RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: What is the smallest positive integer x such that 450x is the cube of a positive integer?
A.2
B.15
C.30
D.60
Answer: C.30
Explanation: 450 = 2 x 3^2 x 5^2 now we need two 2s, one 3 and one 5 to make it perfect cube.
So x= 2^2 x 3 x 5 = 60.
Answer is C.
Question: There are 35 students in a hostel. If the no. of students increases by 10, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
A.304.5
B.340.9
C.342.9
D.345.9
Answer: A.304.5
Explanation: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 10) = x – 1
or, 35x + 42 = 45x – 45
or, x = 8.7
Thus the original expenditure of the mess = 35 x 8.7 = Rs. 304.5
A
Question: A car mechanic purchased four old cars for Rs. 1 lakh. He spent total 2 lakh in the maintenance and repairing of these four cars. what is the average sale price of the rest three cars to get 50% total profit if he has already sold one of the four cars at Rs. 1.2 lakh?
A.1.8 lakh
B.1.1 lakh
C.1.9 lakh
D.8.1 lakh
Answer: B.1.1 lakh
Explanation: Explanation:
Total cost of 4 cars = 1+2 = 3 lakh
Total SP of 4 cars = 3 x 1.5 = 4.5 lakh
SP of 1 car = 1.2 lakh
SP of rest 3 cars = 4.5 - 1.2 = 3.3 lakh
Average SP of all the 3 cars = 1.1 lakh
Answer: B) 1.1 lakh
Question: For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
A.12%
B.26%
C.29%
D.30%
Answer: B.26%
Explanation: In the first plot 20% of 300 seeds germinated, so 0.20 x 300 = 60 seeds germinated.
In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.
Since 60 + 70 = 130 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (130/500) x 100%, or 26%.
Answer: B.
Question: A not-so-good clockmaker has four clocks on display in the window. Clock #1 loses 10 minutes every hour. Clock #2 gains 15 minutes every hour relative to Clock #1 (i.e., as Clock #1 moves from 12:00 to 1:00, Clock #2 moves from 12:00 to 1:15). Clock #3 loses 20 minutes every hour relative to Clock #2. Finally, Clock #4 gains 20 minutes every hour relative to Clock #3. If the clockmaker resets all four clocks to the correct time at 12 noon, what time will Clock #4 display after 6 actual hours (when it is actually 6:00 pm that same day)?
A.5:00
B.5:34
C.5:42
D.6:00
Answer: D.6:00
Explanation: C1 loses 15 minutes every hour. So after 60 minutes have passed, C1 displays that 60-15 = 45 minutes have passed.
C2 gains 15 minutes for every 60 minutes displayed on C1. Thus, the time displayed on C2 is 75/60 = 5/4 the time displayed on C1. So after 60 minutes have passed, C2 displays the passing of (5/4 * 45) minutes.
C3 loses 20 minutes for every 60 minutes displayed on C2. Thus, the time displayed on C3 is 40/60 = 2/3 the time displayed on C2. So after 60 minutes have passed, C3 displays the passing of (2/3 * 5/4 * 45) minutes.
C4 gains 20 minutes for every 60 minutes displayed on C3. Thus, the time displayed on C4 is 80/60 = 4/3 the time displayed on clock 3. So after 60 minutes have passed, C4 displays the passing of 4/3 * 2/3 * 5/4 * 45 = 50 minutes.
C4 loses 10 minutes every hour.
In 6 hours, C4 will lose 6*10 = 60 minutes = 1 hour.
Since the correct time after 6 hours will be 6pm, C4 will show a time of 6-1 = 6pm.
The correct answer is D.
Question: Factor 3x3 - x2y +6x2y - 2xy2 + 3xy2 - y3 =
A.(3x - 2y)(x + y)
B.(3x - y)(x + y)(x - y)
C.(3x - y)(x + y)2
D.(3x - y)(x2 + y2)
Answer: C.(3x - y)(x + y)2
Explanation: Solution:
3x3 - x2y + 6x2y - 2xy2 + 3xy2 - y3=
x2(3x - y) + 2xy(3x - y) + y2(3x-y) =
(3x - y)(x2 + 2xy + y2)=
(3x - y)(x + y)2
Answer C
Question: The maximum number of students among them 1234 pens and 874 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is:
A.91
B.2
C.1001
D.1911
Answer: B.2
Explanation: Explanation:
Required number of students = H.C.F of 1234 and 874 = 2. Answer: B
Question: The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 km. then find the speed of the faster train?
A.58 Kmph
B.68 Kmph
C.78 Kmph
D.55 Kmph
Answer: B.68 Kmph
Explanation: Length of the two trains = 600m + 400m
Speed of the first train = X
Speed of the second train= 48 Kmph
1000/X - 48 = 180
1000/x - 48 * 5/18 = 180
50 = 9X - 120
X = 68 Kmph
ANSWER:B
Question: 20 balls are numbered 1 to 20. A ball is drawn and then another ball is drawn without replacement. What is the probability that both balls have even numbers?
A.7/30
B.3/14
C.9/38
D.4/21
Answer: C.9/38
Explanation: P(1st ball is even) = 10/20
P(2nd ball is also even) = 9/19
P(both balls are even) = 10/20 * 9/19 = 9/38
The answer is C.
Question: A man can row downstream at the rate of 10 Km/hr and upstream at 4 Km/hr. Find man's rate in still water and the rate of current?
A.9,6
B.7,3
C.9,3
D.6,6
Answer: B.7,3
Explanation: Explanation:
Rate of still water = 1/2 (10 + 4) = 7 Km/hr
Rate of current = 1/2 (10-4) = 3 Km/hr
Answer: Option B
Question: What is the next number of the following sequence
10,8,18,16,34,32,....
A.44
B.66
C.55
D.77
Answer: B.66
Explanation: 10
10-2=8
8+10=18
18-2=16
16+18=34
34-2=32
32+34=66
answer will be 66
ANSWER:B
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
A.320$
B.380$
C.420$
D.450$
Answer: D.450$
Explanation: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 55 ) = 21 + 429 => 450
Hence answer will be (D) 450
Question: Two cyclist start on a circular track from a given point but in opposite direction with speeds of 7m/s and 8m/s. If the circumference of the circle is 360meters, after what time will they meet at the starting point?
A.20sec
B.15sec
C.30sec
D.24sec
Answer: D.24sec
Explanation: They meet every 360/7+8 = 24sec
Answer is D
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A.12
B.9
C.8
D.6
Answer: A.12
Explanation: A's 1 hour's work = 1 ;
4
(B + C)'s 1 hour's work = 1 ;
3
(A + C)'s 1 hour's work = 1 .
2
(A + B + C)'s 1 hour's work = ( 1 + 1 ) = 7 .
4 3 12
B's 1 hour's work = ( 7 - 1 ) = 1 .
12 2 12
Therefore A alone will take 12 hours to do the work.
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 120 km downstream?
A.60/18
B.30/29
C.60/12
D.60/13
Answer: D.60/13
Explanation: Speed downstream = 20 + 6 = 26 kmph.
Time required to cover 60 km downstream = d/s = 120/26
= 60/13 hours.
Answer:D
Question: Given that 268x74= 19432, find the value of 2.68x.74.
A.1.9432
B.1.0025
C.1.5693
D.1.0266
Answer: A.1.9432
Explanation: Solution
Sum of decimals places	=(2+2)
= 4.
Therefore,	= 2.68×.74
= 1.9432
Answer A
Question: There is a truck driver starts from one place to pick another person at
another place. The driver goes to that place by 6 AM and then picking him
he returns back.one day the other person woke a bit early and started
walking towards the first place.one the way he meets truck driver and joins
him and both went back to the first place. This day the other person came
20 min early to the time he usually comes to the first place?Tell the time
when the driver met the second person that day?
A.5.10 AM
B.5.20 AM
C.5.40 AM
D.5.50 AM
Answer: D.5.50 AM
Explanation: Given that the first person reaches the first place by 6.00 AM
But,one day the second person reached the place 20 min early.
and met the first person on the way ad reached the stop at 6.00 AM.
Therfore,They would have met at 5.50 AM.
ANSWER:D
Question: The length of a rectangular plot is thrice its width. If the area of the rectangular plot is 675 sq meters, then what is the width (in meters) of the rectangular plot?
A.12
B.15
C.18
D.21
Answer: B.15
Explanation: Area = L*W = 3W^2 = 675
W^2 = 225
W = 15
The answer is B.
Question: List K consists of 14 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K?
A.5
B.6
C.7
D.8
Answer: D.8
Explanation: Answer = D = 8
If least = -4, then largest = 9
Range = 9 - 1 = 8
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
A.18
B.99
C.77
D.66
Answer: A.18
Explanation: 1500 ---- 270
100 ---- ? => 18%
Answer: A
Question: A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $120,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $150,000 in the first year, an increase in annual salary of 10% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
A.$3,500
B.$5,000
C.$2,500
D.$9,700
Answer: D.$9,700
Explanation: Team K's contract = $120,000 + $120,000*1.2 + $120,000*1.2*1.2 + $50,000 = $486,800
Team L's contract = $150,000 + $150,000*1.1 + $150,000*1.1*1.1 = $496,500
The difference = $9,700.
Answer: D.
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
A.62.5
B.62.3
C.62.7
D.62.2
Answer: A.62.5
Explanation: CP = 47.50
SP = 47.50*(125/100)
= 59.375
MP*(95/100)
= 59.375
MP = 62.5
Answer:A
Question: If each side of a square is increased by 6%, find the percentage change in its area?
A.10.68%
B.8.72%
C.9.28%
D.12.36%
Answer: D.12.36%
Explanation: let each side of the square be a , then area = a x a
New side = 106a / 100 = 53a /50
New area =(53a x 53a) / (50 x 50) = (2809a²/2500)
increased area== (2809a²/2500) - a²
Increase %= [(309a²/2500 ) x (1/a² ) x 100]% = 12.36%
answer :D
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 7 runs. His new average is:
A.38 runs
B.37 runs
C.39 runs
D.40 runs
Answer: A.38 runs
Explanation: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 7
= 11x + 77 = 10x + 108
= x = 31.
New average = (x + 7) = 38 runs.
Answer:A
Question: Two men starting from the same place walk at the rate of 5 kmph and 5.5 kmph respectively. What time will they take to be 8.0 km apart, if they walk in the same direction?
A.12 hrs
B.14 hrs
C.15 hrs
D.16 hrs
Answer: D.16 hrs
Explanation: Sol.
to be 0.5 km apart, they take 1 hour.
To be 8.0 km apart, they take [1/0.5 * 8.0] hrs = 16 hrs.
Answer D
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
A.388
B.150
C.288
D.269
Answer: B.150
Explanation: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer:B
Question: Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 9x +3 = 0?
A.28.3
B.1.45
C.2.78
D.6.84
Answer: A.28.3
Explanation: a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab]/ab
a + b = -9/1 = -9
ab = 3/1 = 3
Hence a/b + b/a = [(-9)2 - 2(3)]/3 = 56/4 = 28.3.
A)
Question: If Rahul rows 15 km upstream in 3 hours and 21 km downstream in 3 hours, then the speed of the stream is
A.5 km/hr
B.4 km/hr
C.2 km/hr
D.1 km/hr
Answer: D.1 km/hr
Explanation: Explanation:
Rate upstream = (15/3) kmph
Rate downstream (21/3) kmph = 7 kmph.
Speed of stream (1/2)(7 - 5)kmph = 1 kmph
Option D
Question: How many factors of 2475 are odd numbers greater than 1?
A.3
B.4
C.17
D.6
Answer: C.17
Explanation: prime factors of 330 are 2^1,3^2,5^2 and 11^1
total divisors = (power if a prime factor+1)
total no. of odd factors(3,5,11) = (2+1)(2+1)(1+1) =18
since we need odd divisors other than 1 =>18-1 = 17 odd divisors
C is the answer
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
A.11
B.190
C.188
D.177
Answer: B.190
Explanation: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec ,Answer:B
Question: By selling 100 pencil, a trader gains the cost of 20 Pencil. Find his gain percentage?
A.26 1/3%
B.51 1/3%
C.20%
D.53 1/3%
Answer: C.20%
Explanation: C
20%
Let the CP of each pencil be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 20 pencil = Rs. 20
Profit% = 20/100 * 100 = 20%
Question: If the personal income tax rate is lowered from 45% to 30%, what is the differential savings for a tax payer having an annual income before tax to the tune of $48000?
A.$3500
B.$5000
C.$3150
D.$7200
Answer: D.$7200
Explanation: Saving = (45-30)% of 48000 = 7200.
Answer:D
Question: When p is divided by W, the remainder is 4. All of the following are possible values of W, except for which of the following?
A.13
B.31
C.49
D.57
Answer: D.57
Explanation: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....
by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be W expressed in the form of 9x+4
In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition
Correct Answer - D
Question: There arr 4 prime numbers in ascending order. The multiplication of 1st 3 is 385 and that of last 3is 1001. what is the last number is
A.8
B.10
C.12
D.13
Answer: D.13
Explanation: Explanation:
abcbcd=3851001=>ad=513
abcbcd=3851001=>ad=513
So d = 13
D
Question: If n is an integer, then the least possible value of |33 - 5n| is?
A.0
B.1
C.2
D.3
Answer: C.2
Explanation: |33 - 5n| represents the distance between 33 and 5n on the number line. Now, the distance will be minimized when 5n, which is multiple of 5, is closest to 33. Multiple of 5 which is closest to 33 is 35 (for n = 7), so the least distance is 2: |33 - 35| = 2.
Answer: C.
Question: An error 2% in excess is made while measuring the side ofa square. The % of error in the calculated area of the square is?
A.4.14%
B.4.04%
C.4.23%
D.4.67%
Answer: B.4.04%
Explanation: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404 x 100 % = 4.04%
100 x 100
B
Question: A single discount equivalent to the discount series of 25%, 20% and 15% is?
A.31.8
B.31.1
C.31.6
D.49
Answer: D.49
Explanation: Explanation:
100*(75/100)*(80/100)*(85/100) = 51
100 - 51 = 49
Answer: D
Question: In a certain archery competition, points were awarded as follows: the first place winner receives 11 points, the second place winner receives 7 points, the third place winner receives 5 points and the fourth place winner receives 2 points. No other points are awarded. John participated several times in the competition and finished first, second, third, or fourth each time. The product of all the points he received was 15400. How many times did he participate in the competition?
A.5
B.6
C.7
D.8
Answer: C.7
Explanation: 15400 = 2*2*2*5*5*7*11
John participated 7 times.
The answer is C.
Question: The mass of the sun is approximately 4 × 10^30 kg and the mass of the moon is approximately 8 × 10^12 kg. The mass of the sun is approximately how many times the mass of the moon?
A.4.0 × 10^(−18)
B.2.5 × 10^17
C.5 × 10^17
D.2.5 × 10^19
Answer: C.5 × 10^17
Explanation: Mass of sun = x * Mass of moon
x = Mass of sun / Mass of moon = (4 × 10^30) / (8 × 10^12) = 2^2*2^-3*10^18 = 10^18/2= 5*10^17
Ans. C) 2.5 × 10^17
Question: One train is traveling 45 kmph and other is at 10 meters a second. Ratio of the speed of the two trains is?
A.5:4
B.9:4
C.5:6
D.5:0
Answer: A.5:4
Explanation: Explanation:
45 * 5/18 = 10
25:20 => 5:4
Answer: Option A
Question: The scoring system in a certain football competition goes as follows: 3 points for victory, 1 point for a draw, and 0 points for defeat. Each team plays 20 matches. If a team scored 14 points after 5 games, what is the least number of the remaining matches it has to win to reach the 40-point mark by the end of the tournament?
A.6
B.7
C.8
D.9
Answer: A.6
Explanation: To get 40 points as end of season we need another 26 points or more from remaining 15 matches:
Option A= 6*3+9*1=27
hence option A-6
Question: y = x^2 + bx +64 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?
A.-65
B.-64
C.-32
D.32
Answer: B.-64
Explanation: As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form ofax^2+bx+c=0,
The product of the roots =c/a= 64/1=256 and the sum of the roots =-b/a=-b
64 can be expressed as product of two numbers in the following ways:
1 * 64
2 * 32
4 * 16
The sum of the roots is maximum when the roots are 1 and 64 and the maximum sum is 1 + 64 = 65.
The least value possible for b is therefore -65.
B
Question: In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
A.32 hrs
B.8 hrs
C.2 hrs
D.6 hrs
Answer: C.2 hrs
Explanation: Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs = 4 * 1/2 = 2 hrs.
Answer: C
Question: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 60 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?
A.18/79
B.1/6
C.1/300
D.1/50
Answer: C.1/300
Explanation: So there are 900 cars that they have to search.. Each takes 60mins, total of 54000 mins.. Have to find in 180 mins.. Prob180/54000 = 1/300 (ANSWER C)
Question: Shekar scored 76, 65, 82, 67 and 95 marks in Mathematics, Science, Social studies, English and Biology respectively. What are his average marks?
A.65
B.77
C.75
D.85
Answer: B.77
Explanation: Explanation :
Average= (76+65+82+67+95)/5 = 385/5 =77
Hence average=77
Answer : B
Question: In a house, there are dogs, cats and parrot in the ratio 3:7:5. If the number of cats was more than the number of dogs by a multiple of both 9 and 7. What is the minimum number of pets in the house?
A.945
B.630
C.252
D.238
Answer: A.945
Explanation: Explanation :
Let, the number of Dogs, Cat and Parrots be 3k, 7k and 5k respectively.
Then, According to the question,
=>7k−3k=63p. (where p is any positive integer).
As the number is a multiple of both 9 and 7, it has to be multiple of 63.
=>k=63p/4.
Minimum value of p for which k is a natural number is 4.
Thus, k=63.
Hence, the number of pets are (63x5) + (63x3) + (63x7) i.e 315 +189+ 441= 945.
Answer : A
Question: A certain bakery has 6 employees. It pays annual salaries of $14,000 to each of 2 employees, $16,000 to 1 employee, and $17,000 to each of the remaining 3 employees. The average (arithmetic mean) annual salary of these employees is closest to which of the following?
A.$15,200
B.$15,500
C.$15,800
D.$16,000
Answer: C.$15,800
Explanation: Let the salary for each person be 14. Thus, the bakery ends up getting 2 + 3*3 = 11 as extra. This again has to be divided among 6 people. 12/6 = 2 which makes it 14+2 =16. Thus, as it is 11/6, it will be somewhere close to 16 and less than that. Also, 1/6 = 0.166. Thus 10/6 = 1.66 which gives the final salary after redistribution as 15.66. Correct answer is C.
_________________
Question: One water pump can fill half of a certain empty tank in 4 hours. Another pump can fill half of the same tank in 4.5 hours. Working together, how long will it take these two pumps to fill the entire tank?
A.1 7/13
B.4 5/8
C.3 1/4
D.4 4/17
Answer: D.4 4/17
Explanation: One pump can fill a tank in 4 hours and another in 4.5 hours
so the rate at which both can half fill the tank is (1/4+1/4.5) => 17/36
Thus half of the tank can be filled in 36/17
so for filling the complete tank => 36/17*2 = 72/17 =4 4/17
ANSWER:D
Question: Two numbers are less than third number by 35% and 37% respectively. How much percent is the second number less than by the first
A.8%
B.10%
C.33%
D.41%
Answer: C.33%
Explanation: Let the third number is x.
then first number = (100-35)% of x
= 65% of x =65x/100
Second number is (63x/100)
Difference =65x/100 - 63x/100 = x/50
So required percentage is, difference is what percent of first number
(x/50 * 100/65x * 100 )% = 33% ANSWER :C
Question: Which of the following is closest to the difference between sum of all proper fractions (fractions less than 1) in the form 1/x , where x is a positive digit, and the product of all proper fractions in the form y/(y+1), where y is a positive digit?
A.2.82
B.2.72
C.1.82
D.1.72
Answer: D.1.72
Explanation: First term = 1/2 +1/3 +1/4 +1/5 +1/6 +1/7 +1/8 + 1/9
Second term = 1/2 * 2/3 * 3/4 * 4/5 * 5/6 * 6/7 * 7/8 * 8/9 * 9/10 = 1/10
First term - Second term = 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 +1/8 + 1/9 - 1/10
Now rearrange the above equation for simplification:
= (1/2 + 1/5 - 1/10) +( 1/3 + 1/6 + 1/9) + (1/4 + +1/8) +1/7
= 6/10 + 11/18 + 3/8 +1/7
6/10 , 11/18, 3/8 are approximately equal to 0.5
=0.5+0.5+0.5+0.14 = 1.64
The closest answer choice is D
Question: What annual instalment will discharge a debt of Rs 1092 due in 3 years at 12% simple interest?
A.Rs.325
B.Rs.545
C.Rs.560
D.Rs.550
Answer: A.Rs.325
Explanation: Explanation:
Let each instalment be Rs.x .
Then, [x + (x × 12 × 1)/100] + [ x + (x × 12 × 2)/100] + x =1092
( 28x/25 ) + ( 31x/25 ) + x = 1092
(28x + 31x + 25x) = (1092 * 25)
x = (1092 × 25)/84= 325
∴ Each instalment = Rs. 325
Answer: A
Question: If (64)2 - (36)2 = 20 x a, then a = ?
A.70
B.120
C.180
D.140
Answer: D.140
Explanation: 20 x a = (64 + 36)(64 - 36) = 100 x 28
a = (100 x 28)/20 = 140
ANSWER:D
Question: The length of a rope, to which a cow is tied, is increased from 19 m to 30 m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. Use π = \\frac{22}{7}\\) in your calculations.
A.1696 sq m
B.1694 sq m
C.1594 sq m
D.1756 sq.m
Answer: B.1694 sq m
Explanation: Explanatory Answer
The cow can graze the area covered by the circle of radius 19m initially, as the length of the rope is 19m.
Area of a circle = π * (radius)2
Therefore, the initial area that the cow can graze = 22/7 * 19(2) sq m.
When the length of the rope is increased to 30m, grazing area becomes = 22/7 * 30(2) sq m.
The additional area it could graze when length is increased from 19m to 30m
= 22/7 * (30square - 19square) sq m.
22/7 * (30 + 19)(30 - 19) = 22/7 * 49 * 11 = 1694 sq m.
Choice B
Question: A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 20 per kg, then his gain percent is
A.7%
B.13%
C.14%
D.15%
Answer: A.7%
Explanation: Explanation:
Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 20) = Rs. 160.
Profit = 160 - 150 = 10
So, Profit % = (10/150) * 100 = 7%
Option A
Question: If a man can cover 24 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
A.118 km
B.162 km
C.324 km
D.1887 km
Answer: C.324 km
Explanation: 24 m/s = 24 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 24 * 18/5 * 15/4 km = 324 km.
Answer: C