1 : 8
=> Quantity of water
=
16
×
1
8
=
2
=16×18=2 litre
A)
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the numbers is 720, then the other is:
A.8
B.10
C.12
D.4
Answer: C.12
Explanation: Other number =	(12 x 600)/720 = 10.
ANSWER :C
Question: The Expenditure of an woman increase consistently by 30% per year. If her present expenditure is Rs. 1000 then what will her expenditure be after 3 years ?
A.2107
B.2197
C.2187
D.2177
Answer: B.2197
Explanation: Explanation :
Expenditure = 1000 x 1.3 x 1.3 x 1.3 = 2197
Answer : Option B
Question: find the least number that when divided by 16,18 and 20 leaves the same remainder 4 in each case but it is completely divisble by 7
A.2884
B.2994
C.2784
D.3254
Answer: A.2884
Explanation: LCM of 16,18,20 is 720...
(720+4)is not divisible by 7...
(720*2+4)not divisible by7..
.
.
(720*4+4)divisible by 7....
so the ans is... 2880+4=2884
ANSWER:A
Question: The total car population in a Chennai is 900 out of which 500 are made by Honda. Out of every 100 Honda cars, 90 are red in color, but only 60% of the total car population is red. Find the % of non-Honda cars that are red
A.20.5%
B.22.5%
C.21.5%
D.10.5%
Answer: B.22.5%
Explanation: Total Honda brand red cars = 90/100 *500 = 450
Total red cars = 60/100*900 = 540
No. of Non-Honda cars = 900-500 = 400
No. of Non-Honda red cars = 540 - 450 = 90
% of Non-Honda red cars = 90/400*100 = 22.5%
Answer : B
Question: 517 x 517 + 483 x 483=?
A.79698
B.80578
C.500578
D.81268
Answer: C.500578
Explanation: =(517)^2 + (483)^2
=(500+17)^2 + (500-17)^2
=2[(500)^2+(17)^2]
=2[250000+289]
=2 x 250289 = 500578
Answer is C
Question: A certain quantity is measured on two different scales, the L-scale and the S-scale, that are related linearly. Measurements on the L-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the L-scale corresponds to a measurement of 100 on the S-scale?
A. 20
B. 36
C. 48
D. 60
Answer: C. 48
Explanation: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that L increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, L will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
Question: 4,25,49,121,169,289,361,529,
A.149
B.169
C.841
D.920
Answer: C.841
Explanation: 29^2= 841 because follow sequence of square of the prime numbers
ANSWER:C
Question: If the set S is composed of the following numbers {99, 100, 100, 105, 106, 111, 128}, which of the following is largest?
A.The average (arithmetic mean) of set S
B.The median of set S
C.The mode of set S
D.The range of set S
Answer: A.The average (arithmetic mean) of set S
Explanation: A) 99, 100, 100, 105, 106, 111, 128 = 749 and its mean is 749/7 = 107.
B) The list is of 7 numbers and median is 105.
C) Mode is number of repetition of a number in the list , here it is 100.
D) Range = Max value - min value = 128 -99 = 29.
E) SD = square root of (sum of ( mean of series - number)^2 ) / n =>< 100
IMO option A is correct answer..
Question: J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 8 hours and M worked for 4 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance?
A.a)4y
B.b)3y
C.c)6y
D.d)8y
Answer: B.b)3y
Explanation: J and M were both paid x dollars
If M gave Y dollars from her X to J then at the end
J will have X+Y dollars
M will have X- Y dollars
Now since the hourly wages have to be same then
Hourly wage of J = (X+Y) / 8 (Since J worked for 8 hrs)
Hourly wage of M = (X-y) /4 (Since M worked 4 hrs less than J)
Equating both
(X+Y)/8=(X-Y)/4
on simplifying X=3y
Answer B
Question: Working at their respective constant rates, machine A makes 100 copies in 10 minutes and machine B makes 150 copies in 15 minutes. If these machines work simultaneously at their respective rates for 30 minutes, what is the total number of copies that they will produce?
A. 250
B. 600
C. 675
D. 700
Answer: B. 600
Explanation: Machine A can produce 100 *30/10= 300 copies
And, Machine B can produce 150* 30/15= 300 Copies
Total producing 600 Copies.
B is the answer
Question: A work can be finished in 20 days by 10 women. The same work can be finished in fifteen days by 20 men. The ratio between the capacity of a man and a woman is
A.1:3
B.4:3
C.2:3
D.2:1
Answer: C.2:3
Explanation: Work done by 10 women in 1 day = 1/20
Work done by 1 woman in 1 day = 1/(10×20)
Work done by 20 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×20)
Ratio of the capacity of a man and woman =1/(15×20) : 1/(10×20) = 1/15 : 1/10
= 1/3 :1/2 = 2:3
Option C
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
A.8925
B.8960
C.8970
D.8900
Answer: A.8925
Explanation: Principal= Rs. ( (100x4016.25)/(9x5)
=Rs. 401625/45
= Rs. 8925.
answer :A
Question: What is the percentage increase in the area of a rectangle, if each of its sides is increased by 20%?
A.42%
B.43%
C.45%
D.44%
Answer: D.44%
Explanation: Let original length =l
original breadth =b
Then original area =lb
Length is increased by 20%
⇒ New length =l×120100=1.2l
Breadth is increased by 20%
⇒ New breadth =b×120100=1.2b
New area =1.2l×1.2b=1.44lb
Increase in area = new area - original area
=1.44lb−lb=0.44lb
Percentage increase in area
=increase in areaoriginal area×100=0.44lblb×100=44%
Answer is D.
Question: In a class,7 students like to play Basketball and 8 like to play Cricket. 3 students like to play on both Basketball and Cricket. How many students like to play Basketball or Cricket or both?
A.12
B.15
C.16
D.18
Answer: A.12
Explanation: Draw a Venn Diagram yourself !
B + C - BC = Number of students that play either Basketball or Cricket
7 +8 - 3 = 12
A)
Question: The second of two numbers is two less than three times the first. Find the numbers if there sum is
66.
A.7-19
B.8-20
C.10-16
D.17-49
Answer: D.17-49
Explanation: We are looking for two numbers.
#1 - x
#2 - 3x â€“ 2
The sum is 66. #1 + #2 = 66
Substituting x + 3x â€“ 2 = 66
4x â€“ 2 = 66
4x = 68
x = 17
The first number is 17, the second number is two less than three times 17 or 49.
correct answer D
Question: If 1/2 of the air in a tank is removed with each stroke of a vacuum pump, what fraction of the original amount of air has been removed after 5 strokes ?
A.31/32
B.7/8
C.1/4
D.1/8
Answer: A.31/32
Explanation: Left After 1st stroke = 1/2
Left After 2nd stroke = 1/2 * 1/2 = 1/4
Left After 3rd stroke = 1/2 * 1/4 = 1/8
Left After 4th stroke = 1/2 * 1/8 = 1/16
Left After 5th stroke = 1/2 * 1/16 = 1/32
So removed = 1- 1/32 = 31/32
Question: The original price of a certain TV set is discounted by g percent, and the reduced price is then discounted by 2g percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?
A.P(1 - 0.03x + 0.02x^2)
B.P(1 - 0.03g + 0.0002g^2)
C.P(1 - 0.03x + 0.002x^2)
D.P(1 - 2x^2)
Answer: B.P(1 - 0.03g + 0.0002g^2)
Explanation: Youcansolve this problem with number plugging.
Say the original price was $10 and g=50. Then after the first reduction the price would become $5 and after the second reduction of 2*50=100% the rprice would become $0.
Now, since P is not zero, then the expression in the brackets must be zero for g=50. Only answer choice B works.
Answer: B.
On this problem - number pluggin is not giving me the answer.. I initially used g = 10, then g = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.
100 (1-0.03(10) + 0.0002 (10)^2)
100 (1-0.3 + 0.0002 (100))
100 (0.7 + 0.02)
100 (0.68) = 68????
double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B..
Question: The sum of ages of 5 children born at the intervals of 3 years each is 55 years. What is the age of the youngest child?
A.5 years
B.4 years
C.6 years
D.7 years
Answer: A.5 years
Explanation: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 55
5x = 25
x = 5.
Age of the youngest child = x = 5 years.
A)
Question: An alloy of copper and zinc contains copper and zinc in the ratio 5 : 4. Another alloy of copper and zinc contains copper and zinc in the ratio 3 : 6. In what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc?
A.4 : 1
B.6 : 1
C.1 : 3
D.2 : 1
Answer: C.1 : 3
Explanation: Let Alloy_1 be x units, and let Alloy_2 be y units.
So, fraction of copper in Alloy_1 = 5x/9, and fraction of zinc in Alloy_1 = 4x/9.
Similarly, fraction of copper in Alloy_2 = 3y/9, and fraction of zinc in Alloy_2 = 6y/9.
Mixing them, we get
copper = 5x/9 +3y/9; zinc = 4x/9 + 6y/9
So, 5x+3y = 4x+6y
-> x = 3y
-> x/y =1/3
So, they must be mixed in the ratio 1 : 3
Answer : C
Question: A salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 290 items for $150 each, what will her monthly salary be?
A.$1,500
B.$1,800
C.$2,100
D.$3,700
Answer: D.$3,700
Explanation: Ans : 1000+ 7.5 % * 150 * (290-50) = $ 3700
ANSWER:D
Question: In how many years will a sum of Rs 800 and 10% per annum completed semiannually becomes Rs.926.10?
A.1 years
B.2 years
C.1 years 6 months
D.2 years 6 months
Answer: C.1 years 6 months
Explanation: 800 ------------->926.10926.10-800=126.10Ist six month =40IInd 6 month=40+2=42IIIrd 6 month=40+4.1=44.140+42+44.1=126.1Answer C
Question: The sum of the even numbers between 1 and n is 95*96, where n is an odd number, then n=?
A.167
B.175
C.183
D.191
Answer: D.191
Explanation: Let n-1 = 2a.
2+4+...+2a = 2*(1+2+...+a) = 2*(a)(a+1)/2 = (a)(a+1) = 95*96
Then a = 95 and n = 191.
The answer is D.