RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in five hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
A.65 minutes
B.66 min
C.56 minutes
D.69 minutes
Answer: B.66 min
Explanation: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 5 hours.
His speed = 180/5 = 36 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 36 + 10 = 46km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 3.9 hours respectively. Hence difference in the time taken = 1.1 hours = 66 minutes.
ANSWER:B
Question: Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 5 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?
A.6
B.9
C.9 1/2
D.22.5
Answer: D.22.5
Explanation: rate z/rate y=2/5
time z/time y=5/2
5/2*9=22.5 minutes
D
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
A.221
B.144
C.666
D.888
Answer: B.144
Explanation: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144
Answer:B
Question: If the cost price of 22 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
A.20% loss
B.37.5 % profit
C.37.5 % loss
D.30.33% loss
Answer: B.37.5 % profit
Explanation: Explanation :
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 22 articles = Rs. 22.
Selling price of 16 articles = Rs. 22
Therefore, Selling price of 22 articles is :-
=>22/16Ã—22
=>30.25.
Therefore, Profit = Selling price - Cost price.
=>30.25âˆ’22=8.25
Hence, the percentage of profit = profit x 100/C.P.
=>8.25/22Ã—100.
=>37.5% Profit.
Answer : B
Question: The price of 5 kilograms of premium fertilizer is the same as the price of 10 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?
A.y/30
B.5/6*y
C.6/5*y
D.2y
Answer: D.2y
Explanation: Usingpfor premium andrfor regular, I got two equations from the question stem:
5p = 10r and p = r+y
Substitute for p: 5(r+y) = 10r
Distribute: 5r + 5y = 10r
Subtract 5r from both sides: 5y = 5r
Plug back into the first equation: 5p = 10(y)
Distribute: 5p = 10y
Divide both sides by 5: p = 2y
The answer is D.
Question: Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p - 3?
A.10
B.8
C.7
D.3
Answer: D.3
Explanation: p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 -->
In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.
Intersection of values is 6, thus the units digit of p - 3 is 6 - 3 = 3.
Answer: D.
Question: A taxicab fare costs x dollars for the first quarter of a mile and 1/4*x dollars for each quarter of a mile after that. How much will the total cost be for a 3/2 mile ride?
A.3x
B.13/4*x
C.10x
D.5/4*x
Answer: B.13/4*x
Explanation: 3/2 miles = 1+1/2 miles
1+1/2 miles have 6 1/4 miles
1st 1/4 mile will cost= x
Remaining 5 1/4 miles will cost= 5/4 x
Total cost = x + 5/4 x= 9/4 x
ANSWER:B
Question: Find the odd man out. 10,30,50,72,95
A.10
B.30
C.50
D.72
Answer: D.72
Explanation: All except 72 are multiples of 5
Answer is D
Question: The sub-duplicate ratio of 25:49 is
A.4:3
B.5:7
C.6:4
D.1:4
Answer: B.5:7
Explanation: root(25):root(49)=5:7
ANSWER:B
Question: If in a $120 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?
A.40mln
B.50mln
C.60mln
D.70mln
Answer: A.40mln
Explanation: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $120 mln portfolio, x+2x=3x=120 mln from where x=40 mln.
Answer: A
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
A.67 2/16%
B.45 2/17%
C.18 2/11%
D.23 2/13%
Answer: C.18 2/11%
Explanation: C
13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Question: From the word 'INTENSIFICATION', how many independent words can be made with-out changing the order of the letters and using each letter only once ?
A.5
B.4
C.3
D.2
Answer: B.4
Explanation: Explanation:
The words formed are
IN, TEN, INTENS and CATION
Answer: B) 4
Question: If the city centers of New York and London are 3,471 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.)
A.1.75 × 10^7
B.1.83 × 10^7
C.2.10 × 10^8
D.2.10 × 10^9
Answer: C.2.10 × 10^8
Explanation: Distance in Miles = 3471
Given 1 mile = 5280 ft
So 3471 miles = 3471 X 5280 feet ~ 3500 x 5300 = 1.855 x 10^7 feet
1 feet is 12 inches, so the answer : 1.855 x 12 x 10^7 ~ 2.2 x 10^8.
Answer C
Question: List I: 3, 6, 10, 19
List II: x, 3, 10, 8, 19
A. 6
B. 7
C. 8
D. 9
Answer: C. 8
Explanation: We start by calculating the median of the numbers of list I: 3, 6, 10, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers.
median = (6 + 10)/2
median = 16/2
median = 8
The median of list I is 7.
Looking at list II: x, 3, 6, 10, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 8 and therefore x is 8.
The answer is C.
Question: Every minute, G an type 55 words while H can type 70 in the same amount of time. IF they have 20 minutes to complete a 500 word document, how much time remains when they have finished typing the document? Answer in fractions.
A.290/77
B.1250/77
C.500/77
D.154/77
Answer: A.290/77
Explanation: MInutes it takes for G to type 1 word: 1/55
Minutes it takes for H to type 1 word: 1/70
Minutes it takes for G and H to type 1 word: 1/55+1/70=5/154
Minutes it takes for G and H to type 500 words: 500x(5/154)=1250/77
MInutes remaining: 20-1250/77=290/77
Answer is A
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
A.6620
B.1879
C.2779
D.2672
Answer: A.6620
Explanation: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Question: Simplify: 2005-2000+10
A.1805
B.4509
C.2601
D.4508
Answer: A.1805
Explanation: 2005-2000+10
=2005-(2000/10)
=2005-200
=1805.
Answer is A
Question: Find the Greatest Number that will devide 43, 91 and 183 so as to leave the same remainder in each case
A.4
B.7
C.9
D.13
Answer: A.4
Explanation: Explanation:
Required Number = H.C.F of (91- 43), (183- 91) and (183-43)
= H.C.F of 48, 92, and 140 = 4. Answer: A
Question: I. a^2 + 11a + 30 = 0,
II. b^2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?
A.If a < b
B.If a ≤ b
C.If a > b
D.If the relationship between a and b cannot be established
Answer: B.If a ≤ b
Explanation: Explanation:
I. (a + 6)(a + 5) = 0
=> a = -6, -5
II. (b + 5)(b + 1) = 0
=> b = -5, -1 => a ≤ b
Option B
Question: At what rate percent on simple interest will Rs.900 amount to Rs.950 in 5 years?
A.1.11%
B.5.93%
C.4.33%
D.5.33%
Answer: A.1.11%
Explanation: 50 = (900*5*R)/100
R = 1.11%
ANSWER:A
Question: A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive?
A.200
B.300
C.400
D.500
Answer: A.200
Explanation: Let the share of each nephews be Rs.x.
Then,share of each daughter=rs4x;share of each son=Rs.5x;
So,5*5x+4*4x+2*x=8600
25x+16x+2x=8600
=43x=8600
x=200;
Answer is A.
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: If one-third of one-fourth of a number is 30, then three-tenth of that number is:
A. 35
A.23
B.87
C.108
D.54
Answer: C.108
Explanation: Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 30
Number is 360 then 360 Ã— 3/10 = 108
Answer: C
Question: Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?
A.25/33
B.31/44
C.41/55
D.53/66
Answer: C.41/55
Explanation: Total possible ways to choose 4 students out of 12 = 12C4 = 495
The number of ways to choose 4 students with no green shirts = 9C4 = 126
P(no green shirts) = 126/495 = 14/55
P(at least 1 green shirt) = 1 - 14/55 = 41/55
The answer is C.
Question: A, B, C, D, E and F are six cities which are collinear in the same order. The distance between any two adjacent cities is equal. A bus starts at A for city F. It takes 25 minutes for the bus to travel from one city to another and stops for 5 minutes at each place. If the bus reaches E at 8:55, then at what time did it reach station B?
A.7:25
B.7:30
C.7:35
D.7:40
Answer: A.7:25
Explanation: Explanation:
Between B and E there are two intermediary stations C and D. For traveling from B to C, from C to D and from D to E it takes 3 * 25 = 75 minutes. At each of C and B it halts of 5 minutes. Hence, the time taken to reach E after starting at B is 85 minutes. i.e. one hour 25 minutes. Hence, it started at 7:30 at B. =>it reached B at 7:25.
ANSWER IS A
Question: The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 6 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?
A.20 km
B.30 km
C.40 km
D.50 km
Answer: B.30 km
Explanation: Number of stops in an hour: 60/5 = 12
Distance between stops: 60/12 = 5 km
Distance between Yahya's house and Pinedale Mall: 5 x 6 = 30 km
IMO, correct answer is "B."
Question: What number should replace the question mark?
1, 31, 59, 85, 109, ?
A.131
B.145
C.165
D.178
Answer: A.131
Explanation: A
131
Add 30, 28, 26, 24, 22
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 3: 00 p.m., at what time were there 32 million bacteria in the dish?
A.6: 00 p.m.
B.9: 00 p.m.
C.6: 00 a.m.
D.8: 00 a.m.
Answer: B.9: 00 p.m.
Explanation: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 3 PM, we get 9 AM as the answer.
Option B
Question: A man can row 8 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.98
B.7.98
C.7.96
D.5.87
Answer: C.7.96
Explanation: M = 8
S = 1.2
DS = 9.6
US = 6.8
x/9.6 + x/6.8 = 1
x = 3.98
D = 3.98 * 2 = 7.96
Answer:C
Question: On the number line, the number p is twice as many units from -2 as -2 is from 5. If p is less than –2, what is the value of p ?
A.–16
B.–10
C.–6
D.10
Answer: A.–16
Explanation: Distance between -2 and 5 = 7
Since number p is twice as many units from -2 as -2 is from 5
, therefore p can be -16 Since , p is less than -2 ,
the value of p = -16
Answer A
Question: At a certain conference, 62% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 20% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
A. 18.0%
B. 62.0%
C. 79.2%
D. 77.5%
Answer: D. 77.5%
Explanation: Refer to the table in the attachment:
Let y= No. of members who have paid in Full
20 % members paid in full and did not register in advance = 0.2y
62 % registerd in advance and paid in full.
So if total No. of members = 100, then 62 members paid Full and registered in advance.
Hence total members who paid full amount = 0.2y + 62 =y
0.8y =62
Hence y = 77.5
i.e. 77.5 out of 100 or 77.5 %
Ans. D
Question: Find the odd man out
2880, 482, 96, 24, 8, 4, 4
A.482
B.96
C.24
D.8
Answer: A.482
Explanation: from the right side
4*1=4,
4*2=8
8*3=24
24*4=96
96*5=480 but here given 482 so it's not.
480*6=2880
ANSWER:A
Question: A prize of $500 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
A.$160
B.$220
C.$280
D.$300
Answer: A.$160
Explanation: Total value of the prize =$500
Number of people = 20
2/5 of 500 (=$200) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 500-200 = $300. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20=140.
Thus the maximum award can be = 300-140 = $160, hence A is the correct answer.
Question: A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is
A.18%
B.20%
C.22%
D.24%
Answer: B.20%
Explanation: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 135
Required gain = 8%,
So Selling price = Rs 108
Discount = 135 - 108 = 27
Discount% = (27/135)*100 = 20%
Option B
Question: William earned $3,200 per month as a
teacher for the ten months from September
to June. Then he took a job as a barista at a
local café, where he earned $2,000 per
month during July and August. What was
his average monthly pay for the 12 months?
A.$2,400
B.$2,800
C.$2,600
D.$3,000
Answer: D.$3,000
Explanation: E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a
barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into
the formula for the mean:
mean=sum of values/number of values=>36.000/12=3.000
correct answer D)$3.000
Question: What is the largest positive integer n for which 3^n divides 44^44?
A.0
B.9
C.8
D.7
Answer: A.0
Explanation: The digit sum of 44444444 is when remainder obtained 44444444 divided by 9
44444444 = (45−1)44(45−1)44
Each term is a multiple of 9 but the last term which is (−1)44(−1)44 = 1
So the digit sum of 44444444 is 1.
Now the divisibility rule for 3, 9, 27... is the sum of the digits should be divisible by 3, 9, 27 respectively. In each case the digit sum is either multiple of 3 or 9.
So for any value of n > 1, the given expression is not divisible by 3n
Answer:	A
Question: A fair coin is tossed repeatedly. If heads appears on first 5 tosses what is the probability that tail appears on the next two tosses?
A.1/6
B.1/5
C.1/3
D.1/4
Answer: D.1/4
Explanation: Explanation :
Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.
1/2 * 1/2 = 1/4
Answer : D
Question: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?
A.277
B.810
C.888
D.166
Answer: C.888
Explanation: 12 men 120 acres 36 days
54 men ? 54 days
120 * 54/12 * 54/36
10 * 54 * 3/2
54 * 15 = 810
Answer: C
Question: What is the unit digit in {(6374)^1793 x (625)^317 x (341)^491)}?
A.0
B.1
C.2
D.3
Answer: A.0
Explanation: Unit digit in (6374)1793 = Unit digit in (4)1793
= Unit digit in [(42)896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Option A
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
A.3
B.6
C.9
D.4
Answer: D.4
Explanation: 4 years
Answer: D
Question: Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 2 hours?
A.60X/Y.
B.120X/Y.
C.60Y/X.
D.120Y/X.
Answer: D.120Y/X.
Explanation: Kramer can pack X boxes per min.
Therefore in 2 hrs(120 mins)he can pack 120X boxes.
If there are Y boxes in one case then then the total number of cases packed by Kramer = 120X/Y
ANSWER:D
Question: If w/x = 1/3 and w/y = 3/4, then (x + y)/y =
A.13/4
B.6/5
C.7/5
D.8/5
Answer: A.13/4
Explanation: W/X = 1/3=>x=3w and W/Y = 3/4=>y=(4/3)w
(X+Y)/Y = (3w+4/3w)/(4/3w)=(13/3w)/(4/3w)=13/4
Correct Option: A
Question: There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ?
A.20
B.30
C.50
D.60
Answer: D.60
Explanation: Explanation:
Let x and y be the number of deer and peacocks in the zoo respectively. Then,
x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
Answer: D
Question: How many different three-digit multiples of 5 can be composed of digits 1, 2, 3, 4, and 5 if none of the digits is repeated?
A.3
B.6
C.8
D.12
Answer: C.8
Explanation: can you explain your method. i solved it differently
XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 4 possible choices.
X can be any of the 3 possible choices.
4+3+1= 8
C
Question: An empty pool being filled with water at a constant rate takes 8hours to fill to 2/5 of its capacity.how much more time will it take to finish filling the pool?
A.5hr 30min
B.5hr 20min
C.4hr 48min
D.3 hr 12min
Answer: A.5hr 30min
Explanation: As pool is filled to 2/5 of its capacity then 2/5 of its capacity is left to fill.
To fill 3/5 of the pool took 8 hours --> to fill 2/5 of the pool will take 8/(3/5)*2/5=16/3 hours = 5 hours 20 minutes (because if t is the time needed to fill the pool then t*3/5=8 --> t=8*5/3 hours --> to fill 2/5 of the pool 8*5/3*2/5=16/3 hours will be needed).
Or plug values: take the capacity of the pool to be 5 liters --> 3/5 of the pool or 3 liters is filled in 8 hours, which gives the rate of 3/8 liters per hour --> remaining 2 liters will require: time = job/rate = 2/(3/8) = 16/3 hours = 5 hours 30 minutes.
Answer: A.
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 5,000, how much money did investors B and C earn in total?
A.$15,000
B.$4,900
C.$5,600
D.$9,500
Answer: A.$15,000
Explanation: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 5000
5x = 5000=>x=1000
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x =15*1000= 15,000
Answer A
Question: When the positive integer A is divided by 4 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 4 and 7, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?
A.12
B.24
C.28
D.16
Answer: C.28
Explanation: A = 4k+3 = 7j+4
B = 4m+3 = 7n+4
A-B = 4(k-m) = 7(j-n)
Thus A-B is a multiple of 4 and 7, so it is multiple of 28.
The answer is C.
Question: If the sum of a set of 5 different positive prime numbers is 94, what is the difference between larger 2 prime numbers between them?
A.11
B.12
C.23
D.17
Answer: B.12
Explanation: All prime numbers apart from 2 are odd.
Even + Even = Even
Odd + Even = Odd
Odd + Odd = Even
We are given 5 different prime numbers, whose sum is 94 i.e even
If we include 2, we will have 4 odd prime numbers and one even.
This sum would be odd
If we exclude 2, we will have 5 odd numbers.
This sum would be even
Hence 2 is included.
The possible 5 no. are = 11+7+2+43+31 = 94
difference between larger 2 prime numbers between them = 43 - 31 = 12
Ans - B
Question: If the height of an equilateral triangle RBC is equal in length to the hypotenuse of an isosceles right triangle DEF, a side of ΔRBC is how many times as long as a leg of the right triangle DEF?
A.(√2)/(√3)
B.(√3)/(√2)
C.√2
D.(2√2)/(√3)
Answer: D.(2√2)/(√3)
Explanation: Side of the equilateral triangle RBC = 2m ----> height = m * sqtr(2)
Hipotenuse of the right triangle RBC = m * sqrt(3) ----> side = m * sqtr(3) / sqtr(2)
Question is 2m/m * sqtr(3) / sqtr(2) = 2*sqrt(2)/sqrt(3)=D
Question: There are two numbers. If 40% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
A.3/7
B.5/8
C.6
D.6/7
Answer: B.5/8
Explanation: Let the two numbers be x and y.
40/100 * x + y = 5/4y
=> 2/5 x = 1/4 y => x/y = 5/8
B)
Question: Two cubes of their volumes in the ratio 64 : 1331. The ratio of their surface area is:
A.1.5:5
B.2:5
C.3:5
D.4:11
Answer: D.4:11
Explanation: The ratio of their surface area is
64 : 1331
4 : 11
Answer is D.
Question: 56 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is :
A.33.0
B.37.66
C.32.1
D.31.23
Answer: B.37.66
Explanation: Explanation:
Let the two parts be (56 - x) and x.
Then, 10 (56 - x) + 22x = 780
=> 12x = 220
=> x = 20.
Bigger part = (56 - x) = 37.66.
Answer: B) 37.66
Question: A man purchases the milk at Rs. x/litre and sells it at Rs. 2x/liter stillhe mixes 2liters water with every 6liters of pure milk. What is the profit %?
A.100.12%
B.123.16%
C.154.66%
D.166.66%
Answer: D.166.66%
Explanation: Let the cost price of 1 litre pure milk be Re.1, then
\inline \begin{Bmatrix} 6 & litres(milk) & \rightarrow & CP=Rs.6\\ 2 & litres(water) & \rightarrow & CP=Rs.0 \end{Bmatrix}\rightarrow CP=Rs.6 only
and 8 litre mixture \rightarrow SP \rightarrow 8 x 2 = Rs.16
Profit %= 166.66%
D
Question: With both valves open, the pool will be filled with water in 48 minutes. The first valve alone would fill the pool in 2 hours. If the second valve emits 50 cubic meters of water more than the first every minute, then what is the capacity E of the pool?
A.9000 cubic meters
B.10500 cubic meters
C.11750 cubic meters
D.12000 cubic meters
Answer: D.12000 cubic meters
Explanation: D. 12000 cubic meters.
If both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in (48*120)/(120-48) = 80 minutes.
Now, if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120x and also 80 (x+50).
or, 120x = 80 (x + 50).
or x = 100.
Hence, the capacity of pool = 120x = 12000 cubic meters.
Question: The probability of pulling a black ball out o f a glass is 1/X. The probability of pulling a black ball out of a glass and breaking the glass is 1/Y. What is the probability of breaking the glass?
A.1/(XY).
B.Y/X
C.X by Y
D.1/(X+Y).
Answer: C.X by Y
Explanation: pulling a black ball out of a glass and breaking the jar both are independent events.
For 2 independent events, we know, P(a) * P(b) = P(a∩b)
If Prob of pulling a black ball out of a glass = P(a) and Prob of breaking the glass= P(b)
1/x * P(b) = 1/y ---> P(b) = x/y
Hence, answer should be C.