RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A person's present age is two-fifth of the age of his father. After 8years, he will be one - half of the age of his father. How old is the father at present ?
A.A)40
B.B)48
C.C)32
D.D)45
Answer: A.A)40
Explanation: Let the father's present age be x years
Then the person's present age = 2x/5
(2x/5)+8 = 1/2(x+8)
2(2x+40) = 5 (x+8)
x = 40
Answer is A
Question: Each of eight different locks has a matching key. The keys are randomly reassigned to the locks. What is the probability that exactly two of the keys fit the locks to which they are reassigned?
A.1/8
B.1/6
C.1/64
D.3/8
Answer: C.1/64
Explanation: I was just going over probability questions.
can some one explain me what's wrong in my approach here.
Probability of choosing one right key out of 8 is 1/8.
Probability of choosing another right key is 1/8.
since the question is asking for 2 right keys , probability is multiplication of both = 1/8 * 1/8 = 1/64.
Ans C
Question: A person purchased a TV set for Rs. 17000 and a DVD player for Rs. 6250. He sold both the items together for Rs. 31150. What percentage of profit did he make?
A.16.97%
B.87.97%
C.33.97%
D.17.97%
Answer: C.33.97%
Explanation: The total CP = Rs. 17000 + Rs. 6250 = Rs. 23250 and SP
= Rs. 31150
Profit(%) = (31150 - 23250)/23250 * 100
= 33.97%
Answer:C
Question: If each edge of a cube is doubled, then its volume :
A.Becomes 8 times
B.Becomes 9 times
C.is double
D.Becomes 6 times
Answer: A.Becomes 8 times
Explanation: Sol.
Let original edge = a. Then, volume = a³
New edge = 2a. So, new volume = (2a)³ = 8a³
∴ Volume becomes 8 times
Answer A
Question: The current birth rate per thousand is 42, where as corresponding death rate is 22 per thousand. The net growth rate in terms of population increase in percent is given by?
A.2.0%
B.3.2%
C.3.9%
D.4%
Answer: A.2.0%
Explanation: Net growth on 1000 = 42-22 = 20
Net growth on 100 = 20*100/1000 = 2.0%
Answer is A
Question: John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
A.40 ml
B.60 ml
C.70 ml
D.80 ml
Answer: C.70 ml
Explanation: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2 =310
By rule of alligation,
concentration of water in mixture1 (29)
concentration of water in pure water (1)
Mean concentration
(310)
1−310=710
310−29=790
=> Quantity of mixture1 : Quantity of water
=710:790=110:190=1:19
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water =1:19
=> Quantity of water =630×19=70 ml
C
Question: Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest and the other is a savings account with r% annual compound interest. If both accounts have the same balance after two years, what is the value of r?
A.11
B.14.25
C.18.5
D.20
Answer: D.20
Explanation: Let the amounts deposited on both accounts be $100.
Then we'd have that 100+100∗0.22+100∗0.22=100(1+r)2100+100∗0.22+100∗0.22=100(1+r)2 --> 144=100(1+r)2144=100(1+r)2 --> (1+r)2=1.44(1+r)2=1.44 --> 1+r=1.21+r=1.2 --> r=0.2
Answer is D
Question: A bag contains 8 red and 4 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
A.4/7
B.2/3
C.5/8
D.1/4
Answer: B.2/3
Explanation: Total number of balls = 8+4 = 12
number of white balls = 8
Probability = 8/12 = 2/3
Answer is B
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
A.2298
B.1000
C.2888
D.2771
Answer: B.1000
Explanation: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut = 10 * 10 * 10 = 1000
Answer:B
Question: Mary, Peter, and Lucy were picking chestnuts. Mary picked twice as much chestnuts than Peter. Lucy picked 2 kg more than Peter. Together the three of them picked 26 kg of chestnuts. How many kilograms did each of them pick?
A.6
B.7
C.1
D.8
Answer: A.6
Explanation: Let xx be the amount Peter picked. Then Mary and Lucy picked 2x2x and x+2x+2, respectively. So
x+2x+x+2=26x+2x+x+2=26
4x=244x=24
x=6x=6
Therefore, Peter, Mary, and Lucy picked 6, 12, and 8 kg, respectively.
Answer:A
Question: How many three digit numbers W are divisible by 78 or 91?
A.17
B.19
C.20
D.21
Answer: B.19
Explanation: The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well-- 13*7*6=91*6=546
So total number of multiples W--11+9 -1 =19.
Hence Answer is 19.B
Question: A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:
A.22
B.24
C.26
D.23
Answer: C.26
Explanation: Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140 x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.
Answer is C.
Question: When divided by 5, x has a remainder of 4 and y has a remainder of 2. Which of the following could be the remainder when x + y is divided by 10?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: x = 5k+4 and y = 5j+2
x+y = 5(j+k) + 6
When divided by 10, the remainder is either 6 or 1.
The answer is A.
Question: If a = 0.1039, then the value of âˆš4a2 - 4a + 1 + 3a is:
A.0.1039
B.0.2078
C.1.1039
D.2.1039
Answer: C.1.1039
Explanation: Explanation:
âˆš4a2 - 4a + 1 + 3a = âˆš(1)2 + (2a)2 - 2 x 1 x 2a + 3a
=âˆš(1 - 2a)2 + 3a
= (1 - 2a) + 3a
= (1 + a)
= (1 + 0.1039)
= 1.1039
ANSWER IS C
Question: The difference between two numbers is 1356. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is
A.240
B.270
C.295
D.360
Answer: B.270
Explanation: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Smaller number = 270
ANSWER:B
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently eight spaces behind player B, what is the probability that player B will be frozen after player A rolls?
A.1/12
B.5/36
C.1/6
D.1/3
Answer: B.5/36
Explanation: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 8 (as A is 8 spaces behind B) = 5 ( (2,6), (3,5), (4,4), (5,3), (6,2) )
So, the probability = 5/36 (Option B)
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
A.31.5
B.31.8
C.31.6
D.31.3
Answer: C.31.6
Explanation: 100*(80/100)*(90/100)*(95/100)
= 68.4
100 - 68.4 = 31.6
Answer:C
Question: For four days of work, a clerk had daily earnings of $120, $110, $120, and $120 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?
A.Between $50 and $100
B.Between $20 and $40
C.Between $20 and $60
D.Between $0 and $10
Answer: D.Between $0 and $10
Explanation: The standard deviation is between 0 and 10.
The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(110-(120*3+110)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.
Answer : D
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 9720 votes were polled, then how many valid votes did B get?
A.1888
B.2999
C.3159
D.2777
Answer: C.3159
Explanation: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 9720
32.5k = 32.5k/100k * 9720 = 3159
The number of valid votes polled in favour of B is 3159.
Answer: C
Question: A man walking at a rate of 15km/hr crosses a bridge in 35 minutes. The length of the bridge is?
A.1250m
B.1750m
C.950m
D.1000m
Answer: B.1750m
Explanation: Speed = 15*5/18 = 15/18 m/sec
Distance covered in 35 minutes = 15/18 *35 *60 = 1750 m
Answer is B
Question: A Refrigerator is available for $39000 cash or $17000 as down payment followed by five equal monthly instalments of $4800 each. The simple rate of interest per annum under the instalment plan would be
A.18%
B.19%
C.21.2%
D.21.81%
Answer: D.21.81%
Explanation: Simple interest SI = (P*R*T)/100
where P is the principal amount
R is the rate of interest
and T is time in years
the way I see it: For Refrigerator on down payment of 17,000, customer is not paying any interest. it is the remaining sum which will be paid for 5 months that will bear an interest. Therefore, the principal amount for which interest is being charged is 39,000 - 17,000 = 22,000
For this 22,000 a total sum of 5*4800 = 24,000 was pain. (Time is five months, so T = 5/12, as T is in years.)
thus, SI = 2000 or
2000 = (P*R*T)/100
2000 = (22,000*R*5)/(100*12)
R = (2,000*12*100)/22,000*5
R = 21.81%
Therefore answer is D
Question: A boat crossed a lake from East to West at the speed of 5 km/h, entered a river and covered twice as much distance going upstream at 4 km/h. It then turned around and stopped at the south shore of the lake. If it averaged 3.6 km/h that day, what was its approximate downstream speed?
A.4
B.5
C.6
D.7
Answer: C.6
Explanation: One way of solving this is:
Speed of boat on still water (lake)=5kmph
Speed upstream = 4kmph = speed in still water - speed of river => speed of river = 1kmph
=>Speed downstream = speed in still water + speed of river = 5+1 =6kmph
Ans is C
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
A.2777
B.2987
C.1200
D.9977
Answer: C.1200
Explanation: CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer: C
Question: If |x^2 − 20| = x, which of the following could be the value of x?
A.-5
B.-4
C.1
D.4
Answer: D.4
Explanation: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.
First, let's assume that x^2-20 is negative.
-(x^2 - 20) = x
x^2 + x - 20 = 0
(x+5)(x-4) = 0
x = 4 or x = -5 (However, x can not be negative.)
Then x = 4 is a possible value for x.
The answer is D.
Question: If a company allocates 25 percent of its budget to advertising, 30 percent to capital improvements, and 35 percent to salaries, what fraction of its budget remains for other allocations?
A.1/10
B.1/5
C.1/4
D.1/3
Answer: A.1/10
Explanation: 100%-(25%+30%+35%)=10% remains for other allocations --> 10% = 10/100 = 1/10.
Answer: A.
Question: 3 candidates in an election and received 1136, 5636 and 11628 votes respectively. What % of the total votes did the winning candidate gotin that election?
A.40%
B.55%
C.57%
D.63.2%
Answer: D.63.2%
Explanation: Total number of votes polled = (1136 + 5636 + 11628) = 18400
So, Required percentage = 11628/18400 * 100 = 63.2%
D
Question: The difference between compound and d simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
A.28882
B.27772
C.23123
D.Rs.13500
Answer: D.Rs.13500
Explanation: P = (184*106) / [6 2/3 * 6 2/3 *(300 *6 2/3)]
P = 13500
Answer: D
Question: A vendor sold two things at same cost of 13 RS with one item at 25%profit and other at 20%loss,by this transaction he made profit or loss by how much
A.0.65 loss
B.0.70 loss
C.0.80 loss
D.0.55 loss
Answer: A.0.65 loss
Explanation: CP when profit of 25% = 10.4
CP when loss of 20% = 16.25
Total CP = 26.65
Total SP = 26.00
Total loss = 0.65
ANSWER:A
Question: The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 6 revolutions ? (use Ï€ = 22â„7)
A.40 m2
B.44 m2
C.52.8 m2
D.36 m2
Answer: C.52.8 m2
Explanation: Required area covered in 5 revolutions
= 6 Ã— 2Ï€rh = 6 Ã— 2 Ã— 22â„7 Ã— 0.7 Ã— 2 = 52.8 m2
Answer C
Question: A is four times as fast as B. If B alone can do a piece of work in 60 days, in what time can A and B together complete the work?
A.10
B.12
C.22
D.28
Answer: B.12
Explanation: A can do the work in 60/4 i.e., 15 days.
A and B's one day's work = 1/15 + 1/60 = (4 + 1)/60 = 1/12
So A and B together can do the work in 12 days.
Answer: B
Question: Divide 71 into 2 parts such that 1 part exceeds the other by 8. What are the 2 no.'s in that part?
A.17
B.21
C.31
D.45
Answer: C.31
Explanation: Let $let n$ be the smaller and 71 - n be the larger number. Now, since the larger number exceeds the smaller number by 7, we can form the equation
larger number – smaller number = 7
which is equivalent to
Simplifying, we have 71 - 2n = 7. This gives us 2n = 78 which implies that the larger number is . The smaller is 71-39=31.
C
Question: The owner of an art shop conducts his business in the following manner. Every once in a while he raises his prices fo x%, then a while later he reduces all the new prices by x%. After one such up-down cycle the price of a painting decreased by $ 441. After a second up-down cycle the painting was sold for $ 1944.81. What was the original price of the painting in $?
A.2756.25
B.2256.25
C.2500
D.2000
Answer: B.2256.25
Explanation: firstly, i will eliminate E because it's too much..
the 1st time reduction is 441
but the price after 2 times reduction is 1944.81
So, we can cut D and B ..
now only 2756 and 2500 left
the final price is 1944.81..
C); 2500 - 1944 = ~550
B); 2756 - 1944 = ~800
because the first reduction is 441 so the 2nd reduction should be lower than 441
but in C ; 550-441 = ~110 .. its too much reduction in the 2nd round
so B; 800-441 = ~ 360 seems quite good..
ANSWER:B
Question: A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The area of the lawn is (1/6) hectares. Find the length and breadth of the lawn.
A.50
B.30
C.20
D.40
Answer: A.50
Explanation: Let length = 2x meters and breadth = 3x meter.
Now, area = (1/6 )x 1000 m2 = 5000/3m2
So, 2x * 3x = 5000/3 <=> x2 = 2500/9 <=> x = 50/3
therefore Length = 2x = (100/3) m = 33(1/3) m and Breadth = 3x = 3(50/3) m = 50m.
Answer is A
Question: V is the volume of a cylinder; the radius of the cylinder is 2.4. The height of the cylinder is 550% more than the radius. Which of the following is true?
A.100 < V < 300
B.300 < V < 500
C.500 < V < 700
D.700 < V < 900
Answer: B.300 < V < 500
Explanation: As we see the answers are in form of range we can use approximation
Volume of cylinder is πr^2h
Given π= 22/7 and r = 2.4 so r^2 ~ 6 and h = 6.5 * 2.4 ~ 16
So 22/7 * 6 * 16 ~ 302
so answer should be
B. 300 < V < 500
Answer : B
Question: An instrument manufactured by a company consists of two parts A and B. In manufacturing part A, 9 out of 100 are likely to be defective and in manufacturing part B, 5 out of 100 are likely to be defective. Calculate the probability that the instrument will not be defective.
A.0.86.
B.0.91
C.0.95
D.0.97
Answer: A.0.86.
Explanation: Explanation :
Let, A ≡ event that part A is non- defective.
B ≡ event that part B is non- defective.
A and B are independent events.
AB ≡ event that part A and part B both are non-defective so that instrument is not defective.
=> P(AB) = P(A) x P(B).
=> [ 1 - P(~A)] x [ 1 - P(~B)].
Here, P(~A)= 9/100 = probability of part A being defective
and, P(~B) = 5 / 100 = probability of part B being defective.
=> P(AB) = [1- (9 / 100 ) ] x [1- (5 / 100)].
=> 0.91 x 0.95.
=> 0.86.
Hence, the required probability is 0.86.
Answer : A
Question: The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ration of the number of boys to the number of girls in the class is:
A.2:3
B.1:2
C.4:5
D.5:4
Answer: A.2:3
Explanation: Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3.
ANSWER A
Question: What is the sum of odd integers from 35 to 55, inclusive?
A.495
B.1,500
C.1,240
D.1,120
Answer: A.495
Explanation: Number of odd integers = (55-35)/2 + 1
= 20/2 + 1
= 11
Sum of odd integers = (35+55)/2 * 11
= 495
Answer A
Question: The average of 35 students in a class is 16 years. The average age of 21 students is 14. What is the average age of remaining 14 students?
A.18 years
B.21 years
C.12 years
D.19 years
Answer: D.19 years
Explanation: Sum of the ages of 14 students
= (16 * 35) - (14 * 21) = 560 - 294 = 266
Required average = (266/14)
= 19 years.
Answer: D
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.287m
B.180m
C.279m
D.267m
Answer: B.180m
Explanation: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Question: The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 20, what is the age of the youngest sibling?
A.14
B.15
C.16
D.17
Answer: C.16
Explanation: x + (x+3) + (x+5) + (x+8) = 80
4x + 16 = 80
4x = 64
x = 16
The answer is C.
Question: Find the fourth proportional to 1.4,3.2 and 6.5?
A.13.19
B.14.09
C.14.86
D.15.36
Answer: C.14.86
Explanation: Formula= Fourth proportional =(b x c)/a
a=1.4 , b=3.2 and c=6.5
(3.2 x 6.5)/1.4=14.86
C
Question: What would be the perimeter of the square whose side is equal to the diameter of the circle whose perimeter is 52.5 cm?
A.52.5
B.60.2
C.66.8
D.74.25
Answer: C.66.8
Explanation: Diameter of the circle= perimeter/Ï€ = 52.5x7/22 = 16.70
Perimeter of the square=16.70x4=66.8cm
Answer: C
Question: A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
A.3.6 sec
B.18 sec
C.36 sec
D.72 sec
Answer: C.36 sec
Explanation: CATEGORY
Formulae
Examples
DIRECTIONS : Problems based on Trains.
11.	A train 280 m long, running with a speed of 63 km/hr will pass a tree in
A. 15 sec.
B. 16 sec.
C. 18 sec.
D. 20 sec.
Solution
Speed	= (63 x 5/18) m/sec
= 35/2 msec
Time taken	= (280 x 2 /35)m/sec
= 16 sec.
12.	A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is ihe length of the train?
A. 120 metres
B. 180 metres
C. 324 metres
D. None of these
Solution
13.	A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
A. 3.6 sec
B. 18 sec
C. 36 sec
D. 72 sec
Solution
Speed of train relative to jogger	= (45 - 9) km/hr
= 36 km/hr
= (36 x 5/18) m/sec
= 10 m/sec
Distance covered	= (240+120) m
= 360 m
Time taken	= (360 / 10)sec
= 36 sec.
Answer C
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
A.100
B.110
C.179
D.209
Answer: D.209
Explanation: Explanation:
In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.
Hence we have 4 options as given below
We can select 4 boys ...(option 1)
Number of ways to this = 6C4
We can select 3 boys and 1 girl ...(option 2)
Number of ways to this = 6C3 × 4C1
We can select 2 boys and 2 girls ...(option 3)
Number of ways to this = 6C2 × 4C2
We can select 1 boy and 3 girls ...(option 4)
Number of ways to this = 6C1 × 4C3
Total number of ways
= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3
= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]
=
6
×
5
2
×
1
+
6
×
5
×
4
3
×
2
×
1
×
4
=6×52×1+6×5×43×2×1×4
+
6
×
5
2
×
1
×
4
×
3
2
×
1
+
6
×
4
+6×52×1×4×32×1+6×4
=
15
+
80
+
90
+
24
=209
D)
Question: The maximum numbers of students among them 671 Note books and 610 pencils can be distributed in such a way that each student gets the same number of note books and same number of pencils is
A.91
B.910
C.61
D.1911
Answer: C.61
Explanation: olution
Required number of students.
= H.C.F of 671 and 610.
â€¹=â€º 61.
Answer C
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: S = (1 + 2 + 3)/2 = 3
=> No triangle exists.Answer: A
Question: What is the smallest integer E greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10?
A.21
B.41
C.E=121
D.241
Answer: C.E=121
Explanation: Or u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder E as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.C
Question: In jar A there are 3 white balls and 2 green ones, in jar B there is one white ball and three green ones. A jar is randomly picked, what is the probability of picking up a white ball out of jar A?
A.2/5
B.3/5.
C.3/10
D.3/4
Answer: C.3/10
Explanation: Prob of picking jar A = 1/2
Prob of picking a white ball from jar A = 3/5
Prob of picking up a white ball out of jar A = 1/2*3/5 = 3/10
Hence, answer will be C.
Question: A and B started a business jointly A's investment was thrice the investment of B and the period of his investment was two times the period of investment of B. If B received Rs. 4000 as profit, then their total profit is
A.23477
B.28000
C.28877
D.1987
Answer: B.28000
Explanation: Explanation:
Suppose B invested Rs. x for y months. Then, A invested Rs. 3x for 2y months.
So, A : B = (3x * 2y) : (x * y) = 6xy : xy = 6 : 1.
B's profit : Total profit = 1 : 7.
Let the total profit be Rs. x Then, 1/7 = 4000/x or x = 28000.
Answer: B) 28000
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.
A.20
B.21
C.22
D.23
Answer: D.23
Explanation: Number of members in the team = 11
Let the average age of of the team = x
=> (Sum of ages of all 11 members)/11=x
=> Sum of the ages of all 11 members = 11x
Age of the captain = 26
Age of the wicket keeper = 26 + 3 = 29
Sum of the ages of 9 members of the team excluding captain and wicket keeper
=11x−26−29=11x−55
Average age of 9 members of the team excluding captain and wicket keeper
=(11x−55)/9
Given that (11x−55)/9=(x−1)
⇒11x−55=9(x−1)
⇒11x−55=9x−9
⇒2x=46
⇒x=46/2
=23 years
Answer is D.
Question: In a span of 24 hours, how many times would the two hands of a clock point exactly in opposite directions ?
A.10
B.11
C.23
D.22
Answer: D.22
Explanation: Explanation:
In every hour, the two hands (minute and hour) of the clock would be exactly opposite to each other once. But, from 5 o'clock to 6 o'clock and from 6 o'clock to 7 o'clock (a span of hours), they would be exactly opposite only once (at exact 6 o'clock).
Thus, during the span of 12 hours, the two hands would be exactly opposite 11 times. Hence, in the span of 24 hours they would be exactly opposite 22 times.
ANSWER D
Question: The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?
A.81 years
B.21 years
C.51 years
D.31 years
Answer: C.51 years
Explanation: Age of the teacher
= (37 * 15 - 36 * 14) years
= 51 years.
Answer: C