RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: A large petrol tank has two inlet tubes (a large one and a small one) and one outlet tube. It takes 3 hours to fill the tank with the large inlet tube. On the other hand, it takes 6 hours to fill the tank with the small inlet tube. The outlet tube allows the full tank to be emptied in 9 hours.
What fraction of the tank (initially empty) will be filled in 0.64 hours if all three tubes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).
A.0.25
B.0.26
C.0.27
D.0.28
Answer: A.0.25
Explanation: Solution:
In one hour,
Soln 1:
the large inlet tube fills 1 / 3 of the tank;
the small inlet tube fills 1 / 6 of the tank;
the outlet tube empties 1 / 9 of the tank; and therefore
all three tubes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank.
Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.
Soln 2:
Let V be the total volume of the tank. From equation (1),
Flow Rate (large inlet tube) = V / 3
Flow Rate (small inlet tube) = V / 6
Flow Rate (outlet tube) = V / 9.
Substituting in equation (2),
Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9).
Using the above result in equation (1),
Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ].
Note that V cancels out on simplifying the above expression.
Fraction of the tank that will be filled in 0.64 hours =
0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.
Answer A
Question: A man can row downstream at the rate of 16 Km/hr and upstream at 6 Km/hr. Find man's rate in still water and the rate of current?
A.9,6
B.11,5
C.9,3
D.6,6
Answer: B.11,5
Explanation: Explanation:
Rate of still water = 1/2 (16 + 6) = 11 Km/hr
Rate of current = 1/2 (16-6) = 5 Km/hr
Answer: Option B
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much? Look at this series: 5, 43, 15, 33, 25, ...What number should come next?
A.10
B.40
C.23
D.13
Answer: C.23
Explanation: C23This is an alternating addition and subtraction series. In the first pattern, 10 is added to each number to arrive at the next. In the second, 10 is subtracted from each number to arrive at the next.
Question: If x/|y| = -sq. root 25 which of the following must be true?
A.x^2 = 25 * y^2
B.x = y
C.x = y^2
D.x^2 = y^2
Answer: A.x^2 = 25 * y^2
Explanation: x/|y| = -sq. root 25
x= -sq. root (25) |y|
Squaring both sides
x^2= ( -sq. root 25 |y|) ^2=25 * y^2
A is the answer
Question: A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
A.3 hrs 65 min
B.3 hrs 45 min
C.3 hrs 48 min
D.3 hrs 25 min
Answer: B.3 hrs 45 min
Explanation: Time taken by one tap to fill the tank = 3 hrs.
Part filled by the taps in 1 hour = 4 * 1/6 = 2/3
Remaining part = 1 - 1/2 = 1/2
2/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min
So, total time taken = 3 hrs 45 min.
Answer: B
Question: A circular path of 25 m radius has marginal walk 3 m wide all round it. Find the cost of leveling the walk at 25p per m2?
A.Rs..49.00
B.Rs.40.15
C.Rs.124.93
D.Rs.42.53
Answer: C.Rs.124.93
Explanation: Explanation:
π (28^2 - 25^2) = 22/7 * (784-625) = 499.71
499.71 * 1/4 = 124.93
Answer: Option C
Question: When 4 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?
A.32
B.81
C.60
D.120
Answer: D.120
Explanation: Explanation:
Let the number be
4 + 1/2[1/3(a/5)] = a/15
=> 4 = a/30 => a = 120
Answer:D
Question: If 4 people are selected from a group of 10 married couples, what is the probability that none of them would be married to each other?
A.1/33
B.2/63
C.1/3
D.43/62
Answer: D.43/62
Explanation: If we are to select 4 people from 10 couples WITHOUT any restriction, how many ways can we make the selection? 20!/4!16! =4845
If we are to select 4 people from 10 couples WITH restriction that no married couple can both make it to the group, only a representative?
10!/4!6! = 210
But we know that to select a person from each couple, take 2 possibilities
210*2*2*2*2 = 3360
Probability = Desired/All Possibilities =3360/4845 = 43/62
Answer: D
Question: (8^15)+(16^13)+(4^24) = ?
A.(4)*(2^29+1)
B.(6)*(2^48)
C.(9)*(2^49)
D.(28)*(2^53)
Answer: A.(4)*(2^29+1)
Explanation: I think you are assuming that (X^Y) + (X^Z) is = (X^Y+Z) which is not true, as it only applies to multiplication. Rather it would have to be (X^Y)(X^Z) = (X^YZ)
So when you simplify down to 2^48 + 2^52 + 2^48 you cannot just add exponents.
Here's how my brain works with this one,
Step 1: Recognize a common base.
(8^16) + (16^13) + (4^24) = ((2^2)^16) + ((2^4)^13) + ((2^2)^24) = (2^48) + (2^52) + (2^48)
Step 2: Recognize the factor and pull out of the equation.
= (2^48)(1 + (2^4) + 1)
= (2^48)(1 + 16 + 1)
= (2^48)(18)
Step 3: Recognize this is not an answer and adapt.
(2^48)(18) = (2^48)(2)(9) = (2^49+1)(4)
Answer is A.
Question: . A bag contains five white and four red balls. Two balls are picked at random from the bag. What is the probability that they both are different color?
A.2/20
B.1/9
C.5/9
D.6/4
Answer: C.5/9
Explanation: Explanation:
Two balls can be picked from nine balls in â¹Câ‚‚ ways.
We select one white ball and one red ball from five white balls and four red balls. This can be done âµCâ‚ . â´Câ‚ ways.
The required probability = (5 * 4)/â¹Câ‚‚ = 20/36 = 5/9
C
Question: Find the odd man out, 4, 9, 25, 35, 36, 64
A.9
B.35
C.36
D.None of these.
Answer: B.35
Explanation: The pattern:
2*2
3*3
5*5
6*6
8*8
35 is not a square number.
ANSWER: B
Question: What least number must be subtracted from 13294 so that the remainder is exactly divisible by 97?
A.3
B.5
C.7
D.9
Answer: B.5
Explanation: Sol.
On dividing 13924 by 97, we get remainder = 5.
∴ Required number to be subtracted = 5.
Answer B
Question: The greatest number by which the product of three consecutive multiples of 5 is always divisible is
A.54
B.750
C.152
D.162
Answer: B.750
Explanation: Solution
Required number	= Product of first three multiplies of 3
= (5 Ã— 10 Ã— 15)= 750.
Answer B
Question: There are certain diamonds in a shop.
1 thief stole half of diamonds and 2 more.
2 thief stole half of remaining and 2 more
3 same as above
4 same as above.
5 came nothing was left for that.how many diamonds was there??
A.50
B.60
C.70
D.80
Answer: B.60
Explanation: Let diamonds are x.
1.x/2+2=(x+4)/2,remaining=x-(x+4/2)=>( x-4)/2
2. remaining/2+2 i.e (x-4)/4+2=x+4/4, remaining=(x-4)/4-(x+4)/4=>x-12/4
3. (x-12)/8+2=(x+4)/8,remaining= (x-12)/4-(x+4)/8=>(x-28)/8
4.(x-28)/16+2=x+4/16, remaining= (x-28)/8-(x+4)/16=>(x-60)/16
5. (x-60)/16=0 so x=60
ANSWER:B
Question: Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, in Country R's currency, for a person in that country whose annual income is Z?
A.50+Z/200
B.50+3Z/100
C.50+Z/40
D.100+Z/50
Answer: C.50+Z/40
Explanation: 50+Z/40=C
Question: A bus trip of 280 miles would have taken 1 hour less if the average speed V for the trip had been greater by 5 miles per hour. What was the average speed V, in miles per hour, for the trip?
A.35
B.40
C.45
D.50
Answer: A.35
Explanation: The time is the distance/speed. The time difference is 1 hour.
280/V - 280/(V+5) = 1
280(V+5) - 280V = (V)(V+5)
1400 = (V)(V+5)
35*40 = (V)(V+5)
V = 35 mph
The answer is A.
Question: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number W?
A.60
B.80
C.40
D.120
Answer: B.80
Explanation: (1 + 1/8)x - (1 - 1/4)x = 30
(9/8)x - (3/4)x = 30
x = 80=W
Answer: B
Question: A man can row 5 kmph in still water. When the river is running at 2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
A.5.75
B.5.7
C.5.76
D.4.2
Answer: D.4.2
Explanation: M = 5
S = 2
DS = 7
US = 3
x/7 + x/3 = 1
x = 2.1
D = 2.1 * 2 = 4.2 Answer: D
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 30 cm?
A.827 cm2
B.570 cm2
C.285 cm2
D.178 cm2
Answer: B.570 cm2
Explanation: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (30)
= 570 cm2
Answer:B
Question: A is twice as good a work man as B and together they finish a piece of work in 16 days.The number of days taken by A alone to finish the work is :
A.36 days
B.24 days
C.46 days
D.16 days
Answer: B.24 days
Explanation: Solution
(A’s 1 day’s work): (B’s 1 day’s work)= 2 : 1.
(A + B)'s 1 day’s work = 1/16
Divide 1/14 in the ratio 2 : 1.
∴ A’s 1 day’s work = (1/14 x2/3)= 1/24
Hence,A alone can finish the work in 24 days.
Answer B
Question: A petrol pump owner mixed leaded and unleaded petrol in such a way that the mixture contains 10% unleaded petrol. What quantity of leaded petrol should be added to 1 ltr mixture so that the percentage of unleaded petrol becomes 5%?
A.1000 ml
B.900 ml
C.1900 ml
D.1800 ml
Answer: A.1000 ml
Explanation: In 1 lit mixture quantity of unleaded petrol = 100 ml
Let x ml leaded petrol be added, then
5% of (1000 + x) = 100 ml
or, 5 (1000 + x) = 100 × 100
⇒ x = 5000⁄5 = 1000 ml
Answer A
Question: In order to obtain an income of Rs. 680 from 10% stock at Rs. 120, one must make an investment of
A.5363
B.8160
C.2368
D.1987
Answer: B.8160
Explanation: To obtain Rs. 10, investment
= Rs. 120.
To obtain Rs. 680, investment =
= Rs. 8160.
Answer: B
Question: A number is doubled and 9 is added. If resultant is trebled, it becomes 57. What is that number
A.5
B.10
C.12
D.14
Answer: A.5
Explanation: Explanation:
=> 3(2x+9) = 57
=> 2x+9 = 19
=> x = 5
Answer: Option A
Question: A reduction of 20% in the price of salt enables a lady to obtain 10kgs more for Rs.100, find the original price per kg?
A.2.6
B.2.1
C.2.5
D.2.4
Answer: C.2.5
Explanation: 100*(20/100) = 20 --- 10
? --- 1 => Rs.2
100 --- 80
? --- 2 => Rs.2.5
Answer: C
Question: The least number which should be added to 2497 so that the sum is exactly divisible by 5,6,4 and 3 is :
A.3
B.13
C.23
D.33
Answer: C.23
Explanation: Solution
L.C.M. of 5,6,4 and 3 = 60. on dividing 2497 by 60, the remainder is 37.
∴ Number to be added = (60-37) = 23. Answer C
Question: 5 identical snow plows can clear an iced parking lot in 2 hours. How long would it take 6 such snow plows to clear the same parking lot?
A.1 hour, 20 minutes
B.2 hours, 30 minutes
C.3 hours
D.7 hours, 30 minutes
Answer: A.1 hour, 20 minutes
Explanation: 6/5 as many plows will take 5/6 as many hours --> 2*5/6=5/3 hours = 1 hour, 20 minutes.
Answer: A.
Question: 180 candies are distributed to children with the same number of candies for each child. What can’t be the range which includes the number of children?
A.1~10
B.10~20
C.35~45
D.65~75
Answer: D.65~75
Explanation: 180 = 2^2*3^3*5
There are factors in each range except for 65~75
The answer is D.
Question: A certain car can travel 40 minutes on a gallon of gasoline at 70 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 60 mph?
A.15%
B.30%
C.25%
D.20%
Answer: D.20%
Explanation: Let, Tank capacity = T gallon
Used Fuel = (T-8) gallons
Distance Travelled (@70 miles/hr) = 80 miles
Distance travelled in 1 gallon = Distance travelled in 40 mins (@60 miles/hr) = (70/70)*40 = 40 miles
Fuel used to travel 80 miles = (80/40) = 2 gallon
i.e. Used fuel = (T-8) = 2 gallon
i.e. T = 10 Gallons
i.e. Used Fuel = (2/10)*100 =20%
D
Question: A TV is purchased at Rs. 5000 and sold at Rs. 4000, find the lost percent.
A.10%
B.20%
C.25%
D.28%
Answer: B.20%
Explanation: Explanation:
We know, C.P. = 5000
S.P. = 4000
Loss = 5000 - 4000 = 1000
Loss%=(Loss/ Cost∗100)%=(1000/ 5000∗100)%=20%
Option B
Question: There are 7 baskets numbered from 1 to 7 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
A.90
B.120
C.250
D.720
Answer: D.720
Explanation: Each child takes a total of 1+2+3+4+5+6+7 = 7*8/2 = 28 apples.
The total number of apples taken by 10 children is 10*28 = 280
The number of apples left in the end is 1000 - 280 = 720 apples.
The answer is D.
Question: Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.
A.40 min
B.45 min
C.35 min
D.20 min
Answer: A.40 min
Explanation: Dist = speed * time
time = 2hr 45 min = 11/4 hr
==> 4*11/4 = 11 km
new speed = 16.5 kmph
==> 11/16.5 = 40 min
ANSWER A
Question: A bat is bought for Rs.450 and sold at a gain of 20% find its selling price
A.s.430/-
B.s.480/-
C.s.400/-
D.s.540/-
Answer: D.s.540/-
Explanation: 100 % ------> 450
120 % ------> 450 *(120/100)
Selling price = Rs.540/-
D
Question: Sandy is younger than Molly by 6 years. If their ages are in the respective ratio of 7:9, how old is Molly?
A.21
B.24
C.27
D.36
Answer: C.27
Explanation: S = M - 6
S / M = 7/9
9S = 7M
9(M-6) = 7M
M = 27
The answer is C.
Question: (51+52+53+………+100) is equal to:
A.2525
B.2975
C.3225
D.3775
Answer: D.3775
Explanation: (51+52+53+………+100) = (1+2+3+…….+100)- (1+2+3+4+……+50)
= (100*101)/2 - (50*51)/2
= (5050-1275)= 3775.
Answer: D
Question: The height of cylinder is 14 Cm and its diameter is 10 Cm. The volume of the cylinder is:
A.4400
B.2200
C.5500
D.1100
Answer: D.1100
Explanation: h = 14 Cm and r = 5 Cm
Cylinder volume = πr(power2)h = (22/7 × 5 × 5 × 14) Cm(power3) = 1100 Cm(power3)
Answer is D.
Question: A diner is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. If the diner picks one type of lettuce, one type of tomato, and one type of olive for the salad, how many total options does the diner have for the salad?
A.9
B.11
C.24
D.48
Answer: C.24
Explanation: 2*3*4 = 24
The answer is C.
Question: How many consecutive zeros are there at the end of 100! (100 factorial) ?
A.21
B.22
C.23
D.24
Answer: D.24
Explanation: number of zeros will be 24
Reason 100/5=20
20/5=4
so the total number of 5 will be 20+4=24
ANSWER:D
Question: Find the area of a parallelogram with base 32 cm and height 22 cm?
A.281
B.284
C.704
D.640
Answer: C.704
Explanation: Area of a parallelogram = base * height
= 32 * 22
= 704 cm2
Answer: C
Question: The average of squares of first 11 consecutive even numbers is:
A.164
B.174
C.184
D.194
Answer: C.184
Explanation: 2(n+1)(2n+1)/3
(2*12*23)/3
=2*4*23
=184
ANSWER:C
Question: A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.1 per sq m?
A.675, Rs.1350
B.575, Rs.675
C.1350, Rs.675
D.1450, Rs.775
Answer: B.575, Rs.675
Explanation: Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 1 = Rs. 675
ANSWER:B
Question: Sue's trail mix is 30% nuts and 70% dried fruit. Jane's trail mix is 60% nuts and 40% chocolate chips. If the combined mixture of Sue and Jane's trails mix contains 35% nuts, what percent of the combined mixture is dried fruit?
A.48.3%
B.52.8%
C.55.5%
D.58.3%
Answer: D.58.3%
Explanation: 35% is 5%-points above 30% and 25%-points below 60%.
So the ratio of Sue's mix to Jane's mix is 5:1.
5/6*70% = 58.3%
The answer is D.
Question: Line Q has the equation 5y – 3x = 30. If Line S is perpendicular to Q, has an integer for its y-intercept, and intersects Q in the second quadrant, then how many possible Line S’s exist? (Note: Intersections on one of the axes do not count.)
A.22
B.33
C.36
D.41
Answer: A.22
Explanation: 5y - 3x = 30 and so y = 3x/5 + 6
When x = 0, then y = 6.
When y = 0, then x = -10
The slope is 3/5, so the slope of line S is -5/3.
Through the point (-10, 0), 0 = -5(-10)/3 + c
The y-intercept is c = -50/3 < -16.
Thus the perpendicular line S can have y-intercepts from -16 up to 5.
The number of possible lines is 16 + 5 + 1 = 22
The answer is A.
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $ 42 more. What was his original selling price?
A. $770
B. $660
C. $700
D. $1100
Answer: B. $660
Explanation: Let the original purchase price be X
So original selling price at 10% profit = 1.1X
If product is purchased at 10% less of original = 0.9X
Profit of 30% on this price = 1.3(0.9X)
He would have received $42 more in second scenario => 1.3(0.9X) - 1.1X = 42
=> 0.07X = 42
=> X = $600
Original purchase price = $600
Hence, original selling price (at 10% of profit) = 1.1(600) = $660
Option B
Question: Ratio between Rahul and Deepak is 4:3, After 6 Years Rahul age will be 18 years. What is Deepak present age?
A.22
B.15
C.77
D.9
Answer: D.9
Explanation: Present age is 4x and 3x,
=> 4x + 6 = 18 => x = 3
So Deepak age is = 3(3) = 9
Answer: D
Question: Two men start from opposite banks of a river . They meet 340 meters away from one of the banks on forward journey. After that they meet at 170 meters from the other bank of the river on their backward journey. What will be the width of the river (in meters)?
A.750
B.850
C.900
D.980
Answer: B.850
Explanation: let p,q are two persons then their speeds be a,b->m/hr
x----340----------------------|---(d-340)---------y
in forward journey
time taken by p=340/a;
time taken by q=d-340/b;
in forward journey, time taken by p=time taken by q
so 340/a=d-340/b
a/b=340/d-340------------(1)
after that they continue their journeyand reach other banks
now in backward journey,
x---------------(d-170)--------------------------|-----170------y
distance travelled by p from meet 1 to meet 2 = (d-340)+170
distance travelled by p from meet 1 to meet 2 =340+(d-170)
now time taken by p= time taken by q
(d-340)+170/a=340+(d-170)/b
(d-340)+170/340+(d-170)=a/b---------(2)
from 1&2
340/(d-340)=(d-340)+170/340+(d-170)
340/(d-340)=d-170/d+170
340d+57800=d^2-340d-170d+57800
340d=d^2-510d
d^2-850d=0
d(d-850)=0
d=0 ord=850
so width of the river is 850
ANSWER:B
Question: The price of sugar is increased by 9%. By how much percent should a home maker reduce her consumption of sugar to have no extra expenditure?
A.(700/107) %
B.(107/100) %
C.(900/109)%
D.(7/100)%
Answer: C.(900/109)%
Explanation: Old price = $100 (assume);
Old consumption = 1 kg (assume).
New price = $109.
We want the spendings to remain at $100.
(New consumption)*109 = 100 --> (New consumption) = 100/109 kg.
Percent decrease = Change/Original *100 = (1 - 100/109)/1*100 = 900/109%.
Answer: C.
Question: A man buys an article for 16% less than its value and sells it for 16% more than its value. His gain or loss percent is:
A.no profit, no loss
B.20% profit
C.less than 35% profit
D.more than 35% profit
Answer: D.more than 35% profit
Explanation: Let the article be worth Rs. x.
C.P. 84% of Rs. x = Rs. 84x/100
S.P. = 116% of Rs. x = Rs. 116x/100
Gain = (116x/100 - 84x/100) = Rs. 8x/25
Gain % = 8x/25 * 100/84x * 100 = 38 2/21 % > 35%
ANSWER:D
Question: Currently apples cost 60 cents/pound. Due to a disease affecting the apple trees it is expected that next month apples will cost 200% more than they do currently. How much are apples expected to cost next month?
A.200 cents /pound
B.150 cents /pound
C.160 cents /pound
D.180 cents /pound
Answer: D.180 cents /pound
Explanation: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 60 cents/pound + (200/100)(60 cents/pound)
= 60 cents/pound + 120 cents/pound
= 180 cents /pound
Answer : D
Question: Jim and Renee will play one game of Rock, Paper, Scissors. In this game, each will select and show a hand sign for one of the three items. Rock beats Scissors, Scissors beat Paper, and Paper beats Rock. Assuming that both Jim and Renee have an equal chance of choosing any one of the hand signs, what is the probability that Renee will win or draw?
A.5/6
B.2/3
C.1/2
D.5/12
Answer: B.2/3
Explanation: There are 3*3=9 combinations (cases) possible. In 3 cases there will be a tie (rock-rock, scissors/scissors, paper/paper). Now, out of 6 cases left Jim and Renee have equal chances of winning, so in 3 cases Jim will win and in other 3 Renee will win. So the probability Renee winning the game or drawing is (favorable outcomes) / (total # of outcomes) = 6/9 = 2/3
Answer: B
Question: Which of the following is the lowest positive integer that is divisible by 4, 5, 6, 7, 8, 9, and 10?
A.1680
B.1950
C.2230
D.2520
Answer: D.2520
Explanation: The number needs to be divisible by 2^2, 5, 2*3, 7, 2^3, 3^2, and 2*5.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520
The answer is D.
Question: The sum of three consecutive even numbers is 60. Find the middle number of the three?
A.14
B.60
C.18
D.70
Answer: B.60
Explanation: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 60
6P = 60 => P = 10.
The middle number is: 10P = 60.
ANSWER:B
Question: In an electric circuit, two resistors with resistances x and y are connected in parallel. If R is the combined resistance of these two resistors, then the reciprocal of R is equal to the sum of the reciprocals of x and y. What is R if x is 3 Ohms and y is 5 Ohms?
A.15/8
B.3/8
C.5/8
D.7/15
Answer: A.15/8
Explanation: 1/R = 1/x + 1/y
1/R = 1/3+1/5 = 8/15
R = 15/8
The answer is A.
Question: sale of Rs 6835, Rs. 9927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6600 ?
A.5591
B.2477
C.2877
D.2676
Answer: A.5591
Explanation: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6600 x 6) - 34009]
= Rs. (39600 - 34009)
= Rs. 5591
Answer: A
Question: If 90 percent of 600 is 50 percent of x, then x=?
A.100
B.1000
C.1080
D.1020
Answer: C.1080
Explanation: 0.9 * 600 = 0.5 * x
x = 9/5 * 600 = 1080
Question: A Person X started at 3 hours earlier at 40km/h from a place P, then another person Y followed him at 60km/h. Started his journey at 3 O'clock, afternoon. What is the diference in time when X was30 km ahead of Y and when Y was 30 km ahead of X?
A.8h
B.3h
C.6h
D.3h
Answer: B.3h
Explanation: Explanation:
Time ( when X was 30 km ahead of Y) = (120-30)/20 =4.5h
Time ( when Y was 30 km ahead of X) = (120+30)/20 = 7.5 h
Thus, required difference in time = 3h
Answer: B
Question: A grocer has a sale of Rs. 5124, Rs. 5366, Rs. 5808, Rs. 5399 and Rs. 6124 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 5400?
A.4079
B.4579
C.5579
D.5679
Answer: B.4579
Explanation: Total sale for 5 months = Rs. (5124 + 5366 + 5808 + 5399 + 6124) = Rs. 27821.
Required sale = Rs. [ (5400 x 6) - 27821 ]
= Rs. (32400 - 27821)
= Rs. 4579.
ANSWER:B
Question: A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?
A.10:12:14
B.12:24:28
C.20:22:12
D.20:49:64
Answer: D.20:49:64
Explanation: Explanation :
Ratio in which A,B and C shared the profit = 5 : 7 : 8
Assume that the ratio of their investment = a:b:c
Then 14a : 8b : 7c = 5 : 7 : 8
Good to go, we got the equation. Now it's a matter of time to find a, b and c
14a/8b = 5/7
=> 98a = 40b
=> b = 98a/40 = 49a/20 ---(1)
14a/7c =5/8
=> 2a/c =5/8
=> 16a = 5c
=> c = 16a/5 ---(2)
a : b : c = a : 49a/20 : 16a/5 = 1 : 49/20 : 16/5 = 20 : 49 : 64. Answer : Option D