RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The least number of complete years in which a sum of money put out at 20% C.I. will be more than doubled is?
A.7
B.4
C.5
D.3
Answer: B.4
Explanation: Explanation:
P(1 + 20/100)n > 2P or (6/5)n > 2
Now, (6/5 * 6/5 * 6/5 * 6/5) > 2. So, n = 4 years.
Answer:B
Question: What Is The Smallest Positive Integer That Leaves A Remainder Of 1 When Divided By 2, Remainder Of 2 When Divided By 3, A Remainder Of 3 When Divided By 4, And A Remainder Of 9 When Divided By 10?
A.58
B.59
C.60
D.61
Answer: B.59
Explanation: remainder of 1 when divided by 2: (2-1=1)
remainder of 2 when divided by 3: (3-2=1)
remainder of 3 when divided by 4: (4-3=1)
remainder of 9 when divided by 10: (2-1=1)
so N+1 should be divisible by 2,3,4,10
(where N is desired number)
L.C.M. of 2,3,4,10 = 60 (= N+1)
N = 59
ANSWER:B
Question: Of the four numbers, whose average is 100, the first is one-fourth of the sum of the last three. The first number is ?
A.28
B.29
C.80
D.48
Answer: C.80
Explanation: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 100 or x = (100 * 4) / 5 = 80
Answer: C
Question: If the mobile is bought by rs 490 and sold by rs 465.50.find loss%.
A.3%
B.2%
C.7%
D.5%
Answer: D.5%
Explanation: sol. cp=rs490,sp= 465.50.
loss=rs(490-465.50)=rs 24.50.
loss%=[(24.50/490)*100]%=5%
Ans:D
Question: Suppose 6 monkeys take 6 minutes to eat 6 bananas. How many monkeys would it take to eat 18 bananas in 18 minutes?
A.9
B.10
C.11
D.6
Answer: D.6
Explanation: One monkey takes 6 min to eat 1 banana , so in 18 mins 1 monkey will eat 3 bananas , so for 18 bananas in 18 min we need 18/3 =6 monkeys
ANSWER:D
Question: A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variables costs averaging $5 per item. If the manufacturer’s selling price per item is $15, how many items the manufacturer produce and sell to earn an annual profit of $150,000?
A.2,858
B.18,667
C.28,000
D.35,000
Answer: C.28,000
Explanation: Let the items manufactured or sold bex
130000+5x = 15x-150000
10x = 280000
x = 28000
Ans:C
Question: The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 768 sq meters, then what is the width (in meters) of the rectangular plot?
A.24 m
B.16 m
C.35 m
D.54 m
Answer: B.16 m
Explanation: Area = L*W = 3W^2 = 768
W^2 = 256
W = 16
The answer is B.
Question: A bag with 100 kgs potatoes have 99% water. It is kept in the open under the sunlight. After sometime, little amount of water got evaporated and reduced to 98%. What is the weight now ?
A.40 kg
B.50 kg
C.60 kg
D.70 kg
Answer: B.50 kg
Explanation: let the reduced weight be x kg
(100-99)% of 100 kg = (100-98)% of x kg
1% of 100 = 2% of x
x = (1*100)/2 = 50 kg
ANSWER:B
Question: A company can manufacture 1000 phones in a day. One-fifth of the phones produced are defective and one-quarter of all phones produced are rejected by quality control technician. If one-tenth of the nondefective phones are rejected by mistake, and if all the phones not rejected are sold, then what percent of the phones sold by the company are defective?
A.4%
B.16%
C.24%
D.2%
Answer: A.4%
Explanation: We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rejected) and defective. Correct Answer is A
Question: A train leaves Delhi at 9 a.m. at a speed of 30 kmph. Another train leaves at 2 p.m. at a speed of 40 kmph on the same day and in the same direction. How far from Delhi, will the two trains meet?
A.540 km
B.760 km
C.900 km
D.600 km
Answer: D.600 km
Explanation: D
D = 30 * 5 = 150
RS = 40 – 30 = 10
T = 150/10 = 15
D = 40 * 15 = 600 km
Question: The unit digit in the product (784 x 618 x 917 x 463) is:
A.4
B.2
C.9
D.1
Answer: B.2
Explanation: Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2
Answer B) 2.
Question: A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?
A.1 kmph
B.4 kmph
C.5 kmph
D.7 kmph
Answer: A.1 kmph
Explanation: DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph
Answer: A
Question: x is a positive integer of T less than 500. When x is divided by 7, the remainder is 1; when x is divided by 3, the remainder is 2. How many x are there?
A.21
B.22
C.23
D.24
Answer: D.24
Explanation: Took me more than 2 mins to solve.
That's how I did it.
x is between 1-499 included.
Smallest number that can be written as 7n+1 (7*0+1) is 1
Largest number that can be written as 7n+1 is (7*71 +1) is 498
So there are total 72 numbers that can be written as 7n+1
Because x can also be written as 3m+2, we have to see how many numbers that can be written as 7n+1 also can be written as 3m+2
7*0+1 can not be written in the form 3m+2
7*1+1 can be written in the form 3m+2
7*2+1 can not be written in the form 3m+2
7*3+1 can not be written in the form 3m+2
7*4+1 can be written in the form 3m+2
Here we see a sequence that one out of every 4 numbers can be written as 3m+1
72/4= 24 numbers can be written as 3m+1
D is the answer
Question: Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 28km/hr, then find the area of square field.
A.125
B.225
C.325
D.441
Answer: D.441
Explanation: Explanation :
D = 28*3/2 = 42 km. So side of square is 21km, so area – 441km^2
Answer – D
Question: A number when divided by a divisor leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
A.34
B.37
C.38
D.39
Answer: B.37
Explanation: Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
B
Question: A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 5.2 hours, then the distance covered at 40 kmph is
A.130 km
B.120km
C.100km
D.124km
Answer: D.124km
Explanation: Let the partial distance covered at 40 kmph be X
Let the another partial distance covered at 60 kmph be (250 - x)
Thus, x/40 - (250 - x)/60 = 5.2
or, x/40 + (250 - x)/60 = 5.2
or, (3x + 500 - 2x)//120 = 5.2
or 500 + x = 624
x=124
ANSWER:D
Question: A cuboidal block 6cm x 9cm x 12cm is cut up into an exact number of equal cubes.The least possible number of equal cubes will be
A.6
B.9
C.24
D.30
Answer: C.24
Explanation: Volume of block=(6x9x12)= 648cm3
Side of largest cube = H.C.F of 6,9,12 = 3cm
Volume of the cube=(3x3x3)=27cm3
Number of cubes=(648/27)=24 ANSWER : C
Question: In a class there are 19 boys and 10 girls. In how many ways can a boy and a girl be selected?
A.288
B.500
C.277
D.190
Answer: D.190
Explanation: We can select one boy from 19 boys in 19 ways.
We select one girl from 10 girls in 10 ways
We select a boy and girl in 19 * 10 ways i.e.,
= 190 ways.
Answer: D
Question: What will Rs.1500 amount to in three years if it is invested in 20% p.a. compound interest, interest being compounded annually?
A.2400
B.2592
C.2678
D.2540
Answer: B.2592
Explanation: Here P=1500, R=20% n=3 Find A
Substituting in the compound int. formula
A=P(1+R/100)^3, we get A=Rs.2,592
ANSWER:B
Question: Find the average of all prime numbers between 10 and 30.
A.30
B.33.6
C.39.8
D.18.6
Answer: D.18.6
Explanation: Sol.
There are six prime numbers between 10 and 30.
They are 11, 13, 17, 19, 23, 29
âˆ´ Required average = [11+ 13+ 17+19+ 23+ 29 / 6] = 112/ 6 = 18.6
Answer D
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm, there are 15 buffaloes, 8 oxen, and 24 cows. The fodder for these cattle is available for 24 days. If 40 more cows and 15 more buffaloes are brought in, how many days will the fodder last?
A.10
B.12
C.15
D.18
Answer: B.12
Explanation: 2 oxen = 3 buffaloes = 4 cows
Also: 15 buffaloes + 8 oxen + 24 cows
= 10 oxen + 8 oxen + 12 oxen = 30 oxen
There is enough fodder for 1 oxen for 30*24 days.
40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen
The new total is equal to 60 oxen instead of 30 oxen.
30*24 / 60 oxen = 12 days
The answer is B.
Question: Simplify: 0.72*0.43+0.12*0.34
A.0.3504
B.0.4209
C.0.4889
D.0.6412
Answer: A.0.3504
Explanation: Given exp. = 0.72*0.43+(0.12*0.34) = 0.3096+0.0408 = 0.3504
Answer is A
Question: A can do a job in 18 days and B can do it in 30 days. A and B working together will finish thrice the amount of work in ------- days?
A.21 ½ days
B.22 ½ days
C.33 3/4 days
D.12 ½ days
Answer: C.33 3/4 days
Explanation: Explanation:
1/18 + 1/30 = 8/90 = 4/45
45/4 = 45/4 *3 = 33 3/4 days
Answer: C
Question: 54, 61, 57, 9, 55, 4, 9.
Which of the following numbers is lower than the median but greater than the mean of the set of the numbers in the list?
A.19
B.30
C.47
D.54
Answer: C.47
Explanation: Yes, it can be solved with observation even without approximation in 30 sec.
Just observe given numbers: 4,9, 9, 54, 55, 57,61,
Median is very easy to tell - its 55. Now we want a number lower than 54 and greater than mean. How many numbers are lower than 54? DE are already out.
Now, we have 19, 30 and 47 and we want a number among these which is greater than mean. logically whatever be the mean, if one value out of these 5 has to be greater than mean it has to be 47. (Notice, if 19 is more than mean then 47 is also. If 30 is more than mean, 47 is also. )
Hence C it is!
Question: The ratio of the radius of two circles is 1: 3, and then the ratio of their areas is?
A.1: 8
B.1: 1
C.1: 9
D.1: 4
Answer: C.1: 9
Explanation: r1: r2 = 1: 3
Πr12: Πr22
r12: r22 = 1: 9
Answer:C
Question: The length of the rectangular field is double its width. Inside the field there is square shaped pond 8m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field?
A.32 m
B.31 m
C.30 m
D.35 m
Answer: A.32 m
Explanation: A/8 = 8 * 8 => A = 8 * 8 * 8
x * 2x = 8 * 8 * 8
x = 16 => 2x = 32
ANSWER A
Question: 1/2, 1/4, ....
In the sequence above each term after after the first one-half the previous term. If x is the tenth term of the sequence, then x satisfies which of the following inequalities?
A.0.1 < x < 1
B.0.01 < x < 0.1
C.0.001 < x < 0.01
D.0.0001 < x < 0.001
Answer: A.0.1 < x < 1
Explanation: In the Sequence notice that the sequence is just the 1/(2^n) ...
so for 1st term=1/2^1=1/2
2nd term=1/(2^2)1/4, 3rd term=1/(2^3)=1/8 and so on...
Thus the 10th term will be 1/(2^10)=1/1024
Roughly, 1/1024 can be 1/1000=0.001 but since denominator is a bit more than 1000 therefore the actual value will be a bit less than 0.001.
thus the ans will lie btw. 0.1 and 1.(A)
Question: If d is a positive integer greater than 1, what is the sum of the multiples of d from d to d^2, inclusive?
A. d(d + 1)(d-1)
B. d^2(d + 1)/2
C. d^2(d-1)
D. (x^3 + 2x)/2
Answer: B. d^2(d + 1)/2
Explanation: Ans :- B=d^2(d + 1)/2
I substituted 3 in all answer choices.
Option B and C were both satisfying the condition.
So i substituted 4 instead of 3 in all answer choices,
Only B option satisfied.
Question: At a certain zoo, the ratio of sea lions to penguins is 4 to 11. If there are 84 more penguins than sea lions at the zoo, how many sea lions are there?
A.24
B.36
C.48
D.72
Answer: C.48
Explanation: The ratio as mentioned = 4/11
also
sea lion + 84 = penguins
or,
4x+84=11x
x=84/7=12
number of sea lions= 12*4=48
ANSWER:C
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent W?
A.20%
B.80%
C.100%
D.180%
Answer: C.100%
Explanation: C.
Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
W=[(2 - 1)/1] * 100% = 100%
Question: if length of rectangle is increased by 10%, and breadth is decreased by 10%.what will it effect on area of rectangle?
A.it will have no effect
B.1% increase
C.1% decrease
D.2% increase
Answer: C.1% decrease
Explanation: let initial length=l,and breadth=b
area=l*b
new length=l*110%=[l*110/100]=11l/10,new breadth=9b/10
new area=11l/10*9b/10=99/100lb
decrease in area=[lb-99/100lb]=lb/100=% decrease=[lb/100*1/lb*100]=1%
answer C
Question: if p/q=3/4
then3p+6q=?
A.25/4
B.25/2
C.20/4
D.33/4
Answer: D.33/4
Explanation: 3p+6q=?
Divided by q,
3(p/q)+6=x
3*(3/4)+6=33/4
ANSWER:D
Question: If 9x-3y=12 and 3x-5y=7 then 6x-2y = ?
A.9
B.8
C.7
D.5
Answer: B.8
Explanation: Consider 9x - 3y = 12.........divide both sides by 3: 3x - y = 4............now multiply both sides by 2: 6x - 2y
= 8
Answer:B
Question: Anand and Deepak started a business investing Rs. 6,000 and Rs. 8,000 respectively. Out of a total profit of Rs.4,600. Deepak's share is?
A.s. 2600.31
B.s. 2628.57
C.s. 2450.32
D.s. 3400.41
Answer: B.s. 2628.57
Explanation: Ratio of their shares = 6000 : 8000 = 3 : 4
Deepak's share = Rs. (4600 * 4/7) = Rs. 2628.57 ANSWER "B
Question: The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 34 ?
A.440
B.512
C.550
D.620
Answer: D.620
Explanation: Large numbers are made in two ways:
Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.
31*2 = 62 (large prime number)
2^6 = 64 (many small prime numbers)
To get a sum as large as 34 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.
You are left with 620 which is 31*2*2*5 (sum greater than 34)
Answer (D)
Question: A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
A.1.2
B.1.9
C.1.7
D.1.5
Answer: D.1.5
Explanation: M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5
Answer: D
Question: 16.02 Ã— 0.0001 = ?
A.0.1602
B.0.001602
C.1.6021
D.0.01602
Answer: B.0.001602
Explanation: 16.02 Ã— 0.0001 = 0.001602
The answer is B.
Question: For how many different pairs of positive integers (a, b) can the fraction 2/15 be written as the sum 1/a + 1/b ?
A.4
B.5
C.8
D.9
Answer: D.9
Explanation: (1/a)+(1/b)=215
I. 1/a+1/b=1/15+1/15(a,b)=(15,15)
II. 1/a+1/b=2∗2/15∗2=1/30+3/30(a,b)=10,30)and(30,10)
III.1/a+1/b=2∗3/15∗3=1/45+5/45(a,b)=(45,9)and(9,45)
IV.1/a+1/b=2∗4/15∗4=3/60+5/60(a,b)=(20,12)and(12,20)
Now, we know that the no of different pairs can only be of the form 2k+1. We already have 7 such combinations. Thus, the only value which will satisfy from the given options is 9.
Answer : D
Question: A train 280 m long, running with a speed of 63 km/hr will pass a tree in?
A.18 sec
B.16 sec
C.19 sec
D.11 sec
Answer: B.16 sec
Explanation: :
Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 280 * 2/35
= 16 sec
Answer: B
Question: The maximum number of students among them 1340 pens and 1280 pencils can be distributed in such a way that each student get the same number of pens and same number of pencils?
A.25
B.30
C.20
D.45
Answer: C.20
Explanation: number of pens = 1340
number of pencils = 1280
Required number of students = H.C.F. of 1340 and 1280 = 20
Answer is C
Question: How many gallons of milk that is 10 percent butter-fat must be added to 8 gallons of milk that is 35 percent butterfat to obtain milk that is 20 percent butterfat?
A.6
B.12
C.14
D.16
Answer: B.12
Explanation: Equate the fat:
0.1x + 0.35*8 = 0.2(x + 8) --> x = 12.
Answer: B.
Question: The positive integer f is divisible by 10. What is the remainder of dividing f(2+4)(1+f) by 5?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: When we multiply any of these options: 10*6*11 (f=10) or 20*6*21 (f=20) we end up with numbers ending in 0 which are exactly divisible by 5 leaving no remainder. Hence answer is A.
Question: A certain number when divided by 39 leaves a remainder 19, what is the remainder when the same number is divided by 13?
A.7
B.8
C.9
D.6
Answer: D.6
Explanation: Explanation:
39 + 19 = 58/13 = 6 (Remainder)
Answer: D
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 7. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 7 receives how many more dollars per hour than an employee with a salary grade of 1?
A.$0.50
B.$1.00
C.$1.25
D.$1.50
Answer: D.$1.50
Explanation: Salary grade of 7 is p(7)=9.50+0.25(7–1)=9.50+0.25*6;
Salary grade of 1 is p(1)=9.50 + 0.25(1–1)=9.50;
p(7)-p(1)=9.50+0.25*6-9.50=1.5.
Answer: D.
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 30?
A.30
B.14
C.50
D.42
Answer: A.30
Explanation: Greatest common factor n and 16 is 4 = 2*2 * 2*2
Greatest common factor n and 45 is 3 = 3*3 *5
Greatest common factor n and 30 is = 2*3*5 =30
A
Question: A coin is tossed until sequence HTH appears (H denotes the fall of heads, T denotes the fall of tails). What is the probability W that the game will end after the fourth throw?
A.1/16
B.3/32
C.1/8
D.3/16
Answer: C.1/8
Explanation: Another approach:
Two likely scenarios would be : HHTH or THTH
for each of the scenarios probability would be 1/16
So Probablilty W is 1/16 + 1/16 = 1/8.C
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 42° is?
A.52.6 m2
B.58.8 m2
C.52.8 m2
D.52.3 m2
Answer: C.52.8 m2
Explanation: 42/360 * 22/7 * 12 * 12 = 52.8 m2
Answer: C
Question: A motor starts with the speed of 70 kmph with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms?
A.2 1⁄4 hours
B.4 1⁄2 hours
C.4 hours 5 minutes
D.Cannot be determined
Answer: B.4 1⁄2 hours
Explanation: Distance covered in first two hours = 70 × 2 = 140 km
Distance covered in next two hours = 80 × 2 = 160 km
Distance covered in first four hours
140 + 160 = 300 km
Remaining distance = 345 – 300 = 45 km.
Now, this distance will be covered at the speed of 90 km/hr.
∴ Time taken = 45⁄90 = 1⁄2 hour.
Total time= 4 + 1⁄2 = 41⁄2 hour
Answer B
Question: 0.5, 0.55, 0.65, 0.8, ?
A.3
B.1
C.5
D.8
Answer: B.1
Explanation: B
1
The pattern is + 0.05, + 0.10, + 0.15, .....
Question: The ratio of ducks and frogs in a pond is 37 : 39 respectively. The average number of ducks and frogs in the pond is 150. What is the number of frogs in the pond ?
A.148
B.154
C.156
D.144
Answer: B.154
Explanation: Solution:
Ratio of Ducks and Frogs in Pond,
= 37 : 39.
Average of Ducks and Frogs in Pond,
= 150.
So, total number of Ducks and Frogs in the Pond,
= 2* 150 = 300.
Therefore,
Number of Frogs, = (300 *39)/76 = 154.
Answer: Option B
Question: If each digit in the set of A = (6,7,8,9) is exactly used once, in how many ways can the digits be arranged such that the 6 and 7 are not adjacent?
A.12
B.15
C.18
D.20
Answer: A.12
Explanation: The answer should be = total arrangements - arrangements when 2 and 5 are together.
= 4! - 3! * 2! = 24 -12 = 12
take (6,7),8,9 here there are 3 entities whose number of arrangements are 3! and 2! is the arrangement between 3 and 4
Answer is A
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 13%, then the cost price of the article is:
A.545
B.334
C.555
D.664
Answer: A.545
Explanation: 110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/113 = Rs. 545
Answer: Option A
Question: The largest 4 digit number exactly divisible by 88 is:
A.9800
B.9824
C.9944
D.10000
Answer: C.9944
Explanation: Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
C
Question: A 80 cm long wire is to be cut into two pieces so that one piece will be 3/5th of the other, how many centimeters will the shorter piece be?
A.A)30
B.B)20
C.C)83
D.D)21
Answer: A.A)30
Explanation: Explanation:
1: 3/5 = 5: 3
3/8 *80 =30
Answer: Option A
Question: What is the are of an equilateral triangle of side 16 cm?
A.10
B.99
C.88
D.77
Answer: A.10
Explanation: 36 * 5/18 = 10 mps
Answer: A
Question: A mixture of 150 liters of wine and water contains 10% water. How much more water should be added so that water becomes 25% of the new mixture?
A.10
B.30
C.20
D.15
Answer: B.30
Explanation: Number of liters of water in150 liters of the mixture = 10% of 150 = 10/100 * 150 = 15 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (15 + P) and total volume of mixture is (150 + P).
(15 + P) = 25/100 * (150 + P)
60+4P = 150+P
P = 30 liters.
Answer: B
Question: A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected, if it should have 5 seniors and 5 juniors?
A.Â¹Â²Câ‚… * 10
B.Â¹Â²Câ‚‡ * 10
C.Â¹Â²Câ‚‡ * Â¹â°Câ‚…
D.12 * Â¹â°Câ‚…
Answer: C.Â¹Â²Câ‚‡ * Â¹â°Câ‚…
Explanation: Explanation:
Here, five seniors out of 12 seniors can be selected in Â¹Â²Câ‚… ways. Also, five juniors out of ten juniors can be selected Â¹â°Câ‚… ways. Hence the total number of different ways of selection = Â¹Â²Câ‚… * Â¹â°Câ‚… = Â¹Â²Câ‚‡ * Â¹â°Câ‚…
= Â¹Â²Câ‚… = Â¹Â²Câ‚‡
ANSWER IS C
Question: A began a business with Rs. 85,000. He was joined afterwards by B with Rs. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
A.4 months
B.5 months
C.6 months
D.8 months
Answer: D.8 months
Explanation: Suppose B joined for x months. Then,
Then,(85000 x 12)/(42500 x x) = 3/1
x = 85000 x 12/42500 x 3 = 8.
So, B joined for 8 months.
Answer:D
Question: A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 30,000 and at the same time n is a perfect square and a perfect cube?
A.4
B.5
C.6
D.7
Answer: B.5
Explanation: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.
The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625.
The answer is B.
Question: The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.180 and Rs.120 respectively. What is the sum and the time?
A.Sum = Rs.380 and Time = 4 years
B.Sum = Rs.400 and Time = 6 years
C.Sum = Rs.320 and Time = 4 years
D.Sum = Rs.360 and Time = 5 years
Answer: D.Sum = Rs.360 and Time = 5 years
Explanation: Explanation :
BD = Rs.180
TD = Rs.120
R = 10%
F = BD ×TD/(BD – TD)=180×120/(180–120)=180×120/60=Rs. 360
BD = Simple Interest on the face value of the bill for unexpired time =FTR/100
⇒180 = (360×T×10)/100
⇒180 = 36 × T
⇒ T = 180/36 = 5 years Answer : Option D
Question: The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 80, then 1/m + 1/n is equal to
A.1/35
B.3/35
C.5/37
D.4/63
Answer: D.4/63
Explanation: Answer
We have, m x n = 6 x 210 = 1260
âˆ´ 1/m + 1/n = (m + n)/mn = 80/1260 = 4/63
Correct Option: D
Question: A car driver travels from the plains to the hill station, which are 200 km apart at an average speed of 45km/hr. in return trip, he covers the same distance at an average speed of 20km/hr. the average speed of the car over the entire distance of 400 km is
A.8.95km/hr
B.26.7km/hr
C.27.7km/hr
D.37.9km/hr
Answer: C.27.7km/hr
Explanation: average speed = (2*45*20)/45+20 km/hr
=27.7 km/hr
Answer (C)