RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: There is a ratio of 5 : 4 between two numbers. If forty percent of the first number is 12 then what would be the 50 percent of the second number?
A.12
B.24
C.18
D.Data inadequate
Answer: A.12
Explanation: a⁄b = 5⁄4, b = 4⁄5a Given (40% of a) = 2⁄5a = 12
a = 5 × 6 and b = 4⁄5 × 5 × 6 = 24
∴ 50% of b = 24⁄2 = 12
Answer A
Question: How many liters of water must be added to 18 liters of milk and water containing 10% water to make it 70% water?
A.28
B.32
C.36
D.40
Answer: C.36
Explanation: By rule of alligation:
70% - 10% = 60%
100% - 70% = 30%
Quantity of pure water : Quantity of the mixture = 6 : 3
There are 18 liters of mixture, so we need to add 36 liters of pure water.
The answer is C.
Question: Four people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
A.7/8
B.1/8
C.1/3
D.1/7
Answer: C.1/3
Explanation: Original share of 1 person =1/4
New share of 1 person =1/3
Increase =1/3 -	1/4	=1/12
Required fraction =	(1/12)/(1/4)	=1/3
Answer is C.
Question: A music band that must consists of 4 members is to be formed from a pool of 9 candidates. How many different bands are possible
A.100
B.144
C.126
D.56
Answer: D.56
Explanation: Note that the band must consist of 4 members, not at least 4 members. Hence, all you have to do is 9C4 = 56
Answer (D)
Question: A sum of money invested at compound interest amounts to Rs.800 in 3 years and to Rs.840 in 4 years. The rate of interest per annum is
A.2x1/2%
B.4%
C.5%
D.6x2/3%
Answer: C.5%
Explanation: Solution
S.I. on Rs.800 for 1 year	=Rs[840 - 800]
= Rs.40
Rate	=(100x40/800x1)%
= 5%
Answer C
Question: A sum of Rs. 2691 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum?
A.1656
B.1640
C.1632
D.2789
Answer: A.1656
Explanation: (x*8*3)/100 = ((2691 - x)*3*5)/100
24x/100 = 40365/100 - 15x/100
39x = 39975 => x = 1035
Second sum = 2691 – 1035
=1656
Answer:A
Question: What is the 100th term of the series 2,4,8,14,22?
A.9902
B.9903
C.9904
D.9905
Answer: A.9902
Explanation: this is in the form
the every N th number is (N-1)*N+2
for 1st numner aplly above formula
1st number=0*1+2=2
2nd number=1*2+2=4
3rd number=2*3+2=8
4th number=3*4+2=14
5th number=4*5+2=22
so 100 th number will be
99*100+2=9902.
ANSWER:A
Question: A water tank is one-fifth full. Pipe A can fill a tank in 15 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how many minutes will it take to empty or fill the tank completely?
A.2
B.4
C.6
D.8
Answer: A.2
Explanation: The combined rate of filling/emptying the tank = 1/15 - 1/6 = -1/10
Since the rate is negative, the tank will be emptied.
A full tank would take 10 minutes to empty.
Since the tank is only one-fifth full, the time is (1/5) * 10 = 2 minutes
The answer is A.
Question: A sporting goods store sold 60 Frisbees in one week, some for $3 and the rest for $4 each. If receipts from Frisbee sales for the week totaled $200, what is the fewest number of $4 Frisbees that could have been sold?
A.24
B.12
C.20
D.4
Answer: C.20
Explanation: The wording of the question is slightly misleading. When a question asks what is thefewestthatcouldhave been sold, it is suggesting that there could be many different quantities sold.
In this question however, because we are told that exactly 64 Frisbees have been sold and revenue was exactly $204, there is only one possible solution for the number of $3 and $4 Frisbees sold.
To solve, we have 2 equations and 2 unknowns
Let x = number of $3 Frisbees sold
Let y = number of $4 Frisbees sold
x + y = 60
3x + 4y = 200
x = 60 - y
3(60-y) + 4y = 200
180 - 3y + 4y = 200
y = 20
Answer: C
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all the integers between 1 and 50?
A.1275
B.1542
C.985
D.1024
Answer: A.1275
Explanation: sum = 50*51/2 = 25*51 = 1275
Answer is A
Question: A rectangular wall is covered entirely with two kinds of decorative tiles: regular and jumbo. 1/3 of the tiles are jumbo tiles, which have a length three times that of regular tiles and have the same ratio of length to width as the regular tiles. If regular tiles cover 70 square feet of the wall, and no tiles overlap, what is the area of the entire wall?
A.160
B.240
C.385
D.440
Answer: C.385
Explanation: The number of jumbo tiles = x.
The number of regular tiles = 2x.
Assume the ratio of the dimensions of a regular tile is a:a --> area = a^2.
The dimensions of a jumbo tile is 3a:3a --> area = 9a^2.
The area of regular tiles = 2x*a^2 = 70.
The area of jumbo tiles = x*9a^2 = 4.5(2x*a^2 ) = 4.5*70 = 315.
Total area = 70 + 315 = 385
Answer: C.
Question: If P represents the product of the first 16 positive integers, then P is not a
multiple of:
A.a) 99
B.b) 84
C.c) 72
D.d) 65
Answer: A.a) 99
Explanation: a) 99 = 9*11
b) 84 = 4*7*3
c) 72 =9*8
d) 65 = 5*13
e) 45 =9*5
since 11 is not there in first 15 positive numbers it is the only possibility
A
Question: A number has exactly 32 factors out of which 4 are not composite. Product of these 4 factors (which are not composite) is 30. How many such numbers Q are possible?
A.2
B.4
C.6
D.3
Answer: C.6
Explanation: Firstly , we should note that 1 is NEITHER a prime nor a composite number.The first composite number is 4.Thus, when the problem states that there are 4 factors that are not composite, these nos are 1,2,3,5. Thus, the given number = 2^a*3^b*5^c. Also, (a+1)*(b+1)*(c+1) = 32. We can break down 32 into 3 integers as : 2*2*8 or 4*4*2
Also, the only possible combinations for a,b,c are : 3,3,1 OR 1,1,7. Thus, each combination has 3 possible orders and we have a total of Q= 6 possibilities.
C.
Question: If a man buys 20 lollipops for $90 and sold them for $2 dollars determine his loss
A.$25
B.$30
C.$50
D.$40
Answer: C.$50
Explanation: 20 lollipops = $90, sold each for $2, so he sold 20 lollipops for 20 * $2= $40, Loss = $(90-40), loss = $50. correct answer : (C)
Question: How many 4-digit even numbers are possible such that if one of the digits is 5, the next/succeeding digit to it should be 7?
A.5
B.305
C.365
D.50
Answer: D.50
Explanation: 5700, 5710,......5798, so total 50. Hence Option D.
Question: Jack bought 200 packets of swiss chocolate. He was able to sell 1/2 of them at a 5% profit, another 1/4 of them at zero profit and the remainder was sold at a 10% loss. Find the total profit or loss made by Jack after selling those 200 packets. A packet sold at a loss had a price of $9.
It's a bit confusing to say 5% of profit. Please provide an intuitive answer if possible. Thanks!!
A.0
B.Profit of $10
C.Loss of $25
D.Profit of $30
Answer: A.0
Explanation: A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
100 packets was sold at a 5% profit --> gives profit of 10*0.05*100 = $50.
50 packets was sold at a 10% loss --> gives loss of 10*0.1*50 = $50.
The overall loss is $50 - $50 = $0.
Answer: A.
Question: The cross-section of a stream is a trapezium in shape. If the stream is 10 m wide at the top and the area of cross-section is 640 sq m, the depth of stream is 80m and width at the bottom is?
A.2 m
B.6 m
C.4 m
D.8 m
Answer: B.6 m
Explanation: 1/2 * 80 (10 + b) = 640
b = 6m
ANSWER:B
Question: 1000 men have provisions for 15 days. If 200 more men join them, for how many days will the provisions last now?
A.12.6
B.12.9
C.12.5
D.12.0
Answer: C.12.5
Explanation: 1000*15 = 1200*x
x = 12.5
Answer: C
Question: John and Cindy were each given X dollars in advance for each day they were expected to perform at a community festival. John eventually performed on all 25 days of the festival, while Cindy performed on 5 fewer days than John performed. If Cindy gives John y dollars of her advance payment so that they would have each received the same daily rate, what was John paid in advance, in terms of Y?
A.12Y
B.11Y
C.9Y
D.10Y
Answer: C.9Y
Explanation: Both of them were given X $ each
Cindy to adjust Y $ in advance to John
So Cindy now has (X-Y)$ and John has (X+Y) $ such that their daily rate becomes same
So Rate of CIndy= Rate of John
Also , Cindy works for 20 days and John works for full 25 days
(X-Y) / 20 = (X+Y) / 25
Solving 25x-25y=20x+20y =>5x=45y => x=45/5y
X= 9Y
Answer : C
Question: in a railway station, there are tow trains going. One in the harbour line and one in the main line, each having a frequency of 10 minutes. the main line service starts at 5 o'clock. the harbour line starts at 5.02a.m. a man goes to the station every day to catch the first train. what is the probability of man catchinhg the first train
A.1/5
B.2/5
C.3/5
D.4/5
Answer: D.4/5
Explanation: Probability of catching first train(train1) is 8/10=4/5
ANSWER:D
Question: A dishonest dealer uses a scale of 95 cm instead of a metre scale and claims to sell at cost price. His profit is
A.9%
B.5.26%
C.12%
D.None of these
Answer: B.5.26%
Explanation: Solution
Gain%	= (5 / 95 x 100)%
= 5.26%
Answer B
Question: If xy=9, x/y=36, for positive numbers x and y, y=?
A.1/2
B.2
C.1/3
D.3
Answer: A.1/2
Explanation: Very easy question. 2 variables and 2 easy equations.
xy=9 ---> x=9/y - (i)
x/y=36 ---> replacing (i) here ---> 9/(y^2)=36 ---> y^2=9/36=1/4 ---> y=1/2 or -1/2
The question states that x and y are positive integers. Therefore, y=1/2 is the answer.
Answer A.
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit?
A.337
B.960
C.278
D.211
Answer: B.960
Explanation: Explanation:
Let C.P. = Rs. x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 150% of Rs. 640 = 150/100 * 640 = Rs. 960.
Answer: B
Question: In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiples the integer on the card by the next larger integer. If each possible product is between 25 and 200, then the least and greatest integers on the card could be
A.3 and 15
B.3 and 20
C.5 and 13
D.4 and 14
Answer: C.5 and 13
Explanation: There child draws one number then multiplies that number by the number above it. The number must be more than 25 and less than 200.
x * (x+1)
Answer gives us choices of 3,4 and 5 (JUST ABOVE 25)
3*(3+1) =12 <- WRONG
4*(4+1) =20 <- WRONG
5*(5+1)=30 <-CORRECT AS IT IS ABOVE 25
Answer gives us choices 13,14,15 and 20 (BELOW 200)
Immediately by knowing squares you should be able to rule out 15 (225) and 20 (400). And common sense dictates that as 14^2 is 196 that 14*(14+1) is above 200.
13*(13+1)=182 <- CORRECT
Answer is C) 5 and 13
Question: capacity of A doing work is double than B.if both together finish a work in 21 days,then A alone in how much days can finish the work?
A.16
B.18
C.15
D.20
Answer: B.18
Explanation: let A alone can finish the work in x days.then B alone can finish the work in 2x days.
work of A in 1 days=1/x,and work of B in 1 days=1/2x
(A+B) work in 1 days=[1/x+1/2x]=3/2x
but,(A+B) work in 1 days=1/12
3/2x=1/12,2x=36,x=18
answer B
Question: Sumitra has an average of 56% on her first 7 examinations. How much should she make on her eighth examination to obtain an average of 60% on 8 examinations?
A.88%
B.78%
C.98%
D.Cannot be determined
Answer: D.Cannot be determined
Explanation: Since the weight age of eighth examination is not known, hence can not be determined.
Answer D
Question: Find the number of ways in which 6 different beads can be arranged to form a necklace.
A.30
B.20
C.50
D.60
Answer: C.50
Explanation: Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,6 beads can be arranged to form a necklace in(6-1)! /2ways
= 5*4*3*2/2 = 60 ways
Answer is C
Question: In what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
A.7years
B.6years
C.3years
D.9years
Answer: C.3years
Explanation: Explanation:
Principal = Rs. 1000; Amount = Rs. 1331; Rate = 10% p.a. Let the time be n years. Then,
[ 1000 (1+ (10/100))^n ] = 1331 or (11/10)^n = (1331/1000) = (11/10)^3
n = 3 years
Answer: C
Question: Nr Books bought Nr of People
6 3
7 1
8 5
9 2
What is the median of books bought per person?
A.a) 2
B.b) 4
C.c) 6
D.d) 8
Answer: D.d) 8
Explanation: 6,6,6,7,8,8,8,8,8,9,9
so you will observer that the median of the list is 8. Ans D
Question: If p is a natural number and p! ends with r trailing zeros, then the number of zeros that (5p)! ends with will be
A.a) (p+r) trailing zeros
B.b) (5p+y) trailing zeros
C.c) (5p+5y) trailing zeros
D.d) (p+5y) trailing zeros
Answer: A.a) (p+r) trailing zeros
Explanation: Let p = 1. p! = 1! = 1, which means r= 0
(5p)! = 5! = 120, trailing zeros = 1
1 = 1 + 0 = p + r
Answer (A).
Question: How much interest can a person get on Rs. 7200 at 17.5% p.a. simple interest for a period of two years and six months?
A.Rs. 4150
B.Rs. 3850
C.Rs. 3770
D.Rs. 3150
Answer: D.Rs. 3150
Explanation: I = (7200 * 2.5 * 17.5)/100 = (7200 * 5 * 35)/(100 * 2 * 2)
= Rs. 3150
ANSWER:D
Question: A and B began business with Rs.3000 and Rs.4000 after 8 months, A withdraws Rs.1000 and B advances Rs.1000 more. At the end of the year, their profits amounted to Rs.630 find the share of A.
A.Rs.240
B.Rs.350
C.Rs.340
D.Rs.390
Answer: A.Rs.240
Explanation: Explanation:
(3*8 + 2*4):(4*8 + 5*4)
8:13
8/21 * 630 = 240
ANSWER IS A
Question: By selling 99 pens, a trader gains the cost of 33 pens. Find his gain percentage?
A.33 1/3
B.33 1/5
C.33 1/9
D.33 1/4
Answer: A.33 1/3
Explanation: Let the CP of each pen be Rs. 1.
CP of 99 pens = Rs. 99
Profit = Cost of 33 pens = Rs. 33
Profit% = 33/99 * 100 = 33 1/3%.Answer: A
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 5 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. What is the average age of the team?
A.23 years
B.24 years
C.25 years
D.26 years
Answer: B.24 years
Explanation: EXPLANATION
Let the average age of the whole team by x years.
11x â€“ (26 + 21) = 9(x -1)
11x â€“ 9x = 48
2x = 48
x = 24.
So, average age of the team is 24 years.
Answer B
Question: If x > y^6 > z^7, which of the following statements could be true? I.x>z II.z=x III.x>y>z
A.I,III only
B.I only
C.II only
D.III only
Answer: A.I,III only
Explanation: Answer : A
Question: Balloons are bought at 12 for Rs.10/- and sold at 10 for Rs.12/-. Find the gain or loss percentage?
A.21% Loss
B.21% Gain
C.44 % Profit
D.44 % Loss
Answer: C.44 % Profit
Explanation: Explanation:
12 Balloons -----> Rs.10/-
10 Balloons -----> Rs.12/-
Note: Number of articles bought is must equal to number of articles sold.
10(12 10) ==> 120 100 = Cost price
12(10 12) ==> 120 144 = Selling price
Then, 44/100 × 100 = 44 % Profit
Answer: Option C
Question: A shopkeeper gives a discount of 12, whereas a customer makes cash payment. Let 'p' denotes the percentage, above the cost price, that the shopkeeper must mark up the price of the articles ['p' is an integer] in order to make a profit of x. Which of the following can't be possible value of x?
A.54
B.76
C.96
D.32
Answer: C.96
Explanation: Explanation :
Let, the cost price of one article is Rs r then,
Marked price of the article,
=>r(1+p/100).
The selling price is:-
=>r(1+p/100)(1−12/100).
Profit percentage =x%
=>r(1+p/100)(1−12/100)=r(1+x100).
=>x=25(12+x)/22.
As, p is an integer, x must be multiple of 22.
All the possible values x, less than 100 are k=10,32,54,76,98.
Except option 'C' all the options are possible.
Answer : C
Question: Which is largest prime number?
A.937
B.983
C.991
D.997
Answer: D.997
Explanation: Answer:D
Question: Today Mary’s father is four times as old as Mary. Three years ago, he was 5 times as old. How old is Mary today?
A.6
B.8
C.10
D.12
Answer: D.12
Explanation: Dad's age = 4M
5*(M-3) = 4M-3
M = 12
The answer is D.
Question: mr. depak has $449,774 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
A.$1
B.$2
C.$3
D.$4
Answer: A.$1
Explanation: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+4+9+7+7+4 = 35
If you add 1 , the number is divisible by 6 (35+ 1)
Correct Option : A
Question: In a zoo, the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same five years ago. If the increase in the number of cheetahs in the zoo since then is 2, then what is the increase in the number of pandas?
A. 2
B. 3
C. 5
D. 6
Answer: D. 6
Explanation: One short cut to solve the problem is
c:p = 1:3
c increased to 3
=> 1:3 = 3:x
=> x = 9
=>p increased by 6
D is the answer
Question: In a library, there are certain number of books on a shelf, ranging between 75 and 100. 1/6th of them are fiction and 12.5% of them are non-fiction. Find the number of books.
A.68
B.72
C.96
D.Can't be determined
Answer: C.96
Explanation: Explanation:
12.5% can be written as 1/8th
Since 1/6th of the books are fiction and 1/8th are non-fiction, the total number of books must be exactly divisible by 6 and 8 and should be between 75 and 100.
Therefore, 96 is the only number, which fulfills the above criteria.
Note that the question doesn't imply that there are ONLY two varieties of books.
ANSWER: C
Question: 20. A certain church bell rings the bell twice at half past the hour and four
times at the hour plus an additional number of rings equal to what ever
time it is. How many rings will the clock make from 6:20 in the morning
to 11:10 in the morning?
A.32.
B.75.
C.42.
D.46.
Answer: B.75.
Explanation: @ 6:30 - 2
@ 7 - 4+7 =11
@ 7:30 - 2
@ 8 - 12
@ 8:30 - 2
@ 9 - 13
@ 9:30 - 2
@ 10 - 14
@10:30 - 2
@11:00 -11+4=15
totals to B=75
Question: Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?
A.3/4
B.4/3
C.6/5
D.5/9
Answer: A.3/4
Explanation: n(S)=36
n(E)=27
P(E)=n(S)/n(E)
=27/36
=3/4
Ans: A
Question: Joshua and Jose work at an auto repair center with 4 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
A.1/15
B.1/12
C.1/9
D.1/6
Answer: A.1/15
Explanation: 1) Probability of chosing Josh first = 1/6
Probability of chosing Jose second = 1/5
total = 1/30
Probability of chosing Jose first = 1/6
Probability of choosing Josh second = 1/5
Total = 1/30
Final = 1/30 + 1/30 = 1/15
2) Number of ways two persons can be chosen 6C2 = 15
Number of ways Josh and Jose are the two persons = 1
Total = 1/15
Answer will be A.
Question: How many factors of 440 are odd numbers greater than 1?
A.2
B.4
C.5
D.6
Answer: A.2
Explanation: When factorized, 440 has 4 prime factors. Of these prime factors 2 are odd and 2 are even. Hence total number of odd factors is 2*2(4), which includes 2. The total number of odd factors greater than 1 are 2.(option A)
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
A.Monday
B.Tuesday
C.Wednesday
D.Sunday
Answer: B.Tuesday
Explanation: Explanation:
The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.
Answer: B
Question: Two vehicles A and B leave from Y to X. A overtakes B at 10:30 am and reaches X at 12:00. It waits for two hours and returns to Y. On its way, it meets B at 3 PM and reaches Y at 5 PM. B reaches city X waits for 1 hour and returns to y After how many hours will B reach to Y from the time A overtook him.
A.40.5
B.41.5
C.42.5
D.43.5
Answer: B.41.5
Explanation: Let the distance between City X and Y be D
As given - B leaves City X at 2:00 (12:00 + 2 hrs halt) and reaches City Y at 5:00
So it takes him 3 hours to cover distance D.
Now, A overtakes B at 10:30 and reaches city Y at 12:00 pm , which means that A traveled for 1:30 hr.
Now see,
A takes 3 hrs takes to cover distance D
so in 1.5 hrs A will cover D / 2 distance
Now see another part -
"On its way, it meets B at 3 PM and reaches Y at 5 PM."
Given that - B leaves City Y at 2 PM
So distance covered by A in 1 hr (3 - 2) = D / 3
Now Total Distance covered by B during (A overtaking B + A wait for two hour + A on its way back ) is
D / 2 [when they first overtake] - D / 3 [when they again overtake]
= D / 6
Now Time elapsed during this period (A overtaking B + A wait for two hour + A on its way back )
=1.5 + 2 + 1
=4.5
so to cover D / 6 distance B took 4.5 hr
to cover D distance B will take (4.5 * 6)
= 27 hr.
Now "After how many hours will B reach to Y from the time A overtook him."
Time to reach X after A overtook (D / 2) + wait + Time to reach Y from X (D)
= 13.5 + 1 + 27
= 41.5
ANSWER:B
Question: By selling 22 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
A.83
B.63
C.53
D.33
Answer: D.33
Explanation: 80% --- 22
120% --- ?
80/120 * 22 = 33
Answer:D
Question: In a group of 100 people,60 like volleyball,50 like hockey. How many like both volleyball and hockey?
A.20
B.15
C.10
D.5
Answer: C.10
Explanation: Make a Venn diagram, and enter your data.
Let the number of people who like both volleyball and hockey be x
60-x+x+50-x = 100
x = 10
so number who like both volleyball and hockey = 10
Answer C
Question: A man can row downstream at 20 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
A.3
B.5
C.6
D.4
Answer: B.5
Explanation: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 20 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 30 => x = 15, y = 5. Answer: B
Question: Jim covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
A.15 Kmph
B.18 Kmph
C.19 Kmph
D.20 Kmph
Answer: A.15 Kmph
Explanation: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distance of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
A)
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 17. The larger of the two numbers is:
A.276
B.299
C.391
D.345
Answer: C.391
Explanation: Clearly, the numbers are (23 x 13) and (23 x 17).
Larger number = (23 x 17) = 391.
Answer: Option C
Question: If 25% of a number is subtracted from a second number the second number reduces to its five-sixths. What is the ratio between the first number and the second number?
A.2 : 3
B.3 : 2
C.1 : 3
D.Data inadequate
Answer: A.2 : 3
Explanation: Let the first and second number be x and y respectively.
x - y × 25⁄100 = y × 5⁄6
or, y - x⁄4 = 5⁄6y
or, 1⁄6y = x⁄4y
\ x : y = 2 : 3
Answer A
Question: There are c cities. What is the number of airlines that connected 2 different cities (airline from city A to city B is different with airline from city B to city A)?
A.c(c-1)
B.n(n+1)
C.n(n-1)/2
D.n(n+1)/2
Answer: A.c(c-1)
Explanation: First of all, the possible number of airlines is c. Then, the possible number of airlines departing from one city to another becomes (c-1). Hence, the answer is c(c-1), A
Question: A dishonest grocer professes to sell pure butter at cost price, but he mixes it with adulterated fat and thereby gains 20%. Find the percentage of adulterated fat in the mixture assuming that adulterated fat is freely available?
A.20%
B.25%
C.33.33%
D.40%
Answer: B.25%
Explanation: Say 100g pure butter costs $100
But; $100 is his 25% profit because he just used 80gram pure butter.
80g would have costed him $80 and he sold it for $100 by adding 20g of freely available fat. $100 is 1.20(75)
so;
total weight=100g
fat=20g
25%
B