RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What percent of 5 letter combinations that can be made from the letters of the word SERMONT and in which each letter can be used only once are the combinations in which the first letter is a vowel and the last letter is a consonant?
A.20%
B.23.8%
C.25%
D.30.2%
Answer: B.23.8%
Explanation: a) noof combinations when all 5 letters are different = 7*6*5*4*3
b) noof combinations when first letter is vowel and last is consonant = 2c1*5c1*5*4*3
b/a = 5/21= 0.238
B
Question: If x is a positive, single-digit integer such that 4/3*x, 2x, x, and x + 2, and 4x – 2 form a non-ordered list of consecutive integers, which of the following could be the median of that list?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: The big hints are thatx is a 1-digit integerAND (4/3)x, 2x, x, and x + 2, and 4x – 2 are ALLintegers
For (4/3)x to be an integer, x MUST BE A MULTIPLE OF 3. So, x can equal 3, 6, or 9.
Now let's plug each possible value of x into the terms and see which one yields a list ofconsecutive integers
When x =3, we get the following terms: (4/3)(3), 2(3),3,3+ 2, and 3(3) – 2.
When we evaluate these terms we get: 4, 6, 3, 5 and 10
Rearrange to get: 3, 4, 5, 6, 10. So, when x = 3, we getconsecutive integers.
In this case, the MEDIAN = 5
Since 5 is among the answer choices, we need not test the other 2 values of x (i.e., x = 6 and x = 9)
Answer:
C
Question: If A got 70 marks and B got 80 marks, then what percent of A's mark is B's mark?
A.A)60%
B.B)80%
C.C)65%
D.D)87.5%
Answer: D.D)87.5%
Explanation: A's marks =80 ; B's marks = 70.
Let x% of A = B => x/100 * 80 = 70
=> x = (70 * 100)/80 =87.5
B's marks is 87.5% of A's marks.
ANSWER:D
Question: x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xz is even
2. (z-x)(y-x+1) = 4
3. xy is odd
A.I only
B.II only
C.II only
D.I and II only
Answer: C.II only
Explanation: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1
Statement 1can not be ascertain as is not related to y directly ---not true
Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true
Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.
So, II are always true and hence answer is
C
Question: Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
A.Can't be determined
B.40
C.27
D.24
Answer: D.24
Explanation: Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
Then, (5x+3)/(4x+3)=119
⇒ 45x + 27 = 44x + 33⇒ 9(5x + 3) = 11(4x + 3)
⇒ 45x - 44x = 33 - 27
⇒ x = 6.
Anand's present age = 4x = 24 years.
Answer: D
Question: How many ltrs of water must beadded to 16 ltrs of milk and water containing 10% water to make it 20% water in it?
A.1 liter
B.2 liter
C.3 liter
D.4 liter
Answer: B.2 liter
Explanation: By rule of alligation,
% Concentration
of water in pure water (100)	% Concentration
of water in the given mixture (10)
Mean % concentration
(20)
20 - 10 = 10	100 - 20 = 80
=> Quantity of water : Quantity of the mixture = 10 : 80 = 1 : 8
Here quantity of the mixture = 16 litres
=> Quantity of water : 16 = 1 : 8
=> Quantity of water =16×18=2 liter
B
Question: How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?
A.6400
B.2400
C.5500
D.7400
Answer: A.6400
Explanation: Number of bricks = Volume Of the wall / Volume of 1 brick = (800 x 600 x 22.5) / (25 x 11.25 x 6) = 6400
ANSWER:A
Question: There are 399 doctors and nurses in a hospital. If the ratio of the doctors to the nurses is 8 : 11, then how many nurses are there in the hospital?
A.152
B.209
C.57
D.231
Answer: D.231
Explanation: Given,
The ratio of the doctors to the nurses is 8 : 11
Number of nurses = 11/19 x 399 = 231
ANSWER:D
Question: After decreasing 24% in the price of an article costs Rs.988. Find the actual cost of an article?
A.1667
B.6789
C.1300
D.6151
Answer: C.1300
Explanation: CP* (76/100)
= 988
CP= 13 * 100 => CP
= 1300
Answer: C
Question: 8 couples attend a dance show in a TV channel. A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is at least 1 couple will be selected is :
A.11/31
B.13/37
C.15/39
D.16/37
Answer: C.15/39
Explanation: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)
= 15/39
C
Question: Mohan purchased 15 kgs of rice at the rate of Rs.26 per kg and 8 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?
A.Rs.598
B.Rs.594
C.Rs.596
D.Rs. 595
Answer: A.Rs.598
Explanation: Explanation:
Price of 15 kgs of rice at Rs.26/kg = 15x26 = Rs.390
Price of 8 kgs of pulses at Rs.26/kg = 8x26 = Rs.208
Therefore, Total amount = Rs.390+Rs.208 = Rs.598.
Answer: Option A
Question: The average age of 15 students of a class is 15 years. Out of these, the average age of 7 students is 14 years and that of the other 7 students is 16 years. The age of the 15th student is
A.9 years
B.11 years
C.15 years
D.21 years
Answer: C.15 years
Explanation: Solution
Age of the 15th student	=[15x15-(14x7+16x7)]
= (225 - 210)
= 15 years.
Answer C
Question: A can do a piece of work in 30 days. He works at it for 5 days and then B finishes it in 20 days. In what time can A and B together it?
A.13 8/3 days
B.13 1/3 days
C.13 6/3 days
D.63 1/3 days
Answer: B.13 1/3 days
Explanation: 5/30 + 20/x = 1
x = 24
1/30 + 1/24 = 3/40
40/3 = 13 1/3 days
Answer: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.2681
B.1892
C.1000
D.1345
Answer: C.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: C
Question: Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
A.360
B.120
C.80
D.240
Answer: A.360
Explanation: Total number of arrangements = 6! = 720
In exactly half, Susan will be to the left of Tim, which gives us 360 arrangements
Option (A)
Question: A team of three entered for a shooting competition. The best marks man scored 85 points. If he had scored 92 points, the average scores for. The team would have been 84. How many points altogether did the team score?
A.288
B.245
C.168
D.127
Answer: B.245
Explanation: Explanation:
3 * 84 = 252 - 7 = 245
Answer:B
Question: For all positive integers n and m, the function A(n) equals the following product:
(1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/6 + 6^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number, while B(m) equals the sum of the reciprocals of all the positive integers from 1 through m, inclusive. The largest reciprocal of an integer in the sum that B(25) represents that is NOT present in the distributed expansion of A(5) is
A.1/4
B.1/5
C.1/6
D.1/7
Answer: A.1/4
Explanation: For all positive integers n and m,
A(n) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)…(1 + 1/p_n + 1/p_n^2), where p_n is the nth smallest prime number,
note:i think there's a typo in the above function, A(n) could be (1 + 1/2 + 1/2^2)(1 + 1/3 +1/3^2)(1 + 1/5 +1/5^2)…(1 + 1/p_n + 1/p_n^2)
B(m) = sum of the reciprocals of all the positive integers from 1 through m, inclusive.
A(5), here 5 represents the 5th smallest prime number; the 5th smallest prime number is 11 {2, 3, 5, 7, 11, ...}
A(5) = (1 + 1/2 + 1/2^2)(1 + 1/3 + 3^2)(1 + 1/5 + 5^2)(1 + 1/7 + 1/7^2)(1 + 1/11 + 11^2)
The distributed expansion of A(5) = 1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 +1/7 + 1/9+ 1/10 + 1/11 +1/12 + 1/14+ ...
missing numbers are 1/8, 1/13, 1/16, ....
B(25) = (1 + 1/2 + 1/3 + 1/4 + ... + 1/16 + 1/17 + ... + 1/25)
here the largest reciprocal is 1 and the reciprocals are arranged in descending order based on their values
The largest reciprocal that present in B(25) but not in A(5) is 1/4
Answer A
Question: The product of the digits of the four-digit number h is 36. No two digits of h are identical. How many different numbers are possible values of h?
A.6
B.12
C.24
D.36
Answer: C.24
Explanation: Since the product of the four non-repeating digits is 36, the only possibility is if 1, 2, 3 and 6 are used. These digits can be arranged in 4! ways. Therefore, answer is 24.
ANS :C
Question: The average temperature of a city in the first four days of a month was 36°. The average for the 2nd, 3rd, 4th and 5th day was 38°. If the temperature of the 1st and 5th day were in the ratio 4 : 5, then what is the temperature on the fifth day ?
A.32°
B.35°
C.38°
D.40°
Answer: D.40°
Explanation: Explanation:
The temperature for first 4 days = 4 * 36 = 144
The temperature for last 4 days = 4 * 38 = 152
The difference between the temperatures is (152 – 144) = 8
The ratio of temperature between first and fifth day is 4 : 5
The temperature on fifth day is 5*8 = 40
ANSWER D
Question: Having received his weekly allowance, John spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.96 at the candy store. What is John’s weekly allowance?
A.$3.00
B.$3.20
C.$3.40
D.$3.60
Answer: D.$3.60
Explanation: x = 3x/5 + 1/3*2x/5 + 96
4x/15 = 96
x = $3.60 = $3.60
The answer is D.
Question: The C.I. on a certain sum for 2 years Rs.41 and the simple interest is Rs.40. What is the rate percent?
A.7%
B.5%
C.8%
D.6%
Answer: B.5%
Explanation: SI = 20 + 20
CI = 20 + 21
20 ---- 1
100 ---- ? => 5%
Answer:B
Question: Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?
A.2400 m^2
B.2420 m^2
C.2520 m^2
D.2600 m^2
Answer: C.2520 m^2
Explanation: Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m2 = 2520 m^2
C
Question: The ratio of the present ages of Giri and Hari is 5:8. 12 years hence, the ratio of their ages will be 11:14. Find the difference in their present ages?
A.7 years
B.6 years
C.9 years
D.5 years
Answer: B.6 years
Explanation: Let the present ages of Giri and Hari be 5x and 8x years respectively.
(5x + 12)/(8x + 12) = 11/14
70x + 168 = 88x + 132 => x = 2
Difference in their ages will be the same at all times.
This difference = Difference of their present ages
=> 8x - 5x = 3x => 6 years
Answer: B
Question: A trader bought a car at 30% discount on its original price. He sold it at a 80% increase on the price he bought it. What percent of profit did he make on the original price?
A.18%
B.26%
C.12%
D.32%
Answer: B.26%
Explanation: Original price = 100
CP = 70
S = 70*(180/100) = 126
100 - 126= 26%
Answer: B
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 7 m of the same rod?
A.22.8 kg
B.26.6 kg
C.28 kg
D.26.5 kg
Answer: B.26.6 kg
Explanation: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 7 :: 42.75 : x
=> 11.25 x x = 7 x 42.75
=> x = (7 x 42.75) / 11.25
=> x = 26.6
Answer : B
Question: The radius of a semicircle is 7. What is the approximate perimeter of the semicircle?
A.36
B.25
C.15
D.28
Answer: A.36
Explanation: perimeter of a circle =2pi*r
perimeter of a semicircle = pi*r + 2r
aprox perimiter = 3.14*7 + 2*7 = 35.98 approximately 36
answer A
Question: A train of 24 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
A.2
B.3
C.76
D.6
Answer: B.3
Explanation: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec = 3 mins.Answer: B
Question: Determine the value of 27/31+54/62
A.86/31
B.87/31
C.88/31
D.89/31
Answer: D.89/31
Explanation: Solution:
Both fractions should be reduced before performing arithmetic operations. We get 27/31+2.27/2.31=27/31+27/31=2(27/31)=89/31
Answer D
Question: Praveen age after 10years will be 3 times his age 3years back. what is the present age of Chris?
A.20
B.25
C.10
D.30
Answer: A.20
Explanation: Chris present age= x
after 10years = x+10
3years back = x-3
x+10= 3(x-3)
x=20
Answer is A
Question: Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8310/-. Find out the amount that he borrowed.
A.s. 5266
B.s. 5396
C.s. 5228
D.s. 5218
Answer: B.s. 5396
Explanation: Explanation:
Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)
By formula of simple interest, S.I. = PRT / 100
Where P = The principal, R = Rate of interest as a %, T = Time in years
S.I. = (P * 6 * 9)/100 = 54 P/100
Amount = Principal + S.I.
8310 = P + (54P/100)
8310 = (100P + 54P)/100
8310 = 154P/100
P = (8310 * 100)/154 = Rs. 5396.104
ANSWER: B
Question: The total age of A and B is 11 years more than the total age of B and C. C is how many years younger than A.?
A.16
B.12
C.11
D.20
Answer: C.11
Explanation: (A+B)-(B-C)=11
A-C=11
Answer is C
Question: When 17 is divided by positive integer x, the remainder is 1. For how many values of x is this true?
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: When 17 is divided by x, the remainder is 1 i.e. 1 orange left over after grouping, so x must be greater than 1.
It also means that 16 is completely divisible by x.
Factors of 16 are 1, 2, 4, 8, 16.
Out of these, x can be 2, 4, 8, and 16.
Answer (D).
Question: In an election, candidate A got 80% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favor of candidate?
A.355600
B.380800
C.356500
D.356800
Answer: B.380800
Explanation: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 80 %
Therefore, the number of valid votes polled in favour of candidate A = 80 % of 476000
= 80/100 × 476000
= 38080000/100
= 380800
B)
Question: x, a, z, and b are single digit positive integers. x = ¼ a. z = ¼ b. (10a + b) – (10x + z) could NOT equal
A.33
B.36
C.44
D.63
Answer: C.44
Explanation: From the given equations, a = 4x, b = 4z
(10a+b) - (10x+z) = 40x+4z - 10x-z = 30x +3z = 3(10x+z)
Therefore the resultant should be divisible by 3 which isn't possible only in the case of C.
Hence C is the answer
Question: If a wholesaler distributes items to several outlets (A, B, C and D) in the ratio of 1/12 : 1/13 : 1/15 : 1/2, then find the total number of items the wholesaler distributes?
A.567
B.167
C.267
D.467
Answer: A.567
Explanation: Here, A : B : C : D = 1/12 : 1/13 : 1/15 : 1/2
1) L.C.M of 12 : 13 : 15 : 2 is 780
2) Find the number of books each friend received --------- (To find no. of books each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/12) x 780 = 65
B = (1/13) x 780 = 60
C = (1/15) x 780 = 52
D = (1/2) x 780 = 390
3) Total number of toys = (65 x + 60 x + 52 x + 390 x) = 567 x
Minimum number of pens (x) = 1
Therefore, total number of items = 567 items.
Correct option :A
Question: Rs.560 is divided amongst A, B, C so that 5 times A's share, six times B's share and eight times C's share are all equal. Find C's share?
A.Rs.142.37
B.Rs.152.37
C.Rs.242.37
D.Rs.210
Answer: A.Rs.142.37
Explanation: A+B+C = 560
5A = 6B = 8C = x
A:B:C = 1/5:1/6:1/8
= 24:20:15
15/59 * 560 = Rs.142.37
ANSWER:A
Question: The table below shows the enrollment in various classes at a certain college.
Class | Number of Students
Biology | 65
Physics | 35
Calculus | 40
Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 are enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes?
A.51
B.88
C.90
D.103
Answer: D.103
Explanation: No. of total students = no of students of biology + no of students of physics but not biology + no of students of calculus but not biology and physics
No. of total students = 65 + (35-15) + (40-10-12) = 65+20+18 = 103
Hence, Answer will be D.
Question: Find the odd man out. 3, 5, 15, 75, 1120, 84375
A.15,
B.84375
C.1120
D.75
Answer: C.1120
Explanation: 3
5
3 × 5 = 15
5 × 15 = 75
15 × 75 = 1125
75 × 1125 = 84375
Hence, 1120 is wrong. 1125 should have come in place of 1120
Answer is C
Question: When positive integer n is divided by 3, the remainder is 2. When n is divided by 7, the remainder is 6. How many values less than 100 can n take?
A. 0
B. 2
C. 3
D.6
Answer: D.6
Explanation: a quick approac to this Q is..
the equation we can form is.. 3x+2=7y+5..
3x-3=7y... 3(x-1)=7y...
so (x-1) has to be a multiple of 7 as y then will take values of multiple of 3..
here we can see x can be 1,8,15,22,29 so 5 values till 100 is reached
as (29-1)*3=84 and next multiple of 7 will be 84+21>100..
ans 6.. D
Question: A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is one–fifth of the average o fthe two areas. What is the area of the smaller part in hectares?
A.225
B.280
C.300
D.385
Answer: D.385
Explanation: Solution
Let the areas of the two parts be
x and (700 - x)hectares	= [x - (700 - x)]
= 1 / 5 x [x + (700 - x)/ 2]
= 2x - 700= 70
x = 385.
Answer D
Question: In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 19th board counting from the bottom of the stack. How many boards are in the stack?
A.37
B.36
C.35
D.34
Answer: A.37
Explanation: Counting from the top, after the 20th board, there are 17 boards left to count.
The answer is A.
Question: A tourist purchased a total of $4,500 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
A.$1,430
B.$2,310
C.$3,290
D.$4,270
Answer: D.$4,270
Explanation: Let the number of $10 checks cashed beT
Let the number of $50 checks cashed beF
7 checks cashed;
T+F=7
Now; T can be F+1 OR T can be F-1
Let's check both conditions;
T=F+1
T+F=7
F+1+F=7
2F=6
F=3
T=4
Value cashed = 3*50+4*10=150+40=$190
Let's check the other condition as well;
T=F-1
T+F=7
F-1+F=7
2F=8
F=4
T=3
Value cashed = 4*50+3*10=200+30=$230
The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.
Value cashed = $230
Value lost = 4500-230 = $4270
Ans:D
Question: Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 0: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?
A.4: 45 p.m.
B.2: 20 p.m.
C.5: 20 p.m.
D.5: 35 p.m.
Answer: B.2: 20 p.m.
Explanation: the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 0:20 +2=2:20
Hence answer is B.Hope i am correct
Question: A string of length 40 metres is divided into three parts of different lengths. The first part is three times the second part, and the last part is 23 metres smaller than the first part.
Find the length of the largest part.
A.27
B.4
C.5
D.9
Answer: A.27
Explanation: Explanation :
Let the 2nd piece length be x.
1st piece length is 3x.
3rd piece length is 3x – 23.
Sum of all the pieces is 40.
3x + x + 3x – 23 = 40.
7x = 63.
x = 9.
Lengths of the pieces are 27, 9, 4.
Answer : A
Question: A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is?
A.22
B.88
C.12
D.77
Answer: C.12
Explanation: S.I. for 3 years = (12005 - 9800) = Rs. 2205
S.I. for 5 years = Rs. 2205/3 * 5 = Rs. 3675.
Principal = (9800 - 3675) = Rs. 6125
Hence, rate = (100 * 3675) / (6125 * 5) = 12%
Answer: C
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
A.20:15:16
B.20:15:18
C.20:15:12
D.20:15:11
Answer: C.20:15:12
Explanation: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Question: A recipe for a large batch of fruit juice at a factory calls for 10% oranges, 20% lemons, and 70% limes. if 200 oranges are used, how many lemons are needed?
A.50
B.100
C.200
D.400
Answer: D.400
Explanation: 10%= 200 fruit
100%=2000 fruit
20% of 2000 fruit=400 fruit
400 lemons
ANSWER:D
Question: An article is bought for Rs.500 and sold for Rs.400, find the loss percent?
A.18 2/3%
B.16 7/3%
C.20%
D.16 2/3%
Answer: C.20%
Explanation: 500 ---- 100
100 ---- ? => 20%
Answer:C
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?
A.2(5/11)days
B.3(5/11)days
C.4(5/11)days
D.6(5/11)days
Answer: B.3(5/11)days
Explanation: B
3(5/11)days
A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 2 days.
The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 18 minutes. The waste pipe can empty the full cistern in?
A.8 min
B.7 min
C.5 min
D.9 min
Answer: D.9 min
Explanation: 1/10 + 1/15 - 1/x
= 1/18
x = 9
Answer: D
Question: Ravi and Kavi start a business by investing â‚¹ 2000 and â‚¹ 72000, respectively. Find the ratio of their profits at the end of year.
A.2 : 36
B.5 : 36
C.7 : 36
D.1 : 36
Answer: D.1 : 36
Explanation: Ratio of profit = Ratio of investments
= 2000 : 72000 = 1 : 36
Answer : D
Question: On the average Mr.Jackson has 2 hours to plan for an long hour meeting he talk to his assistant 7 hours to prepare the paper work needed.How much hours should jackson and assistant has t plan for 30 min meeting?
A.4.5 hr
B.4.8 hr
C.4.9 hr
D.5.5 hr
Answer: A.4.5 hr
Explanation: for a 1 hour talk he took total of 9 hr time
1hr=9hr(2+7)
30 min=1/2hr =?
so 9*1/2 div by 1
4.5 hr
ANSWER:A
Question: An engineer undertakes a project to build a road 15 km long in 300 days and employs 30 men for the purpose. After 100 days, he finds only 2.5 km of the road has been completed. Find the (approximate) number of extra men he must employ to finish the work in time.
A.a. 43
B.b. 45
C.c. 55
D.d. 68
Answer: B.b. 45
Explanation: 30 workers working already
Let x be the total men required to finish the task in next 200 days
2.5 km done hence remaining is 12.5 km
Also, work has to be completed in next 200 days (300 - 100 = 200)
We know that, proportion of men to distance is direct proportion
and, proportion of men to days is inverse proportion
Hence, X = (30 * 12.5 * 100) / (2.5 * 200)
thus, X = 75
Thus, more men needed to finish the task = 75-30=45
hence Answer is B
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 180, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
A.31
B.33
C.55
D.77
Answer: A.31
Explanation: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 180 => .1x + 3/4x = 180 => x = 211
211 - 180 = pure gala = 31.
A