RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Find the compound interest on $1200 for 4 years at 20% p.a. if CI is component yearly?
A.$120
B.$150
C.$1288
D.$250
Answer: C.$1288
Explanation: A = P(1 + R/100)^T
= 1200(1 + 20/100)^4
=$2488
CI = $1288
Answer is C
Question: A man is 26 years older than his son. In two years, his age will be twice the age of his son. The
present age of his son is
A.20 years
B.21 years
C.22 years
D.24 years
Answer: D.24 years
Explanation: Explanation:
Let the son's present age be x years. Then, man's present age = (x + 26) years
=> (x + 26) + 2 = 2(x + 2)
=> x + 28 = 2x + 4
So, x = 24
Answer: Option D
Question: 3-6*6+2=
A.A)-31
B.B)-13
C.C)-18
D.D)-17
Answer: A.A)-31
Explanation: 3-6*6+2 = 5-36 = -31...
so the answer is -31... A
Question: Susan, John, Daisy, Tim, Matt,Rose,Lily and Kim need to be seated in 8 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
A.A)20160
B.B)120
C.C)80
D.D)240
Answer: A.A)20160
Explanation: Total number of arrangements = 8! = 40320
In exactly half, Susan will be to the left of Tim, which gives us 20160 arrangements
Option (A)
Question: Will must choose a 3-character computer password, consisting of 2 letter from the alphabet and 1 distinct digits, in any order.From how many different passwords can Will choose?
A.390
B.2,340
C.4,680
D.39,000
Answer: D.39,000
Explanation: 10C1*26C1*25C1 =6500
=>6500 * 3 ! = 39000.
Option E is correct answer...but OA is D.
Question: What will come in place of the question mark (?) in the following questions?
7777/35 =?
A.333.2
B.222.2
C.242.1
D.553.1
Answer: B.222.2
Explanation: B
7777/35 = 222.2
Question: If |x| < x^2, which of the following must be true ?
A.x² >- 1.
B.x² > -2.
C.x² > 0.
D.x² > 1.
Answer: D.x² > 1.
Explanation: |x| < x² implies that x is NONZERO.
Since x is nonzero, |x| > 0 and x² > 0.
Implication:
Both sides of the inequality are positive, allowing us to SQUARE the inequality.
(|x|)² < (x²)²
x² < x⁴.
Since x² > 0, we can safely DIVIDE both sides by x²:
x²/x² < x⁴/x²
1 < x²
x² > 1.
Answer D
Question: From a container having pure milk, 20% is replaced by water and the process is repeated thrice. At the end of the third operation, the milk is?
A.45%
B.49.6%
C.51.2%
D.55%
Answer: C.51.2%
Explanation: Let the total quantity of original milk = 1000gm
Milk after 1st operation = 80% of 1000 = 800gm
Milk after second operation = 80% of 800 = 640gm
Milk after third operation = 80% of 640 = 512gm
Strength of final mixture = 51.2%
Answer is C
Question: A large box contains 15 small boxes and each small box contains 20 chocolate bars. How many chocolate bars are in the large box?
A.A)220
B.B)490
C.C)380
D.D)300
Answer: D.D)300
Explanation: the only thing you have to do is a simple multiply
we have:
15*20
=300
correct answer is:
D) 300
Question: a, b, c, d, and e are positive consecutive integers and a < b < c < d < e.
If the sum of a + b is one less than e, and the product of ab is one more than d, then what is the value of c?
A.3
B.4
C.5
D.6
Answer: B.4
Explanation: Since the integers are consecutive, we can write each as the previous integer +1. For example, b = a+1, and c = b+1. We can also reverse this: a+1 = b, and b+1 = c.
Since ab = d+1, we can also write this ab = e.
Since a+b = e-1, then a+b = ab-1.
Find the pair of consecutive integers whose sum is one less than its product. These numbers are 2 and 3 (sum: 5; product: 6).
Now that we know how the series starts, we can find the value of c. If the first two numbers are 2 and 3, the third number is 4 (option B).
Question: Product of two natural numbers is 11. Then, the sum of reciprocals of their squares is
A.290/289
B.122/121
C.290/90
D.290/19
Answer: B.122/121
Explanation: Explanation:
If the numbers are a, b, then ab = 17,
as 17 is a prime number, so a = 1, b = 17.
1/a2+1/b2=1/1(2)+1/11(2)
=122/121
Option B
Question: If x is a positive integer, which of the following must be odd?
A.x+1
B.x^2+x
C.x^2+x+3
D.x^2−1
Answer: C.x^2+x+3
Explanation: A. X+1 = can be odd or even. Since O + O =E or E + O = O
B. X^2 + X = X(X+1). Since from the above derivation we already know the term X+1 can be Odd or Even, directly substitute here. X(ODD) = Even (When X is Even) or X(EVEN) = EVEN [When X is ODD]
C. Here's the answer. Since we know the term x^2 + X can always take a EVEN number, EVEN + 3 = ODD
Hence C.
Question: A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
A.18 liters
B.17 liters
C.10 liters
D.19 liters
Answer: C.10 liters
Explanation: Explanation:
Number of liters of water in150 liters of the mixture = 20% of 150 = 20/100 * 150 = 30 liters.
P liters of water added to the mixture to make water 25% of the new mixture.
Total amount of water becomes (30 + P) and total volume of mixture is (150 + P).
(30 + P) = 25/100 * (150 + P)
120 + 4P = 150 + P => P = 10 liters.
Answer: C
Question: Sam the Squirrel found a basket
of pine cones one morning. He
decided that every day he would
double the number of pine cones in the basket in
the morning and eat 2 pine cones out of the
basket in the afternoon. At the end of the third
day, there were 34 pine cones in the basket.
How many pine cones were in the basket when
Sam the Squirrel found it?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: We will work backwards to find how many pinecones there were initially.
3rd day:
At the end of the afternoon, Sam had 34.
At the beginning of the afternoon, he had 34 + 2 =36.
At the beginning of the morning, he had 36 ÷ 2 =18.
2nd day:
At the end of the afternoon, he had 18.
At the beginning of the afternoon, he had 18 + 2 = 20.
At the beginning of the morning, Sam had 20 ÷ 2 =10.
1st day:
At the end of the afternoon, Sam had 10.
At the beginning of the afternoon, he had 10 + 2=12.
At the beginning of the morning, he had 12 ÷ 2 = 6
correct answer C
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
A.Rs.17
B.Rs.76
C.Rs.15
D.Rs.72
Answer: C.Rs.15
Explanation: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs. 15.
Answer:C
Question: How many years will it take my savings account initial deposit to double given that I receive just 2% per annum simple interest on the deposited money.
A.50
B.45
C.55
D.35
Answer: A.50
Explanation: P = (P*2*R)/100
100P = P*2*R
100 = 2R
Therefore R = 50 Years
A= 50
Question: The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?
A.6
B.5
C.4
D.2
Answer: A.6
Explanation: S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A
Question: Speed of boat in still water is 9km/hr . if boat moves upstream A to B in 2 hrs. &
B to A in 1 hrs. Then find distance between A&B
A.10km
B.11km
C.12km
D.13km
Answer: C.12km
Explanation: Let speed of stream = s kmph
distance be x
for upstream
(9-s)*2=x (speed*time=distance)
for downstream
(9+s)*1=x
On solving we get x=12km
ANSWER:C
Question: A man can do a piece of work in 5 days, but with the help of his son he can do it in 3 days. In what time can the son do it alone ?
A.7 1/2days
B.6 1/2days
C.5 1/2days
D.4 1/2days
Answer: A.7 1/2days
Explanation: Explanation:
In this type of question, where we have one person work and together work done. Then we can easily get the other person work just by subtracting them. As,
Son's one day work =
(1/3−1/5)=(5−3/15)=2/15
So son will do whole work in 15/2 days
which is =
7 1/2days
Option A
Question: If the product of the integers a, b, c, and d is 1,155 and if a > b > c > d > 1, then what is the value of a – d?
A.2
B.8
C.10
D.11
Answer: B.8
Explanation: 1155 = 3 * 5 * 7 * 11
a = 11
d = 3
a - d = 8
Answer is B
Question: Ravi can do a piece of work in 11 days while Prakash can do it in 22 days. In how many days will they finish it together?
A.5 7/3 days
B.7 1/3days
C.5 1/9 days
D.5 7/3 days
Answer: B.7 1/3days
Explanation: 1/11 + 1/22 = 3/22
22/3 = 7 1/3 days
ANSWER:B
Question: What is 3/5 of 5/7 of 2/3?
A.2/7
B.3/8
C.9/16
D.5/8
Answer: A.2/7
Explanation: 3/5 * 5/7 * 2/3= 2/7
Answer: A
Question: A boat running downstream covers a distance of 10km in 3hr while for covering the same distance upstream, it takes 6hr.
What is the speed of the boat?
A.2.5 kmph
B.3.5 kmph
C.4.5 kmph
D.1.5 kmph
Answer: A.2.5 kmph
Explanation: speed upstream = 10/3
speed of boat down stream = 10/6
speed of boat = 1/2(10/3 + 10 /6 ) = 2.5 kmph
ANSWER:A
Question: Over a ten-year period Pat's income rose from $15,000 to $35,000. What was the percent increase in her income?
A.33 [1][/3]%
B.42.8%
C.133 [1][/3]%
D.142.8%
Answer: C.133 [1][/3]%
Explanation: % Increase(+)/Decrease(-) = (Final Value−InitialValue)/InitialValue∗100
Final Value = $35,000
Initial Value = $15,000
% Increase(+)/Decrease(-) = (35000−15000)/15000∗100
% Increase(+)/Decrease(-) = (20000)/15000∗100=133.33
Answer: Option C
Question: 11
a3
+4b
___
65
If a and b represent positive single digits in the correctly worked computation above, what is the value of the two digit integer ab?
A.12
B.11
C.34
D.544
Answer: B.11
Explanation: 1+3+b=5
b=1
1+a+4=6
a=1
ab=11
ans=B
Question: If Greg buys 5 shirts, 4 trousers and 2 ties, the total cost is $80. If Greg buys 7 shirts, 4 trousers and 2 ties, the total cost is $70. How much will it cost him to buy 2 trousers, 3 shirts and 1 ties?
A.$37.5
B.$64
C.$75
D.$96
Answer: A.$37.5
Explanation: Solution: 5x+4y+2z=80 7x+4y+2z=70
adding both the equations= 12x+8y+4z=150
3x+2y+1z=37.5
ans A
Question: Population is 23000. Population increases by 10% every year, then the population after 3 years is?
A.26630
B.26640
C.36623
D.30613
Answer: D.30613
Explanation: population after 1st year = 23000*10/100 = 2300 ===> 23000+2000 = 25300
population after 2nd year = 25300*10/100 = 2530 ===> 25300+2530= 27830
population after 3rd year = 27830*10/100 = 2783 ===> 27830+2783 = 30613
ANSWER:D
Question: If the L.C.M of two numbers is 720 and their product is 38880, find the H.C.F of the numbers.
A.50
B.30
C.125
D.54
Answer: D.54
Explanation: H.C.F = (Product of the numbers) / (Their L.C.M) = 38880/720 = 54.
ANSWER:D
Question: The sale price sarees listed for Rs.400 after successive discount is 10% and 5% is?
A.298
B.237
C.342
D.876
Answer: C.342
Explanation: 400*(90/100)*(95/100)
= 342
Answer: C
Question: In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 5 : 9. If the shop carries 204 dogs and bunnies total in stock, how many dogs are there?
A.51
B.66
C.98
D.112
Answer: A.51
Explanation: Let us assume the number of dogs, cats and bunnies to be 3x, 5x and 9x
Total dogs and bunnies = 12x.
And we are given that 12x = 204.
Hence x = 17.
Dogs = 3x = 3*17 = 51 (Option A)
Question: A boy has nine trousers and 10 shirts. In how many different ways can he select a trouser and a shirt?
A.50ways
B.90ways
C.100ways
D.108ways
Answer: B.90ways
Explanation: The boy can select one trouser in nine ways.
The boy can select one shirt in 10 ways.
The number of ways in which he can select one trouser and one shirt is 9 * 10
= 90 ways.
Answer: B
Question: The probability that A speaks truth is 3/5 and that of B speaking truth is 4/7. What is the probability that they agree in stating the same fact?
A.18/35
B.18/34
C.18/30
D.18/37
Answer: A.18/35
Explanation: If both agree stating the same fact, either both of them speak truth of both speak false.
Probability = 3/5 * 4/7 + 2/5 * 3/7
= 12/35 + 6/35 = 18/35
Answer:A
Question: In what time will a train 100 metres long cross an electic pole, if its speed be 144 km/hr?
A.2.5 sec
B.4.25 sec
C.5 sec
D.12.5 sec
Answer: A.2.5 sec
Explanation: Sol.
Speed = [144x5/18] m/sec = 40 m / sec.
Time taken = (100/40)sec = 2.5 sec.
Answer A
Question: If the positive integer x is a multiple of 4 and the positive integer y is a multiple of 8, then xy must be a multiple of which of the following?
I. 8
II. 12
III 18
A.II only
B.I and II only
C.I and III only
D.II and III only
Answer: D.II and III only
Explanation: Ans D
From question x/4 is an integer.
x/4 = 2*2*q/4 ---> where q is the integer
Also y/6 = p => y/6 = 2*3*p/6
So, xy = 2*2*2*3 *pq
Thus 2*2*2 = 8 and 2*3*2 = 12 satisfy
D
Question: Look at this series: F2, __, D8, C16, B32, ... What number should fill the blank?
A.A16
B.G4
C.E4
D.E3
Answer: C.E4
Explanation: Explanation: The letters decrease by 1; the numbers are multiplied by 2.
Answer: Option C
Question: Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
A. 5.61
B. 8
C. 10
D. 15
Answer: A. 5.61
Explanation: Old time in minutes to cross 9 miles stretch = 9*60/55 = 9*12/11 = 9.81
New time in minutes to cross 9 miles stretch = 9*60/35 = 9*12/7 = 15.42
Time difference = 5.61
Ans:A
Question: It takes 3 tons of copper ore and 5 tons of iron ore to make one ton of alloy A. How many tons of alloy A can be made from 30 tons of copper ore and 80 tons of iron ore?
A. 18
B. 18 3/4
C. 17
D. 16
Answer: D. 16
Explanation: Yes, you need copper ore:iron ore in the ratio 3:5. Total 8 tons of the mix in this ratio will give 1 ton of alloy A.
If you have 30 tons of copper ore, it is enough for 30/3 = 10 tons of alloy A.
If you have 80 tons of iron ore, it is enough for 80/5 = 16 tons of alloy A.
Since iron ore is available for only 16 tons of alloy A, you can make only 16 tons of alloy A.
The leftover copper ore alone cannot make any alloy A and hence will be leftover only.
Answer must be 16.
(D)
Question: The base of a parallelogram is twice its height. If the area of the parallelogram
is 72 sq. cm, find its height.
A.5cm
B.6cm
C.7cm
D.8cm
Answer: B.6cm
Explanation: Let the height of the parallelogram be x. cm. Then, base = (2x) cm.
2x X x =72  2x^2 = 72  X ^2=36  x=6
Hence, height of the parallelogram = 6 cm
ANSWER B 6cm
Question: If 25% of x is 15 less than 12% of 1500, then x is?
A.660
B.738
C.837
D.840
Answer: A.660
Explanation: 25% of x = x/4 ; 12% of 1500
= 12/100 * 1500 = 180
Given that, x/4 = 180 - 15
=> x/4 = 165 => x = 660.
Answer:A
Question: If 20% of a = b, then b% of 20 is the same as:
A.4% of a
B.25% of a
C.20% of a
D.5% of a
Answer: A.4% of a
Explanation: 20% of a = b
=> b = 20/100a
b% of 20 = (b/100)20 = [(20/100a)/100]20
= (20 × 20 × a)/(100 × 100)
= 4a/100 = 4% of a
A
Question: The average (arithmetic mean) of 7, 8, 10 and 11 equals the average of 2, 9, 13, and
A.7
B.9
C.10
D.12
Answer: D.12
Explanation: 7 + 8 + 10 + 11 = 2 + 9 + 13 + x
36 = 24 + x
Or, x = 12
Hence, Answer will be (D) 12
Question: 34.95 + 240.016 + 23.98 = ?
A.298.946
B.298.694
C.289.496
D.289.469
Answer: A.298.946
Explanation: 34.95
240.016
+ 23.98
--------
298.946
Answer is A.
Question: In 2008, a certain factory produced 20% more widgets than it did in 2007, and its production in 2009 was 120% of its production in 2008. By approximately what percent would its production need to decrease the following year for the factory to produce the same number of widgets it did in 2007?
A.31%
B.35%
C.40%
D.44%
Answer: A.31%
Explanation: Let P be the original level of production in 2007.
Let x be the rate of production in 2010 compared to 2009.
x*1.2*1.2*P = P
x = 1/1.44 = 0.6944 which is a decrease of about 31%.
The answer is A.
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
A.12.9 sec
B.12.1 sec
C.17.9 sec
D.16.8 sec
Answer: B.12.1 sec
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/20 = 12.1 sec.
Answer: B
Question: A network of 20 x 10 squares is given to you.
Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?
A.11550
B.12550
C.15550
D.13550
Answer: A.11550
Explanation: Total number of rectangles and squares will be equal to: (Summation of row numbers) * (Summation of column numbers)
= (1 + 2 + 3 +......+ 19 + 20) * (1 + 2 + 3 +......+ 9 + 10)
= 210 * 55
= 11550
correct answer is A)11550
Question: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
A.(1.5)^4
B.4(1.5)
C.(1.05)^4
D.1 + (0.05)^4
Answer: C.(1.05)^4
Explanation: If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be
1(1.05)^4
1.05^4
C. (1.05)^4
ANSWER:C
Question: In a group of cows and hens, the number of legs are 16 more than twice the number of heads. The number of cows is
A.5
B.8
C.10
D.12
Answer: B.8
Explanation: Explanation:
Let the number of cows be x and the number of hens be y.
Then, 4x + 2y = 2 (x + y) + 16
4x + 2y = 2x + 2y + 16
2x = 16
x = 8.
Answer: B
Question: Find the perimeter and area of the rectangle of length 11 cm and breadth 7 cm.
A.77 cm2
B.121 cm2
C.141 cm2
D.171 cm2
Answer: A.77 cm2
Explanation: length = 11 cm, breadth = 7 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (11 + 7) cm
= 2 × 16 cm
= 32 cm
We know that the area of rectangle = length × breadth
= (11 × 7) cm22
= 77 cm2
ANSWER : A
Question: Three persons invested Rs.9000 in a joint business. The second person invested Rs.1000 more than the first and the third Rs.1000 more than second. After two years, they gained Rs.7200. How much third person will get?
A.2400
B.2429
C.3200
D.2707
Answer: C.3200
Explanation: First persons investment = x
Second persons investment = x + 1000
Third persons investments = x + 2000
x + x + 1000 + x + 2000 = 9000
3x = 6000
x = 2000
Ratio = 2000 : 3000 : 4000
2:3:4
4/9 * 7200 = 3200
Answer:C
Question: A candidate got 33% of the votes polled and he lost to his rival by 833 votes. How many votes were cast?
A.2250
B.2450
C.2650
D.2850
Answer: B.2450
Explanation: Let x be the total number of votes.
0.33x + 833 = 0.67x
0.34x = 833
x = 833/0.34 = 2450
The answer is B.
Question: What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 6), (x, 6)?
A.64
B.81
C.125
D.196
Answer: D.196
Explanation: To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 14.
The area is 14*14 = 196.
The answer is D.
Question: Mangala completes a piece of work in 5 days, Raju completes the same work in 20 days. If both of them work together, then the number of days required to complete the work is?
A.4 days
B.12 days
C.14 days
D.16 days
Answer: A.4 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 = 5 × 20/25 = 4 days
A)
Question: Cost of 16 mirror and 8 comb is Rs.328 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?
A.10
B.12
C.17
D.21
Answer: C.17
Explanation: Let the cost of each pen and pencil be 'p' and 'q' respectively.
16m + 8c = 328 --- (1)
4m + 4c = 96
8m + 8c = 192 --- (2)
(1) - (2) => 8p = 136
=> m = 17
C
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many science books were there at the starting?
A.200
B.300
C.400
D.800
Answer: D.800
Explanation: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
D
Question: A Man can row upstream at 95kmph and downward stream at 47 kmph. Find Man's rate of the current
A.87km/hr
B.20km/hr
C.24km/hr
D.2.8km/hr
Answer: C.24km/hr
Explanation: Rate of the current=1/2(95-47)km/hr
=24km/hr
correct option is :C
Question: A driver would have reduced the time it took to drive from home to the store by 1/3 if the average speed had been increased by 18 miles per hour. What was the actual average speed, in miles per hour, when the driver drove from home to the store?
A.36
B.40
C.44
D.48
Answer: A.36
Explanation: Let R be the original speed and let T be the original time.
Since the distance remains the same (we're just changing the rate and time), any increase in rate or time is met with a decrease in the other term. Decreasing the time by 1/3 would give us:
D = (R)(T) = (2T/3)(x*R)
x = 3/2 since (2T/3)(3R/2) = (R)(T) = D
3R/2 = R + 18
R/2 = 18
R= 36
The answer is A.
Question: Two unbiased coin are tossed .what is the probability of getting atmost one head?
A.3/6
B.2/3
C.3/4
D.1/4
Answer: C.3/4
Explanation: Here S={HH,HT,TH,TT}
Let Ee=event of getting one head
E={TT,HT,TH}
P(E)=n(E)/n(S)=3/4
Option C
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
A.203
B.209
C.211
D.213
Answer: B.209
Explanation: In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.
Hence we have 4 options as given below
We can select 4 boys ...(option 1)
Number of ways to this = 6C4
We can select 3 boys and 1 girl ...(option 2)
Number of ways to this = 6C3 × 4C1
We can select 2 boys and 2 girls ...(option 3)
Number of ways to this = 6C2 × 4C2
We can select 1 boy and 3 girls ...(option 4)
Number of ways to this = 6C1 × 4C3
Total number of ways
= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3
= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]
=
6
×
5
2
×
1
+
6
×
5
×
4
3
×
2
×
1
×
4
=6×52×1+6×5×43×2×1×4
+
6
×
5
2
×
1
×
4
×
3
2
×
1
+
6
×
4
+6×52×1×4×32×1+6×4
=
15
+
80
+
90
+
24
=
209
B)
Question: The ratio of the cost price and the selling price is 4 : 5.The profit percent is :
A.10%
B.20%
C.25%
D.30%
Answer: C.25%
Explanation: Solution
Let C.P. = Rs.4x. Then, S.P. = Rs.5x. Gain = Rs.(5x - 4x) = Rs.x.
∴ Gain % =(x/4x X100) % = 25 %
Answer C
Question: Shreyas bought an article and sold it for 130% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.40250/-?
A.Rs.30962
B.Rs.35640
C.Rs.34250/-
D.Rs.33200
Answer: A.Rs.30962
Explanation: Explanation:
130% of CP = Rs.40250
:. CP = Rs.40250x100/130 = Rs.30962.
Answer: Option A
Question: A invested $400 in a business after 6 months B invested $200 in the business. End of the year if they got $100 as profit. Find B's shares?
A.$100
B.$75
C.$20
D.$120
Answer: C.$20
Explanation: A:B = 400*12:200*6
A:B = 4:1
B's share = 100*1/5 = $20
Answer is C
Question: Tickets for all but 100 seats in a 10,000-seat stadium were sold. Of the tickets sold, 25% were sold at half price and the remaining tickets were sold at the full price of $2. What was the total revenue from ticket sales?
A.$15,840
B.$17,325
C.$18,000
D.$19,800
Answer: B.$17,325
Explanation: 10000 seats --> Full Price : Half Price = 7500 : 2500
Price when all seats are filled = 15000 + 2500 = 17500
100 seats are unsold --> Loss due to unfilled seats = 25 + 2*75 = 175
Revenue = 17500 - 175 = 17325
Answer: B
Question: At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
A.6%
B.6.5%
C.7%
D.7.5%
Answer: A.6%
Explanation: Explanation:
Let the rate be R% p.a.
Then, 1200 x (1 + R/100)2
R = =6%
ANSWER IS A
Question: For all real numbers v, an operation is defined by the equation v* = v - v/3. If (v*)* = 20, then v=
A.36
B.39
C.42
D.45
Answer: D.45
Explanation: (v*)* = (v - v/3) - (v - v/3) / 3
20 = 2v/3 - 2v/9 = 4v/9
v = 45
The answer is D.
Question: How long does a train 110 m long running at the speed of 72 km/hr takes to cross a bridge 134 m length?
A.82.1 sec.
B.12.2 sec
C.19.1 sec.
D.17.1 sec.
Answer: B.12.2 sec
Explanation: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 110 + 134 = 244 m.
Required time = 244/20 = 12.2 sec.
Answer: B
Question: The average of 15 numbers is calculated as 30. It is discovered later on that while calculating the average, one number namely 36 was wrongly read as 26. The correct average is?
A.12
B.26
C.16
D.45
Answer: D.45
Explanation: 15 * 30 + 36 – 26
= 450/10
= 45
Answer: D