RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 100 that is both a prime and a palindrome. What is the sum of the digits of p?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: Given that p is smallest integer greater than 200 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
C
Question: A monkey start climbing up a tree 19 ft tall.Each hour it hops 3 ft and slips back 2 ft. How much time would it take the monkey to reach the top.
A.15 hrs
B.18 hrs
C.19 hrs
D.17 hrs
Answer: D.17 hrs
Explanation: if monkey hops 3ft and slips back 2ft in a hour, it means the monkey hops (3ft-2ft)= 1ft/hr.
similarly in 16hrs it wil be 16ft.
Bt since the height of the tree is 19ft, so if the monkey hops up the tree in the next hr i.e 17th hr then it reaches at the top of the tree.
hence it takes 17 hrs for monkey to reach at the top
ANSWER:D
Question: In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?
A.70
B.66
C.68
D.69
Answer: C.68
Explanation: Solution: Member in group * age increased = difference of replacement
Or, 8*1 = new comer - man going out
Or, new comer = 8+60;
Or, new comer = 68 years.
Answer: Option C
Question: If there are 10 apples and 20 oranges, what is the ratio of apples to oranges?
A.10:20
B.2:4
C.1:2
D.4:8
Answer: C.1:2
Explanation: A ratio should be reduced to the lowest common denominator.
10:20 means 10x:20x which can be written as 1(10):2(10)...
ANSWER:C
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 60 metres?
A.16 seconds
B.76 seconds
C.10.8 seconds
D.12 seconds
Answer: C.10.8 seconds
Explanation: Speed of the boat downstream = 15 + 5
= 20 kmph
= 20 * 5/18 = 50/9 m/s
Hence time taken to cover 60 m
= 60*9/50
= 10.8 seconds.
Answer: C
Question: Find the first term and the common ratio of a G.P whose fourth term is 250 and seventh term is 31,250
A.2/5,25
B.4,5/2
C.1,16
D.2,5
Answer: D.2,5
Explanation: a*r ^3 = 250, a *r ^6 =31,250, r ^3 =31,250/250 = 125
r = 5, a* 125 = 250, a = 2
ANSWER:D
Question: A 600 meter long train crosses a signal post in 40 seconds. How long will it take to cross a 3 kilometer long bridge, at the same speed?
A.4 min
B.5 min
C.3 min 4 sec
D.4 min 5 sec
Answer: A.4 min
Explanation: Explanation:
S = 600/40 = 15 mps
S = 3600/15 = 240 sec = 4 min
ANSWER IS A
Question: Calculate the HCF of 64, 592, 960
A.15
B.16
C.13
D.14
Answer: B.16
Explanation: Explanation:
Lets solve this question by factorization method.
The factors of 64 are: 1, 2, 4, 8, 16, 32, 64
The factors of 592 are: 1, 2, 4, 8, 16, 37, 74, 148, 296, 592
The factors of 960 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
Then the greatest common factor is 16.
Answer: Option B
Question: What is the next number in the series?
1,5,9,13...
A.19
B.17
C.24
D.25
Answer: B.17
Explanation: Adding (0,2,4,6,8,10) to the odd numbers
1+0=1
3+2=5
5+4=9
7+6=13
9+8=17
answer B
Question: A train takes 9 hrs to cover distance with the speed 85kmph. Find distance the train travelled.
A.750
B.850
C.725
D.765
Answer: D.765
Explanation: Length = Speed * time
Length =85kmph * 9 hrs
Length =765km
Ans : (D)
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.16%
B.15%
C.12%
D.22%
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: There is enough provisions for 600 men in an army camp for 25 days. If there were 100 men less, how long will the provision last?
A.10days
B.50days
C.100days
D.150days
Answer: D.150days
Explanation: Exp: We have, M1D1 = M2D2
600*25= 100* D2
D2 = 600*25/100 = 150 days.
Answer: D
Question: A cheese factory sells its cheese in rectangular blocks. A normal block has a volume of 5 cubic feet. If a large block has twice the width, twice the depth, and the same length of a normal block, what is the volume of cheese in a large block in cubic feet?
A.15
B.30
C.20
D.18
Answer: C.20
Explanation: Volume of cube=lbh=5
New cube l ,b, h are increases of l, 2b,2h
New volume of cube =l*2b*2h=4*lbh
=4*5
=20
Answer: C
Question: If the sides of a triangle are 65 cm, 60 cm and 25 cm, what is its area?
A.120 cm2
B.750 cm2
C.216 cm2
D.197 cm2
Answer: B.750 cm2
Explanation: The triangle with sides 65 cm, 60 cm and 25 cm is right angled, where the hypotenuse is 65 cm.
Area of the triangle
= 1/2 * 60 * 25
= 750 cm2
Answer:B
Question: Let S1 be a square of side a. Another square S2 is formed by joining the mid-points of the sides of S1. The same process is applied to S2 to form yet another square S3, and so on. If A1, A2, A3 .. be the areas and P1, P2, P3,…….. be the perimeters of S1, S2, S3,..., respectively, then the ratio (P1 + P2 +P3+ ......) / (A1 + A2 + A3 +.......) equals :-
A.2(1+√2)/a
B.2(2+√2)/a
C.2(2+√2)/a
D.2(1+2√2)/a
Answer: B.2(2+√2)/a
Explanation: Explanation :
side of S1= a, perimeter of S1= 4a, area of S1 = a2
side of S2= a/√2 , perimeter of S2= 2√2a , area of S2 = a2/2
side of S3= a/2 , perimeter of S3= 2a , area of S3= a2/4
So, for P1 + P2 + P3 .... we will have a GP as below
4a + 2√2a + 2a + .....
First term =4a, common ratio = 1/√2, Sum = 4a/( 1-1/√2) = 4√2a/(√2 - 1)
For A1 + A2 + A3....we will have another GP
a2 + a2/2 + a2/4 .....
First term = a2 , common ratio = 1/2 , Sum = 2a2.
Hence, the required ratio :-
i.e (P1 + P2 + P3....) / (A1+ A2+A3....).
=> 4√2a / (√2 - 1) / 2a2.
=> 2√2(√2 + 1)/a.
=> 2(2 +√2)/a .
Answer : B
Question: A survey reveals that the average income of a company’s customers is $45,000 per year. If 40 customers respond to the survey and the average income of the wealthiest 10 of those customers is $75,000, what is the average income of the other 30 customers?
Is there a way to solve this using weighted average concept instead of doing tedious calculations?
A. $27,500
B. $35,000
C. $37,500
D. $42,500
Answer: B. $35,000
Explanation: let x be the average of 30 customers
30*x + 10* 75000 = 40*45000
solving this we have x= 35000
Answer is B.
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 180 m in 18 sec. then find the length of the train?
A.780m
B.180m
C.170m
D.140m
Answer: B.180m
Explanation: Length of the train be ‘X’
X + 120/15 = X + 180/18
6X + 720 = 5X + 900
X = 180m
Answer:B
Question: In a box, there are 7 red, 3 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?
A.2/3
B.8/21
C.3/7
D.7/15
Answer: D.7/15
Explanation: Explanation:
Total number of balls = (7 + 3 + 5) = 15.
Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.
Therefore, n(E) = 7.
P(E) = 7/15.
Answer: Option D
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 10 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :
A.22
B.21
C.88
D.30
Answer: D.30
Explanation: Explanation:
Lot the total number of workers be v Then,
8OOOv = (12000 * 10) + 6000 (v - 10) <=> 2000v = 60000 <=> v = 30
Answer: D) 30
Question: A 4-letter code word consists of letters D, E, and G. If the code includes all the three letters, how many such codes are possible?
A.72
B.48
C.36
D.24
Answer: C.36
Explanation: Note that the correct answer to this question is 36, not 72.
D-DEG can be arranged in 4!/2!=12 ways;
E-DEG can be arranged in 4!/2!=12 ways;
G-DEG can be arranged in 4!/2!=12 ways;
Total: 12+12+12=36.
Answer: C.
Question: 3/4 of 1/2 of 2/5 of 5000 = ?
A.392
B.229
C.753
D.750
Answer: D.750
Explanation: D
750
? = 5000 * (2/5) * (1/2) * (3/4) = 750
Question: If x+y=3 and x2y3 + y2x3=27, what is the value of xy?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: xy=3
As x+y=3
x2y3+y2x3=27
x2y2(y+x)=27
Substituting x+y
x2y2=9
xy=3
ANSWER:C
Question: Without stoppages, a train travels certain distance with an average speed of 250 km/h, and with stoppages, it covers the same distance with an average speed of 125 km/h. How many minutes per hour the train stops ?
A.25
B.30
C.35
D.40
Answer: B.30
Explanation: Due to stoppages, it covers 125 km less .
Time taken to cover 125 km = 125â„250h = 1â„2h
= 1â„2 Ã— 60 min = 30 min
Answer B
Question: A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 14% while buying and by 20% while selling. What is his percentage profit?
A.10.22%
B.20.22%
C.21.22%
D.42.5%
Answer: D.42.5%
Explanation: The owner buys 100 kg but actually gets 114kg;
The owner sells 100 kg but actually gives 80kg;
Profit: (114-80)/80*100=~42.5%
Answer: D.
Question: Three numbers are in the ratio 3:4:5 and their L.C.M. is 600. Their H.C.F is?
A.10
B.30
C.40
D.50
Answer: A.10
Explanation: Let the numbers be 3x,4x and 5x
their L.C.M. = 60x
60x =600
x = 10
The numbers are 3*10 , 4*10 , 5*10
Hence required H.C.F. = 10
Answer is A
Question: A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans, what is the least amount of paint E, in gallons, that must be purchased in order to measure out the portions needed for the mixture?
A.2
B.2 1/2
C.3
D.3 1/2
Answer: B.2 1/2
Explanation: Given W:B = 3:5
That means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture.
But we want least amount of whiteblack paints for minimum of 2 gallons of mixture, so lets reduce keeping same ratio,
1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture, but we want only 2 gallons, lets further reduce
0.75: 1.25 gives 1+1.5 =2.5 gallons of mixture. This looks ok, but lets reduce further just to be sure
0.375: 0.625 gives 0.5 + 1 = 1.5 gallons of mixture, thats less than 2 gallons of mixture, so not acceptable.
So correct ans is 2.5 gallons. B
Question: Statement: The authorities in Society X are cracking down on street hawkers, blaming them for traffic jams near their society.
Actions:
I. Street hawkers should not be allowed during peak hours
II. Street hawkers should be warned and asked not to create chaos.
A.Only I follows
B.Only II follows
C.Either I or II follows
D.Neither I nor II follows
Answer: B.Only II follows
Explanation: Explanation: Here a situation of traffic jam is depicted and the actions mentioned, give different ways for improving the situation.
ANSWER IS B
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
A.33388
B.27889
C.27889
D.59000
Answer: D.59000
Explanation: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000
Answer:D
Question: After working for 4 days, Ashok finds that only 1/3 rd of the work has been done. He employs Ravi who is 60% as efficient as Ashok. How many days more would Ravi take to complete the work?
A.13 1/3 days
B.14 1/3 days
C.15 1/3 days
D.3 1/3 days
Answer: A.13 1/3 days
Explanation: 1/3 ---- 4
1 -------? A = 12
R = 1/12 * 60/100 = 1/20
1 ----- 1/20
2/3 ----? => 13 1/3 days
ANSWER:A
Question: Two, trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is:
A.2:3
B.4:3
C.6:7
D.9:16
Answer: B.4:3
Explanation: Let us name the trains as A and B. Then,
(A's speed) : (B's speed) = √b : √a = √16 : √9 = 4 : 3.
Answer :B
Question: A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.95 less, he could have gained 25%. What is the cost price?
A.372
B.375
C.278
D.475
Answer: D.475
Explanation: CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
95 ----- ? => 475
Answer:D
Question: At a local appliance manufacturing facility, the workers received a 25% hourly pay raise due to extraordinary performance. If one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged, by approximately what percent would he reduce the number of hours that he worked?
A.83%
B.80%
C.20%
D.17%
Answer: C.20%
Explanation: Let's say he works usually 10 hours and earns 100 per hour.
10 * 100 = 1000
10 * 125 = 1250 (this are the new earnings after the raise)
To figure out how much he needs to work with the new salary in order to earn the original 1000:
1000/125 = 8
So he can reduce his work by 2 hours. Which is 20%.
Answer C
Question: 50% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
A.70
B.97
C.84
D.90
Answer: C.84
Explanation: Given, 50% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 50% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/50 =48
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (48 + 120)/2 = 84.
Answer:C
Question: If −y ≥ x, and −x < −7, then which of the following must be true?
A.y = −7
B.y > −7
C.−y > 7
D.y ≤ −7
Answer: C.−y > 7
Explanation: −y ≥ x, and −x < −7
y <= -x < -7
As '-x' is less than '-7' and Y is less than or equal to '-x'
we have y < -7 which is similar to -y > 7.
C) -y > 7
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 11220, how much money did he borrow?
A.11000
B.80288
C.2668
D.2600
Answer: A.11000
Explanation: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 11220
18x + 45x + 39x = (11220 * 100)
102x = 1122000 => x = 11000.
Answer:A
Question: The owner of a furniture shop charges his customer 42% more than the cost price. If a customer paid Rs. 8300 for a computer table, then what was the cost price of the computer table?
A.Rs. 5725
B.Rs. 5845
C.Rs. 6275
D.Rs. 6725
Answer: B.Rs. 5845
Explanation: CP = SP * (100/(100 + profit%))
= 8300(100/142) = Rs. 5845.
ANSWER:B
Question: When Jack picks olives for two hours at three times his regular speed, he picks 20 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed, then
A.Jack picks double the amount of olives Mac picks
B.Mac picks 10 pounds more than Jack
C.Jack picks 10 pounds more than Mac
D.Mac picks 5 more pounds than Jack
Answer: D.Mac picks 5 more pounds than Jack
Explanation: Let's say Jack's regular speed is J olives/hr and Mac's regular speed is M olives/hr
Given:
2*3J = 10 + 5*(4/5)M
3J = 5 + 2M
Question:if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed
Mac picks 2M and Jack picks 4*(3/4)J = 3J
They are asking you for the relation between 3J and 2M. You already know 3J = 5 + 2M
So Jack picks 5 pounds more olives than Mac.
D
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 3 seconds. What is the length of the fast train ?
A.27 7/9
B.16 2/3
C.29 7/9
D.30 7/9
Answer: B.16 2/3
Explanation: Explanation:
As Trains are moving in same direction,
So, Relative Speed = 40-20 = 20 kmph
= 20*(5/18) = 50/9 m/sec
Length of Train= Speed * Time
Length=50/9âˆ—3
=150/9
=16 2/3
Option B
Question: If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Poe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 15 miles ahead of Poe?
A.15
B.60
C.75
D.90
Answer: D.90
Explanation: This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one.
Teena covers 55 miles in 60 mins.
Poe covers 40 miles in 60 mins
So teena gains 15 miles every 60 mins
Teena need to cover 7.5 +15 miles.
Teena can cover 7.5 miles in 30 mins
Teena will cover 15 miles in 60 mins
So answer 30+60= 90 mins=D
Question: What is the average of four tenths and five thousandths?
A.0.2022
B.0.2012
C.0.2025
D.0.2021
Answer: C.0.2025
Explanation: Four tenths = 0.4
Five thousandths = 0.005
The average is (0.4 + 0.005)/2 = 0.2025
Answer: C
Question: Find the area of the quadrilateral of one of its diagonals is 15 cm and its off sets 6 cm and 4 cm?
A.50 cm2
B.60 cm2
C.75 cm2
D.90 cm2
Answer: C.75 cm2
Explanation: 1/2 * 15(6 + 4)
= 75 cm2
Answer: C
Question: The number of ways in which ten candidates A1, A2, ...., A10 can be ranked so that A1 is always above A2 is
A.10!⁄2
B.10!
C.9!
D.8!⁄2
Answer: A.10!⁄2
Explanation: Ten candidates can be ranked in 10! ways. In half of these ways A1 is above A2 and in another half A2 is above A1.
So, required number of ways is 10!⁄2
Answer A
Question: The avg. age of a group of 16 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
A.22 years
B.23 years
C.24 years
D.25 years
Answer: D.25 years
Explanation: Total age of 16 students=16*20=320
If total age of 4 students=x
Then, (320+x)/(16+4) =(20+1), x=100
So average age of new students=100/4= 25 years
ANSWER:D
Question: M = {-6, -5, -4, -3, -2, -1}
T = {-5, -4, -3, -2, -1, 0, 1, 2}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
A.0
B.1/4
C.2/5
D.1/2
Answer: B.1/4
Explanation: We will have a negative product only if 1 or 2 are selected from set T.
P(negative product) = 2/8 = 1/4
The answer is B.
Question: A cistern which could be filled in 9 hours takes 1 hour more to be filled owing to a leak in its bottom.If the cistern is full, in what time will the leak empty it?
A.50hours
B.62hours
C.90hours
D.75hours
Answer: C.90hours
Explanation: Let the leak empty the full cistern in x hours
9x/x-9 = 9+1
x = 90 hours
Answer is C
Question: If the position of the first, sixth digits of the number 2796543018 are interchanged, similarly the positions of the the second and seventh digits are interchanged and so on, which of the following will be the left of seventh digit from the left end?
A.1
B.2
C.6
D.7
Answer: A.1
Explanation: Explanation:
The new number formed is 4 3 0 1 8 2 7 9 6 5
The seventh digit from the left is 7, the 3rd digit from the left of 7 is 1
Answer: A) 1
Question: A solution contains 8 parts of water for every 7 parts of Lemonade syrup. How many parts of the solution should be removed and replaced with water so that the solution will now contain 30% lemonade syrup?
A.1.5
B.1.75
C.2.14
D.2.34
Answer: C.2.14
Explanation: Let the total solution is 150 L with 80 L water70 L syrup.
To make 30% syrup solution, the result solution must have 105 L syrup and 45 L syrup.
Therefore we are taking 25 L of syrup from initial solution and replacing with water.
using urinary method:
70 L syrup in 150 L solution
25 L syrup in 53.6 L solution
We started by multiplying 10
Now to get to the result we need to divide by 25 => amount of solution to be replaced with water = (53.6/25) = 2.14.
Correct option : C
Question: Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of white, and 1 morsel of milk. The pattern repeats after she leaves the morsel of milk. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
A.milk − wheat − wheat
B.wheat − wheat − white
C.white − milk − wheat
D.white − white − white
Answer: A.milk − wheat − wheat
Explanation: In a single round Lucy drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Question: A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park and rest of the park has been used as a lawn. If the area of the lawn is 2109 sq. m, then what is the width of the road?
A.3
B.4
C.5
D.7
Answer: A.3
Explanation: Area of the park = (60 x 40) m2 = 2400 m2.
Area of the lawn = 2109 m2.
Area of the crossroads = (2400 - 2109) m2 = 291 m2.
Let the width of the road be x metres. Then,
60x + 40x - x2 = 291
x2 - 100x + 291 = 0
(x - 97)(x - 3) = 0
x = 3.
A
Question: If a continuous cable 10 meters long was marked off at intervals of 1/3 meter and also 1/4 meter, and then if the cable were cut at each mark, how many different size length of cable would result?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: In this particular example length (10 meter) is just extraneous information.
The location of the marks for 1/3 meter would be 4/12, 8/12, 12/12, etc...
The location of the marks for 1/4 meter would be 3/12, 6/12, 9/12, 12/12, etc...
The distances between marks are 3/12, 1/12, and 2/12.
The answer is C.
Question: Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 1 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full?
A.2.5 hours
B.4.5 hours
C.5.5 hours
D.1 hour
Answer: C.5.5 hours
Explanation: Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 1 hours, Tank A and B can effectively fill 1⁄12 × 1 = 1⁄12 of the tank.
Time taken to fill the remaining 1−(1/12) = 11/12 of the tank = (11/12)/(1/6) = 5.5 hours. Answer : Option C
Question: The ages of Patrick and Michael are in the ratio of 3 : 5 and that of Michael and Monica are in the ratio of 3 : 5. If the sum of their ages is 149, what is the difference between the ages of Patrick and Monica?
A.27
B.64
C.45
D.72
Answer: B.64
Explanation: Ages of P and Mi=3x+5x
Ages of Mi and Mo=3x:5x
Rationalizing their ages. ratio of their ages will be 9x:15x:25x
Sum=47x=149
x=4
Difference if ages of Pa and Mo=25x-9x=16x=16*4=64
Answer B