RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: In a certain mathematical activity, we have five cards with five different prime numbers on them. We will distribute these five cards among three envelope: all could go in any envelope, or they could be broken up in any way among the envelopes. Then in each envelop, we find the product of all the cards in that envelope: that is the “number” of the envelope. An envelope containing no cards has the number 1. We then put the three envelope numbers in order, from lowest to highest, and that is our set. How many different Y sets can be produced by this process?
A. 41
B. 89
C. 125
D. 243
Answer: A. 41
Explanation: Case 1: 1 used envelope => 1 way
Case 2: 2 used envelopes
- 4-1-0: Choose 4 from 5 cards: 5 ways
- 3-2-0: Choose 3 from 5 cards: 10 ways
Case 3: All envelopes used
- 3-1-1: Choose 3 from 5 andno need to choose 1 from 2: 10 ways
- 2-2-1: Choose 2 from 5 and choose 2 from 3, but two groups are the same => (10X3):2 = 15
Total Y: 1+5+10+10+15=41 => Answer: A
Question: Of the 200 employees at company X, 80 are full-time, and 150 have worked at company X for at least a year. There are 20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year. How many full-time employees of company X have worked at the company for at least a year?
A.20
B.30
C.50
D.80
Answer: C.50
Explanation: 200 employees
80 are full-time
150 have worked at company X for at least a year
20 employees at company X who aren’t full-time and haven’t worked at company X for at least a year.
How many full-time employees of company X have worked at the company for at least a year?
200-80=120 employees not full time
120-20= 100 employees not full time who worked over a year
150 employees have worked at company X for at least a year-100 employees not full time who worked over a year = 50 full-time employees of company X have worked at the company for at least a year
C. 50
Question: The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 300% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?
A.4N
B.6N
C.8N
D.10N
Answer: C.8N
Explanation: In 1992, the company's assets were N.
In 1993, the company's assets were N + 3N =4N.
In 1994, the company's assets were 4N + 4N = 8N.
The answer is C.
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 5. What could be the ratio of Cats to dogs in the pet store?
A.1:3
B.20:25
C.1:5
D.2:5
Answer: B.20:25
Explanation: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.
We are told that ax - bx = 5 --> x(a - b) = 5. Since 5 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*5.
The above implies that either x = 1 and a - b = 5 or x = 5 and a - b = 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 13.
For the original question only option which fits is E, 4:5. Cats = 5*4 = 20 and dogs = 5*5 = 25.
Answer: B.
Question: A and B together have Rs. 1210. If of A's amount is equal to of B's amount, how much amount does B have?
A.484
B.460
C.550
D.664
Answer: A.484
Explanation: 4/15 A = 2/5 B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
Therefore, B's share = Rs. (1210 x 2/5)= Rs. 484.
Answer is A.
Question: When 24 is divided by the positive integer d, the remainder is 4. Which of the following statements about d must be true?
I. d is even
II. dis a multiple of 5
III. d is a factor of 20
A.III only
B.I and II only
C.I and III only
D.II and III only
Answer: D.II and III only
Explanation: 24= m*d + 4
m*d=20
put values of m
m=1 d=20
m=2 d=10
m=4 d=5
I. not true
II. true
III. true
D. correct
Question: When 40 per cent of a number is added to another number the second number increases to its 140 per cent. What is the ratio between the first and the second number?
A.3 : 4
B.4 : 3
C.1 : 1
D.Data inadequate
Answer: C.1 : 1
Explanation: Let the first and the second numbers be x and y respect then
y + 40% of x = 140% of y
or, y + 0.4x = 1.4y
or, 0.4x = 0.4y
∴ x : y = 0.4 : 0.4 = 4 : 4
Answer C
Question: In a shop, the cost of 4 shirts, 4 pairs of trousers and 2 hats is $560. The cost of 9 shirts, 9 pairs of trousers and 6 hats is $1,290. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?
A.$50
B.$320
C.$150
D.$100
Answer: C.$150
Explanation: Let x be the price of one shirt, y be the price of one pair of trousers and z be the price of one hat.
4x + 4y + 2z = 560 :
9x + 9y + 6z = 1,290
3x + 3y + 2z = 430 : divide all terms of equation C by 3
x + y = 130 : subtract equation D from equation B
3(x + y) + 2z = 430 : equation D with factored terms.
3*130 + 2z = 430
z = 20 : solve for z
x + y + z = 130 + 20 = $150
correct answer C
Question: One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
A.31
B.32
C.33
D.36
Answer: D.36
Explanation: Let the age of Sooraj and Vimal, 1 year ago, be 6x and 7x respectively.
Given that, four years hence, this ratio would become 7:8
⇒(6x+5):(7x+5)=7:8⇒8(6x+5)=7(7x+5)⇒48x+40=49x+35⇒x=5
Vimal's present age
=7x+1=7×5+1=36
Answer is D.
Question: If a and b are unique prime integers, which of the following must be odd?
A.a−b
B.2a+2b
C.2a−2b
D.2a / 2b
Answer: A.a−b
Explanation: Any number multiplied by 2 has to be an even number. hence
Answer A
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 350 m long platform?
A.44 sec
B.49 sec
C.42 sec
D.47 sec
Answer: D.47 sec
Explanation: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +350)/ 36 * 5/18 = 47 min.
ANSWER:D
Question: A man can row downstream at the rate of 18 Kmph and upstream at 6 Kmph. Find the man’s rate in still water and rate of current?
A.8.5
B.6.0
C.9.5
D.9.0
Answer: B.6.0
Explanation: Rate of still water = 1/2 (down stream + upstream)
= 1/2 (18 + 6) = 12 Kmph
rate of current = 1/2 (down stream - upstream)
= 1/2 (18 - 6)
= 1/2 (12)
= 6 kmph
Answer is B.
Question: An iron cubes of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5 the sides are
A.10 cm, 50 cm
B.20 cm, 100 cm
C.40 cm, 200 cm
D.None of these
Answer: B.20 cm, 100 cm
Explanation: Solution
Let the sides of the sheet be x and 5x.
Then,volume of the sheet= volume of the cube
‹=› x × 5x ×1/2
‹=› 10×10×10
‹=› 5x2= 2000
‹=› x2= 400
‹=› x = 20.
The sides are 20 cm and 100 cm.
Answer B
Question: Pipe A can fill a tank in 10 hr, pipe B in 20hr and pipe C in 40hr. If all the pipes are open in how many hours will tank be filled?
A.1hr
B.30min
C.15min
D.17min
Answer: D.17min
Explanation: Part filled by (A+B+C) in 1hour = 1/10 + 1/20 + 1/40 = 7/40
All the 3 pipes together will fill the tank in 17min Approximately
Answer is D
Question: Find the invalid no.from the following series 15 46 63 71 75 77 78
A.15
B.46
C.71
D.75
Answer: B.46
Explanation: In this question, if you start from the beginning, firstly the difference is 31, then the difference is 17, then the difference is 8. So there is no logic. If you start backwards,you can see that firstly, 1 is added, then 2 is added, then 4 is added, then 8,16 and 32 should have been added. So you have got the right clue. So 15 + 32 the first number should be 47 and afterwards, the series becomes + 16, + 8, + 4and so on. 46
B
Question: The function f(x) is defined for all positive integers x as the number of even factors of x and the function g(x) is defined for all positive integers x as the number of odd factors of x. For positive integers a and b if f(b)*g(a) = 0 and f(a) = 1, which of the following could be the least common multiple of a and b?
A.12
B.16
C.20
D.30
Answer: D.30
Explanation: f(b)∗g(a)=0 : any positive integer has at least one odd factor: 1. Thus, g(a) cannot be 0, which implies that f(b) = 0. This on the other hand means that b is an odd integer (odd integers does not have even factors).
f(a)=1f(a)=1: aa has 1 even factor. This means that aa must be 2 (the only positive integer which has only 1 even factor is 2).
The least common multiple of a=2a=2 and b=odd is 2∗odd. Only option D can be represented this way: 30=2∗1530=2∗15.
Answer: D
Question: The profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448. What should be the sale price for making 55% profit?
A.$480
B.$450
C.$992
D.$870
Answer: C.$992
Explanation: C
Let C.P. = $ x.
Then, 832 - x = x - 448
2x = 1280 => x = 640
Required S.P. = 155% of $ 640 = 150/100 * 640 = $ 992.
Question: In filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be?
A.100 cu.m
B.1000 cu.m
C.10000 cu.m
D.100000 cu.m
Answer: C.10000 cu.m
Explanation: 100 * 10 * 10 = 10000
ANSWER:C
Question: Three boys are ages 4, 6 and 7 respectively. Three girls are ages 5, 8 and 9, respectively. If two of the boys and two of the girls are randomly selected and the sum of the selected children's ages is r, what is the difference between the probability that r is even and the probability that r is odd?
A. 1/9
B. 1/6
C. 2/9
D. 1/4
Answer: A. 1/9
Explanation: Age of Boys r:4, 6, 7
Sum of ages taken 2 at a time: 10,13,11
Ages of Girls:5, 8, 9
Sum of ages taken 2 at a time: 13,17,14
9 Combinations of sum between sets(10,12,11)(13,17,14)
=23,27,24- 16,30,17- 24,28,25
Prob(Even)= 5/9
Prob(Odd) =4/9
Answer=5/9 - 4/9 = 1/9
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 120 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
A.3.6 sec
B.18 sec
C.36 sec
D.72 sec
Answer: C.36 sec
Explanation: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 120 = 360 m.
Time taken = 360/10 = 36 sec
ANSWER:C
Question: A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:
A.1/26
B.1/52
C.2/62
D.2/26
Answer: A.1/26
Explanation: Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E) = n(E)/n(S)
= 2/52
= 1/26
Answer should be A
Question: Today Chris ate 15 jellybeans. Bella ate 2/3 of the jellybeans Chris did, Frances ate 5 more jellybeans than Bella did , and Sandhya ate 20% more than Frances. How many jellybeans did Sandhya eat?
A.18
B.20
C.13
D.25
Answer: A.18
Explanation: A
13
Chris ate 15 jellybeans
Bella ate 2/3 of the jellybeans Chris did.
Bella= 2/3 x 15
=10
Frances ate 5 more jellybeans than Bella.
Frances= 10+5 jellybeans.
=15
Sandhya ate 20% more jellybeans than Frances.
Sandhya = 15 + 15 × 20%
= 15 + 15 × 0.20
= 15 + 3
= 18
Sandhya ate 18 jellybeans.
The correct answer is A.
Question: In a shop 40% of the articles are sold at a profit of 20% and the remaining at a loss of 10%.what is the overall profit/loss?
A.6% loss
B.4% loss
C.2% profit
D.10% loss
Answer: C.2% profit
Explanation: 40*1.2+60*0.9/100=1.02
ANSWER:C
Question: Vijay bought 160 shirts at the rate of Rs. 205 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.s.225
B.s.288
C.s.485
D.s.261
Answer: D.s.261
Explanation: Total CP per shirt = 205 + 1400/160 + 1.75 + 320/160 = Rs. 217.5
SP = CP[(100 + profit%)/100]
= 217.5 * [(100 + 20)/100] = Rs.261.
Answer:D
Question: A number is increased by 10% and then decreased by 10%, the final value of the number is ?
A.decreases by 1%
B.decreases by 2%
C.decreases by 3%
D.decreases by 4%
Answer: A.decreases by 1%
Explanation: Here, x = 10 and y = - 10
Therefore, the net % change in value
= ( x + y + xy/100)%
= [10 - 10 + (10 * -10)/100]% or - 1%
Since the sign is negative, there is a decrease in value by 1%.
ANSWER:A
Question: Mangala completes a piece of work in 9 days, Raju completes the same work in 21 days. If both of them work together, then the number of days required to complete the work is
A.6 days
B.7 days
C.8 days
D.9 days
Answer: A.6 days
Explanation: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 9 Ã— 21/30 = 6 days.
A
Question: What is the probability of getting a sum 9 from two throws of a dice?
A.1/6
B.1/8
C.1/9
D.1/12
Answer: C.1/9
Explanation: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) =n(E)/n(S)=4/36=1/9	.
Answer:C
Question: In a covering a certain distance the speed of A and B are in the ratio of 6: 9, A takes 20 min more, than B to reach the destination. The time taken by A to reach the destination is:
A.1 Hour
B.2 Hours
C.1.5 Hours
D.2.5 Hours
Answer: A.1 Hour
Explanation: Let the speed of A and B are 6x Kmph
and 9x Kmph respectively,
Let the total distance to travel = y Km
y/6x - y/9x = 1/3
y/x(1/18 = 1/3
y = 6x
Required time = 6x/6x = 1 hour
Answer A.
Question: In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day.
A. 215,000
B. 216,000
C. 217,000
D. 218,000
Answer: B. 216,000
Explanation: This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 7-2 = 5 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 5 = 216,000. Hence B.
Question: The expression (5x-2)/(x+3) is equivalent to which of the following?
A.(5-2)/3
B.5 – (2/3)
C.5 – (x)/(x+3)
D.5 – (17)/(x+3)
Answer: D.5 – (17)/(x+3)
Explanation: iven asked to find the value of (5x-2)/(x+3)...
Now take X as 1 then we get 3/4...
From the options check which one gets the same 3/4.
From option D = 5 – (17)/(x+3) => 5 - (17)/(1+3) => 3/4.. All other options will result in some other value..
Answer: D is the correct option
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
A.76
B.21
C.26
D.28
Answer: B.21
Explanation: Explanation:
Lot the total number of workers be v Then,
8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21.
Answer: B
Question: The area of a triangle is with base 4m and height 8m?
A.11
B.10
C.787
D.16
Answer: D.16
Explanation: 1/2 * 4 * 8 = 16 m2
Answer: D
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 400 revolutions. How many revolutions does the second wheel make in covering d feet?
A.400xy
B.400y - x
C.400x - y
D.400x/y
Answer: D.400x/y
Explanation: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
400 = d/(x*pi)
d = 100 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (400 * x * pi) / (y*pi) = 400x/y
Answer (D)
Question: A pupil's marks were wrongly entered as 73 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is :
A.56
B.80
C.20
D.25
Answer: A.56
Explanation: Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (73 - 45)
=> X/2 = 28
=> X = 56.
ANSWER:A
Question: Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?
A.20
B.90
C.10
D.80
Answer: D.80
Explanation: D
80
We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule)
(60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300
D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80.
Question: The cost of a one-family home was $ 120,000 in 1980. In 1988, the price had increased to $ 180,000. What was the percent increase in the cost of the home?
A.60%
B.50%
C.55%
D.40%
Answer: B.50%
Explanation: Percentage Increase = Increase in price / original price *100= (180000-120000)/120000*100=50%
Answer: B
Question: a boy average marks in five subject is 60.he score 90 in math,in physics he scores 95.in rest three in how much maximum subject he can score more than or equal to 95.
A.1
B.2
C.3
D.0
Answer: A.1
Explanation: addition of marks of all five subject=300.
math+physics=185
sum of three subject marks=300-185=115
here it is clearly visible that he can only score more than 95 in one subject if he will score more than 95 in two then it will exceed 115 because marks are not in negative.
answer A
Question: A and B entered into a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more. After 3 more months C joins the business with a capital of Rs. 21000. The share of B exceeds that of C, out of a total profit of Rs. 26400 after one year by
A.Rs. 3200
B.Rs. 3400
C.Rs. 3600
D.Rs. 3800
Answer: C.Rs. 3600
Explanation: Explanation:
A:B: C = 16000*3 + 11000*9:12000*3 + 17000*9:21000*6
= 147:189:126 = 7:9:6
Difference of B and C’s shares =
Rs. [26400 * (9/22) — 26400 * (6/22))
= Rs. 3600
Option C
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 500?
A.4
B.6
C.8
D.10
Answer: C.8
Explanation: To maximize the length of z, we should minimize its prime base. The smallest prime is 2 and since 2^8 = 256 < 500, then the greatest possible length of integer z is 8.
The answer is C.
Question: Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $6.30?
A.426
B.430
C.443
D.410
Answer: D.410
Explanation: I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 packs as we can, then as meny of 50 packs as we can and the remaining envelopes are single ones.
Having 6.3$, we can buy as many as 4 packs of 100 (4 x 1.5$ = 6$). We then have 0.3 $ left. so we buy 10 individual envelopes. If we add up the numbers, we get 400+10=410 envelopes. Answer D
Question: A taxi leaves Point A 5 hours after a bus left the same spot. The bus is traveling 20 mph slower than the taxi. Find the speed of the taxi, if it overtakes the bus in three hours.
A.34
B.32
C.36
D.38
Answer: B.32
Explanation: Let the speed of bus be v - 20, speed of taxi be v
The bus travelled a total of 8 hrs and taxi a total of 3 hrs.
Hence 8 * (v-20) = 3v
8v - 160 = 3v
5v = 160
v = 32 mph
B
Question: The average temperature from Tuesday to Friday is 48°C and from Wednesday to Saturday is 52°C. If the temperature on Tuesday is 42°C, what was it on Saturday?
A.52°C
B.55°C
C.58°C
D.51°C
Answer: C.58°C
Explanation: Temperature on Tuesday + Wednesday + Thursday + Friday = 4 x 48°C = 192°C
Temperature on Tuesday = 42°C
Thus, Wednesday + Thursday + Friday = (192°C - 42°C) = 150°C
Temperature on Wednesday + Thursday + Friday + Saturday = 4 × 52°C = 208°C
Thus, Saturday’s temperature = 208 - 150°C = 58°C
ANSWER:C
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 5.5), (8, 0), (0, -5.5), (-8, 0)?
A.56
B.88
C.112
D.116
Answer: B.88
Explanation: Ares of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 8+8= 16
Length of 2nd diagonal= 5.5+5.5= 11
Area= 1/2*16*11= 88
B is the answer
Question: When positive integer N is divided by positive integer J, the remainder is 11. If N/J = 724.04, what is value of J?
A.140
B.150
C.260
D.275
Answer: D.275
Explanation: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 724.04
Here 724 is the quotient.
Given that Remainder = 11
So, 724.04 = 724 + 11/J
So, J = 275
Question: Find the side of the largest possible square slabs which can be paved on the floor of a room 2 m 50 cm long and 1 m 50 cm broad. Also find the number of such slabs to pave the floor.
A.25, 20
B.30, 15
C.50, 15
D.None of these
Answer: C.50, 15
Explanation: Explanation:
HCF (250, 150) = 50 cm
The number slabs = 250 *150/ 50*50
=15
Answer: C
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
A.34
B.40
C.68
D.88
Answer: D.88
Explanation: Explanation:
We have: l = 20 ft and lb = 680 sq. ft.
So, b = 34 ft.
Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft.
Answer: D
Question: A farmer brought 76 cows, the price of each cow being the same and then sold 20 cows at a profit of 15%, 40 cows at a profit of 19% and the remainder at a profit of 25% making a total profit of Rs.26,280. What is the cost price of each cow?
A.Rs.1000
B.Rs.1800
C.Rs.1500
D.Rs.1400
Answer: B.Rs.1800
Explanation: Let cost price of each Cow is x.
Total Cost of 76 Cows = 76x.
SP of 20 Cows = 20x + 15% of 20x
SP of 20 Cows = 20x + 3x = 23x
SP of 40 Cows = 40x + 19% of 40x = 47.6x
SP of remaining cows (16 cows) = 16x + 25% of 16x = 20x
Total selling price of 76 cows = 23x + 47.6x + 20x = 90.6x.
Total Profit = Rs. 26280
Total SP - Total CP = Total Profit
90.6x - 76x = 26280
14.6x = 26280
x = 1800.
CP of each Cow is Rs. 1800.
ANSWER :OPTION B
Question: Bus 1 and Bus 2 run between cities A and B. Bus 1 leaves city A at the same time Bus 2 leaves city B,
each at a constant rate of speed. Their first meeting is 60 miles from city A. After reaching their
respective destinations and immediately turning around, their second meeting is 30 miles from city B.
What is the distance in miles between city A and city B?
A.90
B.120
C.125
D.150
Answer: D.150
Explanation: let d=distance between cities A and B
bus 1 distance to first meeting=60 miles
bus 1 distance from first to second meeting=(d-60)+30=d-30 miles
bus 2 distance to first meeting=d-60 miles
bus 2 distance from first to second meeting=60+(d-30)=d+30 miles
because both buses take the same time for the pre-meeting leg, and
the same time for the inter-meeting leg, and their speeds remain
constant, their ratios between pre-meeting distance and inter-meeting
distance should be the same
therefore, 60/(d-30)=(d-60)/(d+30)
d^2=150d
d=150 miles
D
Question: If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is?
A.87
B.40
C.37
D.28
Answer: B.40
Explanation: A.M. of 75 numbers = 35
Sum of 75 numbers = 75 * 35 = 2625
Total increase = 75 * 5 = 375
Increased sum = 2625 + 375 = 3000
Increased average = 3000/75 = 40.
Answer:B
Question: A shop produces sarongs. The daily average production is given by 5n + 20, where n is the number of workers aside from the owner. In the first k days, 500 units are produced, and then 5 workers are added to the team. After another k days, the cumulative total is 1300. How many workers were part of the latter production run?
A.A)6
B.B)10
C.C)9
D.D)15
Answer: C.C)9
Explanation: The daily average production is given by 5n + 20- given
In the first k days, 500 units are produced
= (5n+20)K =500
k = 500/5n+20...................................1
5 workers were added = 5(n+5)+20 = 5n +45
cumulative is 1300 .. thus for the current period = 1300 -500 = 800
(5n+45)K= 800
k = 800/5n+45........................................2
equate 1 and 2
500/5n+20 = 800 /5n+45
500(5n+45) = 800(5n+20)
25n + 225 = 40n + 160
-15n = -65
n = 4
thus n+5 = 9
hence C