RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
A.15 cents
B.10 cents
C.5 cents
D.2 cents
Answer: C.5 cents
Explanation: But the mistake there is that when you actually do the math, the difference between $1 and 10 cents is 90 cents, not $1. If you take a moment to actually do the math, the only way for the bat to be a dollar more than the ball AND the total cost to equal $1.10 is for the baseball bat to cost $1.05 and the ball to cost 5 cents.
Option C is correct.
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance travelled by him is:
A.50 km
B.56 km
C.70 km
D.80 km
Answer: A.50 km
Explanation: Let the actual distance travelled be x km.
Then,x/10	= (x + 20)/14
14x = 10x + 200
4x = 200
x = 50 km.
Answer:A
Question: 50 is what percent of 125?
A.35%
B.40%
C.45%
D.50%
Answer: B.40%
Explanation: 50/125×100=50% ANSWER : B
Question: A dog takes 10 leaps for every 2 leaps of a hare. If one leap of the dog is equal to 2 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
A.5:1
B.10:1
C.15:1
D.20:1
Answer: B.10:1
Explanation: Explanation:
Dog : Hare = (10*2) leaps of hare : 2 leaps of hare = 20 : 2.
Answer: B) 10:1
Question: A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%
A.4 kg
B.5 kg
C.8 kg
D.30 kg
Answer: A.4 kg
Explanation: Exp. Water in the given mixture = 10*20/100 =2 kg,
And spirit = (20-2) = 18 kg
Let x kg of water added, Then, x+2/20+x *100 ==25
4x+8 =20+x, or x =4 kg
Answer:A
Question: A cistern has three pipes, A, B and C. The pipes A and B can fill it in 4 and 5 hours respectively and C can empty it in 2 hours. If the pipes are opened in order at 1, 2 and 3 A.M. When will the cistern be empty?
A.3
B.9
C.7
D.5
Answer: D.5
Explanation: 1 to 2 = 1/4
2 to 3 = 1/4 + 1/5 = 9/20
After 3 AM = 1/4 + 1/5 - 1/2 = -1/20
1/4 + 9/20 = 14/20
1 h ---- 1/20
? ----- 14/20
14 hours ==> 5 PM
Answer:D
Question: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers u did Carl drive each way?
A. 350
B. 345
C. 320
D. 280
Answer: D. 280
Explanation: Let us backsolve here.
The answer option has to be divisible by 7 to give us 1/2.
Let us try u=280 km. Time taken will be 3.5 hours and 4 hours.
Hence D is the answer.
Question: Income and expenditure of a person are in the ratio 7 : 6. If the income of the person is Rs. 21000, then find his savings?
A.Rs.3600
B.Rs.3603
C.Rs.3639
D.Rs.3000
Answer: D.Rs.3000
Explanation: Let the income and the expenditure of the person be Rs. 7x and Rs. 6x respectively.
Income, 7x = 21000 => x = 3000
Savings = Income - expenditure = 7x - 6x = x
So, savings = Rs.3000
Answer:D
Question: How many terminating zeroes E does 200! have?
A. 40
B. 48
C. 49
D. 55
Answer: C. 49
Explanation: You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C
Question: At a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 57 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages?
A.7
B.9
C.12
D.15
Answer: D.15
Explanation: 150=57+90+65-32-2x
x=15
D. 15
Question: If the average (arithmetic mean) of three consecutive integers is k + 1, then the product of the greatest and least integer is
A.k2 - 9
B.k^2 + 2k
C.k2 + 4k - 5
D.k2 + 6k + 9
Answer: B.k^2 + 2k
Explanation: n = smallest number
n+2 = largest number
(n + n + 2)/2 = k+1
=> (2n+2)/2 = k+ 1
=> n + 1 = k + 1
=> n = k
So Product of n and n+2 = (k)(k+2)
=k^2 + 2k
Answer - B
Question: A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is?
A.210
B.150
C.160
D.170
Answer: A.210
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 + 140)/25 = x/15 => x = 210 m.
Answer: Option A
Question: If x^y denotes x raised to the power y, Find last two digits of (1141^3843) + (1961^4181)
A.22
B.37
C.29
D.82
Answer: D.82
Explanation: Remember 1 raised to any power will give 1 as unit digit.
To find the digit in the 10th place, we have to multiply, 10th digit in the base x unit digit in the power.
So the Last two digits of the given expression = 21 + 61 = 82
Answer:D
Question: When Jack picks olives for two hours at three times his regular speed, he picks 10 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 70% 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: C.Jack picks 10 pounds more than Mac
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 picks10 pounds more olives than Mac.
C
Question: Find the least number must be subtracted from 165826 so that remaining no.is divisible by 4?
A.1
B.2
C.3
D.4
Answer: B.2
Explanation: On dividing 165826 by 4 we get the remainder 2, so 2 should be subtracted
B
Question: 3-3*8+2=
A.A)2
B.B)-13
C.C)-19
D.D)-17
Answer: C.C)-19
Explanation: 3-3*6+2 = 5-24 = -19...
so the answer is -19... C
Question: At 30 minutes past 6 o'clock, what is the angle between the two hands?
A.15
B.30
C.45
D.60
Answer: A.15
Explanation: The hour hand moves 360 degrees in 12 hours.
The hour hand moves 30 degrees in 1 hour and 15 degrees in 30 minutes.
The minute hand moves 360 degrees in 60 minutes and 180 degrees in 30 minutes.
At 30 minutes past 6, the hour hand has moved 195 degrees.
At 30 minutes past 6, the hour hand has moved 180 degrees.
The angle between the two hands is 15 degrees.
The answer is A.
Question: The number of students in a classroom are a multiple of both 5 and 15.what is the possible total number of students?
A.90
B.70
C.50
D.63
Answer: A.90
Explanation: the number of students in a classroom are a multiple of both 5 and 15,so it must be divisible by 5 and 15
63--ruled out [not divisible by 5 & 15]
70,50&95 are all divisible by 5 but not by 15--wrong
90 is divisible by both 5 and 15 [ 90/5=18 and 90/15=6]
answer : (A)
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
A.17/20
B.1/5
C.19/25
D.1/7
Answer: A.17/20
Explanation: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(Eá´œP) = 10/20 + 8/20 - 1/20 = 17/20
ANSWER A
Question: There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 11,000 after 3 years at the same rate?
A.3641
B.2572
C.4542
D.2343
Answer: A.3641
Explanation: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = Rs. 11000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 11000 x 1 +	10 3	- 1
100
= Rs. 11000 x	331
1000
= 3641.
A
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 3 cups of tea. Last week Mo drank a total of 20 cups of tea and hot chocolate together. If during that week Mo drank 10 more tea cups than hot chocolate cups, then how many rainy days were there last week?
A.2
B.3
C.4
D.5
Answer: A.2
Explanation: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 20 T-C=10 -> T= 15. C=5.
Mo drinks 3 cups of tea a day then number of days that are not rainy = 15/3 = 5
So number of rainy days = 7-5 = 2
A is the answer.
Question: Shobha's Mathematics Test had 75 problems i.e. 10 arithmetic, 30 algebra and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra and 60% 0f the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more questions she would have needed to answer correctly to earn a 60% passing grade?
A.5
B.10
C.15
D.20
Answer: A.5
Explanation: Solution
Number of questions attempted correctly
= (70% of 10 + 40% of 30 + 60% of 35)
= (7 + 12 + 21)
= 40.
Questions to be answered correctly for 60% grade = 60% of 75 = 45.
Required no of questions = (45 - 40) = 5.
Answer A
Question: A train moves past a post and a platform 264 metre long in 8 seconds and 20 seconds respectively. What is the speed of the train
A.79.2 km/hr
B.69 km/hr
C.74 km/hr
D.61 km/hr
Answer: A.79.2 km/hr
Explanation: let length and speed x
train crosses the post in 8 sec
x=8v=train crosses the platform in 20 sec => x+264=20v
v=264/12 = 22m/s
22* 18/5 = km/hr = 79.2 km/hr
ANSWER A
Question: Six machines at a certain factory operate at the same constant rate. If five of these machines, operating simultaneously, take 36 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?
A.6
B.8
C.10
D.12
Answer: A.6
Explanation: The total work is 5*36 = 180 machine hours
The time required for six machines is 180/6 = 30 hours, thus 6 fewer hours.
The answer is A.
Question: A thief steals at a car at 2.30 p.m. and drives it at 50 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
A.6 p.m
B.9 p.m
C.4 p.m
D.2 p.m
Answer: C.4 p.m
Explanation: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
50x = 75(x - 1/2) => x =3/2 hrs.
So, the thief is overtaken at 4 p.m.'
Answer: C
Question: 120 students represent x percent of the boys at a school. If the boys at the school make up 30% of the total school population of x students, what is x?
A.120
B.150
C.180
D.200
Answer: D.200
Explanation: Let B be the number of boys in the school.
120 = xB/100
B = 0.3x
12000=0.3x^2
x^2 = 40000
x = 200
The answer is D.
Question: 20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam?
A.2.
B.4.
C.5.
D.6
Answer: D.6
Explanation: Total Work = 20*3= 60 Beaver hours
12 Beaver * x =60 Beaver hours
x=60/12=5
ANSWER:D
Question: In a class of boys and girls Vikas's rank is 9th and Tanvi's rank is 17th . Vikas's rank among the boys in that class is 4th from the top and 18th from the bottom and Tanvi's rank among the girls is 8th from top and 21st from bottom. In the order of rank, how many girls are there between Tanvi and Vikas?
A.29
B.8
C.2
D.4
Answer: C.2
Explanation: Explanation:
Vikas's rank in the class is 9. So there are 8 people before him. His rank among boys is 4. So 3 boys are before him. So there are 8 – 3 = 5 girls before him.
Tanvi's rank among the girls is 8. So there are 7 girls before her. So number of girls between Vikas and Tanvi is 7 – 5 = 2
Answer: C
Question: If x3−6x2+11x−6=0x3−6x2+11x−6=0 and x3+3x2−6x−8=0x3+3x2−6x−8=0 have one common root between them. What is the value of that root?
A.3
B.2
C.6
D.9
Answer: B.2
Explanation: There are two equations,
x3−6x2+11x−6=0x3−6x2+11x−6=0 - - - (i)
x3+3x2−6x−8=0x3+3x2−6x−8=0 - - - (ii)
So both (i) and (ii) have one root in common and we know that at the root the value of both the equations is 0. Suppose that common root is x then,
x3−6x2+11x−6x3−6x2+11x−6 = x3+3x2−6x−8x3+3x2−6x−8 ⇒⇒ 9x2−17x−2=09x2−17x−2=0
⇒⇒ (x - 2)(9x + 1) = 0 or x = 2 or -1/9. As by applying the Descartes rule in (i) we can see it cannot have any negative root so x = 2.
Why are we getting two values x = 2 and x = -1/9?
x = 2 and x = -1/9 are the pint of intersections of these two equations out of which x = 2 is the point of intersection at x axis therefore this point (x = 2) is the common root as well.
Answer:B
Question: Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
A.35years
B.20years
C.25years
D.30years
Answer: A.35years
Explanation: Let the present ages of X and Y is 5x and 6x
5x+7 / 6x+7 = 6/7
x = 7
X's present age = 5*7 = 35 years
Answer is A
Question: A man buy a book in Rs50 & sale it Rs80. What is the rate of profit ???
A.10%
B.60%
C.30%
D.25%
Answer: B.60%
Explanation: cp=50
sp=80
profit=80-50=30
%=30/50*100=60%
ANSWER:B
Question: A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C
together need 3 hours to finish the same work. In how many hours B can complete the work ?
A.10 hours
B.12 hours
C.16 hours
D.18 hours
Answer: B.12 hours
Explanation: ExplanaƟon:
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12
Work done by B in 1 hour = (7/12)�(1/2) = 1/12
=> B alone can complete the work in 12 hour
Answer: B
Question: What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
A.2300
B.2400
C.3000
D.3500
Answer: C.3000
Explanation: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C
Question: The radius of a wheel is 22.6 cm. What is the distance covered by the wheel in making 750 resolutions?
A.754 m
B.704 m
C.1055.04 m
D.1058.04 m
Answer: C.1055.04 m
Explanation: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 750 resolutions.
= 750 * 2 * 22/7 * 22.6 = 105504 cm
= 1055.04 m
Answer:C
Question: How many times are the hands of a clock at right angle in a week?
A.803
B.830
C.380
D.308
Answer: D.308
Explanation: In 1 day, they are at right angles 44 times.
In a week, they are at right angles 308 times. Answer: Option D
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
A.88 sec
B.89 sec
C.17 sec
D.288 sec
Answer: B.89 sec
Explanation: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec
Answer:B
Question: Machine Z and machine B are each used to manufacture 660 sprockets. It takes machine Z 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine Z. How many sprockets per hour does machine Z produces?
A.6
B.6.6
C.60
D.100
Answer: A.6
Explanation: I think the correct answer is A.
Machine Z produces at a speed of Z sp/hour and B at a speed of B sp/hour.
so, 660/Z=(660/B)+10 and B=1,1 Z--->1,1*660=660+11Z---A=6, so answer A is correct
Question: If an object travels at four feet per second, how many feet does it travel in one hour?
A.30
B.300
C.720
D.14400
Answer: D.14400
Explanation: Speed = 4 feet per second.
1 Hour= 60X60 Seconds = 3600 Seconds.
Total no of feet traveled in 1 hour = 3600X4 = 1800X10 = 14400
Answer D
Question: A table is bought for Rs.400/- and sold at Rs.250/- find gain or loss percentage
A.5%loss
B.10%gain
C.20%gain
D.37.5%loss
Answer: D.37.5%loss
Explanation: Formula = (Selling price ~ Cost price)/Cost price * 100
= (250 - 400)/400 = 37.5% loss
D
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.051. What is the value of x?
A.0.02
B.0.01
C.0.025
D.0.03
Answer: C.0.025
Explanation: Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.06*35 and brand C=0.08*25
Total number of widgets=40+35+25=100
the probability that the widget selected is defective is 0.051=(x*40+0.06*35+0.08*25)/100
=> 40x+2.1+2=5.1
=>40x=1
>x=1/40=0.025
Ans C
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:C will be?
A.1 : 2
B.3 : 5
C.5 : 7
D.6 : 11
Answer: B.3 : 5
Explanation: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : C = 3 : 5
B
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
A.33
B.28
C.77
D.10
Answer: D.10
Explanation: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer: D
Question: A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
A. 20 %
B. 40 %
C. 35 %
D. 32 %
Answer: A. 20 %
Explanation: Assume the revenue in 2000 to be 100. Then in 2003 it would be 150 and and in 2005 180, so from 2003 to 2005 it increased by (180-150)/150=30/150=~20%.
Answer: A
Question: A, B and C started a shop by investing Rs. 4,000, Rs. 12,000 and Rs. 8,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 1,000, then the total profit was :
A.3,000
B.60,000
C.80,000
D.120,000
Answer: A.3,000
Explanation: Sol.
A : B : C = 4000 : 12000 : 8000 = 1: 3 : 2. so, Câ€™s share : Total Profit = 2 : 6
Let the total profit be Rs. x. Then, 2/6 = 1000/x or x
= 1000 * 6/ 2 = 3000.
Answer A
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
A.288
B.267
C.108
D.285
Answer: D.285
Explanation: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285.
Answer: D
Question: If x and y are numbers such that (x+3)(y-3)=0, what is the smallest possible value of x^2 + y^2
A.0
B.3
C.6
D.9
Answer: D.9
Explanation: From (x+3)(y-3)=0 it follows that either x=-3 or y=3. Thus either x^2=9 or y^2=9.
Now, if x^2=9, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 9 + 0 = 9.
Similarly if y^2=9, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 9 = 9.
Answer: D.
Question: The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is?
A.2379
B.2889
C.9288
D.9000
Answer: D.9000
Explanation: Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.
Cost of cheapest item = 3x = Rs. 9000.
Answer: D
Question: Audrey has a bag of apples that weighs 200g. If she uses 62g of apples from the bag to make pies, what percent of her bag did she use?
A.50%
B.29%
C.36%
D.31%
Answer: D.31%
Explanation: Explanation :
Original weight of the bag: 200
Required percentage = (62/200) Ã— 100 = 31%
Answer : Option D
Question: There are 35 students in a hostel. If the no. of students increases by 7, 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.Rs. 30
B.Rs. 34
C.Rs. 42
D.Rs. 48
Answer: C.Rs. 42
Explanation: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
Question: How many positive integers less than 247 are multiple of 4 but NOT multiples of 6?
A.20
B.41
C.42
D.53
Answer: B.41
Explanation: From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 41, as all the other choices are very far away. The numbers 244 will come and complete the list that’s (naughty or nice) under 250. Answer choice B is correct here.
Question: The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 20 runs. Find his average in all the 30 matches?
A.31
B.46
C.88
D.33.33
Answer: D.33.33
Explanation: Total score of the batsman in 20 matches = 800.
Total score of the batsman in the next 10 matches = 200.
Total score of the batsman in the 30 matches = 1000.
Average score of the batsman = 1000/30 = 33.33
Answer:D
Question: A certain theater has 100 balcony seats. For every $2 increase in the price of a balcony seat above $10, 5 fewer seats will be sold. If all the balcony seats are sold when the price of each seat is $10, which of the following could be the price of a balcony seat if the revenue from the sale of balcony seats is $1,060 ?
A.$12
B.$14
C.$10.8
D.$17
Answer: C.$10.8
Explanation: I solved it as follows:
10+2(x) = 100 -5(x)
x= 12
Equation should be (10+$2*x)(100-5x)=1,060, where x is the # of times we increased the price by $2. (10+$2*x)(100-5x)=1,060 --> (5+x)(20-x)=6 --> x=0.4 or x=14.6 --> price=10+$2*0.4=$10.8 or price=10+$2*14.6=$39.2.
Answer: C.
Question: (1/4 + 1/4 ÷ 5/4) / (1/4 x 1/4 + 2 1/4) = ?
A.16/25
B.32/185
C.36/185
D.None of these
Answer: C.36/185
Explanation: Answer
Given expression = (1/4 + 1/4 x 4/5) / (1/16 + 9/4)
= (1/4 + 1/5) / (37/16)
= 9/20 x 16/37
= 36/185
Correct Option: C
Question: In what ratio must tea at Rs.65 per Kg be mixed with tea at Rs.70 per Kg so that the mixture must be worth Rs.6 per Kg?
A.1 : 1
B.3 : 2
C.4 : 3
D.5 : 3
Answer: A.1 : 1
Explanation: Required ratio = 500 : 500 = 1 : 1
Answer A
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 18,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
A.A)7500
B.B)7389
C.C)7379
D.D)8490.57
Answer: D.D)8490.57
Explanation: A:B:C = (20000 * 24) : (18000 * 24) : (20000 * 18) = 20:18:15
B's share = 25000 * 18/53 = Rs.8490.56
Answer: D
Question: A bag contains 3 red, 2 yellow and 4 green balls. 3 balls are drawn randomly. What is the probability that the balls drawn contain balls of different colours?
A.2/7
B.3/5
C.3/11
D.1/4
Answer: A.2/7
Explanation: Total number of balls = 3+2+4 = 9
n(S) = 9C3 = 84
n(E) = 3C1 * 2C1 * 4C1 = 3*2* 4 = 24
Probability = 24/84 = 2/7
Answer is A
Question: In a 1000 m race, A beats B by 80 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
A.145 m
B.172 m
C.268 m
D.129 m
Answer: B.172 m
Explanation: By the time A covers 1000 m, B covers (1000 - 80) = 920 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/920 * 1000/900 = 1000/828 So, by the time A covers 1000 m, C covers 828 m.
So in 1000 m race A beats C by 1000 - 828 = 172 m.
Answer:B
Question: 5.02 can be expressed in terms of percentage as
A.5.02%
B.50.2%
C.209%
D.502%
Answer: D.502%
Explanation: Explanation:
While calculation in terms of percentage we need to multiply by 100, so
5.02 * 100 = 502
Answer: Option D
Question: What is the present worth of Rs. 165 due in 2 years at 5% simple interest per annum?
A.288
B.266
C.120
D.150
Answer: D.150
Explanation: Let the present worth be Rs. x. Then,
S.I. = (165 - x)
(x * 5 * 2) / 100 = (165 - x)
10x = 16500 - 100x
110x = 16500 => x = 150.
Answer: D
Question: The Sum of first N consecutive odd integers is N^2. What is the sum of all odd integers between 13 and 31 inclusive.
A.220
B.364
C.410
D.424
Answer: A.220
Explanation: We're dealing with a sequence of CONSECUTIVE ODD INTEGERS: 13 to 31, inclusive. We're asked for the SUM of this group.
1) Start with the sum of the smallest and the biggest: 13 + 31 = 44
2) Now look at the 'next smallest' and the 'next biggest': 15 + 29 = 44
Now we have proof that there is no middle term. We have 5 bunches of 44
5(44) = 220
A