MU-NLPC/Calc-aqua_rat huggingface dataset:
The number of arrangements that can be made with the letters of the word MOTHER so that the vowels occupy the even places?	Choose the correct option:	A) 48	B) 25	C) 21	D) 3	E) 13

Solution: The word MEADOWS has 7 letters of which 3 are vowels.   -V-V-V-   As the vowels have to occupy even places, they can be arranged in the 2 even places in 2! i.e., 2 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.   Hence the total ways are  24 * 2= 
 24 * 2 = 48
48.   48nswer:48
Answer: A
A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets? Select the correct option: A) 10 % B) 9/2 % C) 8/4 % D) 6/12 % E) 45 5/11 %

Solution: Explanation:   Number of runs made by running = 110 - (3 x 4 + 8 x 6)   = 110 - (60)= 
110 - (60) = 50
50.   Required percentage=(50/110*100)%=45 5/11 %   Answer: 45 5/11 %
Answer: E
Each of the products produced yesterday was checked by worker x or worker y. 0.5% of the products checked by worker x are defective and 0.8% of the products checked by worker y are defective. If the total defective rate of all the products checked by worker x and worker y is 0.6%, what fraction of the products was checked by worker y?	Choose one:
A) 1/5  B) 1/4  C) 1/3  D) 2/5  E) 3/7

Solution: x: 0.5% is 0.1%-points from 0.6%.   y: 0.8% is 0.2%-points from 0.6%.   Therefore the ratio of products checked by y:x is 1:2.   Thus, worker y checked 1/3 of the products.   The answer is 1/3.
Answer: C
There are 5 identical pens and 7 identical books. In how many different ways can a person select at least one object from this set? Choose the correct choice from the following.
A) 11
B) 12
C) 39
D) 47
E) 56

Solution: We can select from 0 to 5 pens and from 0 to 7 books.   Thus the total possible ways to select objects is   6*8= 
  6*8 = 48
48   We must subtract 1 for the case with 0 pens and 0 books.   The answer is 47.
Answer: D
The average of first 15 natural numbers is?	Options:  A) 5.2  B) 5.5  C) 8  D) 9  E) 10

Solution: Sum of 15 natural no. = 240/2= 
240/2 = 120
120   Average=120/15= 
120/15 = 8
8   Answer:8
Answer: C
A train overtakes two persons walking along a railway track. The first person walks at 4.5 km/hr and the other walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
Choose the correct choice from the following choices
A) 81 km/hr
B) 88 km/hr
C) 62 km/hr
D) 46 km/hr
E) 56 km/hr

Solution: Let x is the length of the train in meter and y is its speed in kmph   x/8.4 = (y - 4.5)(10/36) ---(1)   x/8.5 = (y - 5.4)(10/36) ---(2)   Dividing 1 by 2   8.5/8.4 = (y - 4.5)/ (y - 5.4)   => 8.4y - 8.4 × 4.5 = 8.5y - 8.5 × 5.4   0.1y = 8.5 × 5.4 - 8.4 × 4.5   => .1y = 45.9 - 37.8= 
45.9 - 37.8 = 8.1
8.1=> y = 81 km/hr   81 km/hrNSWER:81 km/hr
Answer: A
A man has an investment of $3000 which yields a fixed 305 for every $500 invested. if the man takes out $12.6 for every $500 how long will it take for him to double his investment assuming no compounding of interest.
Choose the correct choice from the following choices.
A) 4	B) 33.8	C) 10	D) 30	E) 37.3

Solution: Annual increase is (500 + 30.5 - 12.6)*6= 
(500 + 30.5 - 12.6)*6 = 3_107.4
3107.4   Hence every year there is an increase of 107.4   for his saving to double he needs additional $4000   therefore $4000/107.4=37.3   correct option is 37.3)37.3
Answer: E
Two representatives must be selected from each of two groups of students. One group consists of three men and one woman, and the other group consists of two women and two man. What is the probability that 2 men and 2 women will be selected ?  Choose one:
A) 1/6  B) 1/4  C) 2/7  D) 1/3  E) 5/12

Solution: Group 1: 3 Men and 1 Woman   Group 2: 2 Men and 2 Woman   Need: 2 Men and 2 women   Case 1: 2 Men from Group 1 and 2 women from group 2 - 3C2*2C2 = 3 ways   Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*1*2*2 = 12 ways   Total Favorable cases = 3+12= 
3+12 = 15
15   Total Possible ways of selecting students 2 from each group= 4C2*4C2 = 6*6= 
6*6 = 36
36   Probability= 15/36 = 5/12   Answer : Option 5/12
Answer: E
A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied.
Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Year-III's name will be chosen?  Select:
A) 1/8  B) 2/9  C) 2/7  D) 3/8  E) 3/9

Solution: Explanation :   Total names in the lottery,   =3×100+2×150+200   =800.   Number of Year-III's names,   =3×100   =300.   The required probability,   =300/800.   =3/8.   Answer : 3/8
Answer: D
A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?  Choose the correct choice from the following choices.
A) 25/42
B) 25/45
C) 25/29
D) 25/87
E) 25/26

Solution: Total fruits = 9   Since there must be at least two apples,   (⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃   = 25/42.   25/42nswer: 25/42
Answer: A
Four hundred students at College Q study a foreign language. Of these, 110 of those students study French, and 170 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from  Pick one.
A) 10 to 40 B) 40 to 100 C) 60 to 100 D) 60 to 110 E) 60 to 200

Solution: 110 students study French   290 students do not study French   170 students study Spanish   230 students do not study Spanish   90 students study neither French nor Spanish   290-230= 
290-230 = 60
60   290-90= 
290-90 = 200
200   E. 60 to 200
Answer: E
A room is 12 meters long, 10 meters wide 8 meters in height. The longest possible rod which can be placed in the room is
Choose the most appropriate option:  A) 16.95 meters  B) 16.80 meters  C) 16.75 meters  D) 16.55 meters  E) 17.55 meters

Solution: Square root of 12^2+10^2+8^2...(Diognal) which is square root of 308 that lies 17<√308<18. Hence the answer should be 17.55 meters
Answer: E
If x is an integer, which of the following must be an even integer?  Choose the correct choice.
A) x^2-x-1
B) x^2-4x+6
C) x^2-5x+5
D) x^2+3x+8
E) x^2+2x+10

Solution: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )   A: x^2-x-1 = -1 { If x = 1 }   B: x^2-4x+6 = 3 { If x = 1 }   C: x^2-5x+5 = 1 { If x = 1 }   x^2+3x+8: x^2+3x+8 = 12 { If x = 1 } & x^2+3x+8 = 18 { If x = 2 }   E: x^2+2x+10 = 13 { If x = 1 }   Thus the only possible answer is (x^2+3x+8)
Answer: D
If Rs. 595 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?
Choose the correct choice from the following choices.
A) s.420	B) s.360	C) s.389	D) s.368	E) s.323

Solution: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4   A:B = 2:3 and B:C = 1:4 = 3:12   A:B:C = 2:3:12   A;s share = 595 * 2/17 = Rs. 70   B's share = 595 * 3/17 = Rs. 105   C's share = 595 * 12/17 =Rs.420.   s.420nswer:s.420
Answer: A
Robert is traveling on his cycle and has calculated to reach point A at 2 p.m. if he travels at 10 km/hr; he will reach there at 12 noon if he travels at 15 km/hr. At what speed must he travel to reach A at 1 p.m.? Choose the correct answer:
A) 17 kmph
B) 13 kmph
C) 12 kmph
D) 18 kmph
E) 97 kmph

Solution: Let the distance traveled be x km.   Then, x/10 - x/15 = 2   3x - 2x = 60 => x = 60 km.   Time taken to travel 60 km at 10 km/hr = 60/10= 
60/10 = 6
6 hrs.   So, Robert started 6 hours before 2. p.m. i.e., at 8 a.m.   Required speed= 60/5= 
60/5 = 12
12 kmph.   Answer: 12 kmph
Answer: C
Sekar started a business investing Rs.25,000 in 1999. In 2000, he invested an additional amount of Rs.10,000 and Rajeev joined him with an amount of Rs.35,000. In 2001, Sekar invested another additional amount of Rs.10,000 and Jatin joined them with an amount of Rs.35,000. What will be Rajeev's share in the profit of Rs.1,20,000 earned at the end of 3 years from the start of the business in 1999?	Choose the correct option
A) Rs.40,000  B) Rs.50,000  C) Rs.70,000  D) Rs.75,000  E) none

Solution: Solution   Sekar:Rajeev:Jatin=	(25000×12+35000×12+45000×12):(35000×24) : (35000×12)   = 1260000 : 840000 : 420000   = 3 : 2 : 1.   Rajeev's share	=Rs.(120000×2/6)   = Rs.40000.   Rs.40,000nswer Rs.40,000
Answer: A
The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 14%, then the cost price of the article is:  Choose one:
A) 500	B) 540	C) 555	D) 664	E) 5598

Solution: 110% of S.P. = 616   S.P. = (616 * 100)/110 = Rs. 560   C.P = (110 * 560)/114 = Rs. 540   Answer: Option 540
Answer: B
A work can be finished in 17 days by twenty eight women. The same work can be finished in seven days by seventeen men. The ratio between the capacity of a man and a woman is  Choose the correct option:
A) 4:3	B) 1:4	C) 2:3	D) 3:2	E) 4:5

Solution: Work done by 28 women in 1 day = 1/17   Work done by 1 woman in 1 day = 1/(17Ã—28)   Work done by 17 men in 1 day = 1/17   Work done by 1 man in 7 day = 1/(17Ã—7)   Ratio of the capacity of a man and woman =1/(17Ã—7) : 1/(17Ã—28) = 1/7 : 1/28   = 1/1 :1/4 = 1:4   Answer is 1:4.
Answer: B
A and B can finish a work in 10 days while B and C can do it in 18 days. A started the work, worked for 5 days, then B worked for 10 days and the remaining work was finished by C in 15 days. In how many days could C alone have finished the whole work ?
Choose one
A) 30 days
B) 15 days
C) 45 days
D) 24 days
E) None of these

Solution: Let C completes the work in x days.   Work done by (A + B) in 1 day = 1⁄10   Work done by (B + 45 days) in 1 day = 1⁄18   A’s 5 days’ work + B’s 10 days’ work + 45 days’s 15 days’work = 1   or (A + B)’s 5 days’ work + (B + 45 days)’s 5 days’ work + 45 days’s 10 days’ work = 1   or 5⁄10 + 5⁄18 + 10⁄x = 1 or x = 45 days   Answer 45 days
Answer: C
Find compound interest on Rs. 5000 at 12% per annum for 1 year, compounded half-yearly. Choose the correct option: A) Rs. 600 B) Rs. 618 C) Rs. 525 D) Rs. 620 E) None

Solution: Principal = Rs.5000, Rate=6% per half year Time = 1 year = 2 half-years Amount = Rs. {5000 x ( 1 + 6/100)2] = Rs. [ 5000 x 53/50 x 53/50 ] = Rs. 5618 C.I. = Rs. (5618 – 5000) = Rs. 618   Answer Rs. 618
Answer: B
Martha has the unique talent of being able to guess other people’s height and weight. For every six people that Martha meets, she consistently guesses the people’s correct height five times, and for every eight people that she meets, she consistently guesses the people’s correct weight six times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?	Answers:
A) 8/27
B) 2/5
C) 485/512
D) 98/125
E) 625/952

Solution: Probability that she guesses the height correctly P(h)=5/6   Probability that she guesses the weight correctlyP(w)=6/8   Probability that she guesses both weight and height correctly(P(h)*P(w))=5/6 * 6/8= 30/48   Now the Q asks about the probability of this happening atleast once.   We calculate it by finding the probability of not being able to guess in any of the three occasions.   Probability of not being able to guess any no. of times =1-30/48=18/48=3/8   For all three occasions P(A)=3/8 * 3/8 * 3/8=27/512   Probability of the event happening atleast once=1- P(A)=1-27/512=485/512   Ans should be 485/512
Answer: C
A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?  Choose the correct choice:	A) 50 kmph	B) 62 kmph	C) 54 kmph	D) 74 kmph	E) 55 kmph

Solution: 62 kmph   54 kmph   S = 240/16 * 18/5= 
240/16 * 18/5 = 54
54 kmph
Answer: B
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?	Pick.
A) 4:5 B) 4:3 C) 4:4 D) 4:8 E) 4:1

Solution: Let us name the trains A and B.   Then, (A's speed) : (4:3's speed)   = √b : √a = √16 : √9   = 4:3   Answer: 4:3
Answer: B
Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following numbers could be the sum of G and H?
Select the correct option: A) 153 B) 150 C) 137 D) 135 E) 89

Solution: Let x be the original 2-digit number.   If each digit is halved, then the sum of G and H is 3x/2.   Note the sum must be a multiple of 3 and less than 150.   Only 135 satisfies these two conditions.   The answer is 135.
Answer: D
The third proportional to 1 and 2 is?	Pick:  A) 8  B) 7  C) 4  D) 5  E) 3

Solution: (2*2)/1= 
(2*2)/1 = 4
4   Answer:4
Answer: C
(A% of 6B + B% of A) is equal to ? Select.
A) A% of B  B) B% of A  C) 7% of AB  D) AB% of 3  E) None

Solution: Answer   A% of 6B + B% of A =6AB/100 + AB/100   = 7AB/100 = 7% of AB   7% of ABorrect Option: 7% of AB
Answer: C
If k is the sum of the digits of integer m, and m=10n, where n is an integer, which of the following must be true? Choose one:
A) k is not divisible by 9
B) The sum of the digits of k is divisible by 3
C) m is a multiple of 10k
D) k is a multiple of 9
E) k is a multiple of 6

Solution: m= 10n i.e n =1,2,3 ,4 etc or -1,-2.-3 ,-4 then m =10,20,30,40 or -10 ,-20 ,-30 ,-40 then k 1,2, 3,4 or -(1+0) , -(2+0) , -(3+0) ,-(4+0) .   ans(m is a multiple of 10k)
Answer: C
A can do a job in 18 days and B can do it in 30 days. A and B working together will finish twice the amount of work in days?  Choose the correct choice
A) 29 ½ days
B) 22 ½ days
C) 92 ½ days
D) 28 ½ days
E) 92 ½ days

Solution: 1/18 + 1/30 = 8/90 = 4/45   45/4 = 11 ¼ *2   =22 ½ days   Answer:22 ½ days
Answer: B
The average of 1st 3 of 4 numbers is 16 and of the last 3 are 15. If the sum of the first and the last number is 13. What is the last numbers?
Select:
A) 6 B) 7 C) 5 D) 4 E) 3

Solution: A + B + 5 = 48   B + 5 + D = 45   A + D = 13   A – D = 3   A + D = 13   2D = 10   D = 5   Answer:5
Answer: C
The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If w of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?	Choose the correct choice from the following choices:	A) y/R	B) y/(R-x)	C) xy/(R-x)	D) wy/(R(R-w))	E) y/(R(R-x))

Solution: y/(R-w)- y/R   if we simplify this we get choice wy/(R(R-w)), which is the correct answer.
Answer: D
If x, y, and z are positive integers such that x^2 + y^2 + z^2 = 64,470, which of the following could be the values of x, y, and z?
I. x = 115, y = 146, z = 173
II. x = 114, y = 142, z = 171
III. x = -115, y = 146, z = 173
Answers.
A) I only	B) II only	C) III only	D) I​ and II	E) I and III

Solution: 10 sec answer if you know how to find the units digit of a number   The number given is of the form of square, so calculate the units digit - Here your objective is to find the sum where last digit is 0   x = 115, so x^2 will have units digit 5   y = 146, so y^2 will have units digit 6   z = 173, so z^2 will have units digit 9   Calculate the units digit , the units digit will be 0   Here III) option gives x=-115..(115^2) and(-115^2) are equal.   Hence this will be our answer is option I and III.
Answer: E
A and B together can do a piece of work in 30days. A having worked for 16days, B finishes the remaining work alone in 44days. In how many days shall B finish the whole work?	Choose the correct choice from the following choices: A) 60 B) 12 C) 24 D) 30 E) 45

Solution: Let 60's 1day work = x   B's 1day work = y   x+y = 1/30   16x+44y = 1   x = 1/60   y = 1/60   B's 1 day work = 1/60   B alone can finish the job in 60 days   60nswer is 60
Answer: A
In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination? Select the correct option:  A) 28000  B) 30000  C) 32000  D) 33000  E) None of these

Solution: Explanation :   Let the number of candidates applied for the examination = x   Given that 5% of the applicants were found ineligible.   It means that 95% of the applicants were eligible (∴ 100% - 5% = 95%)   Hence total eligible candidates = 95x/100   Given that 85% of the eligible candidates belonged to the general category   It means 15% of the eligible candidates belonged to other categories(∴ 100% - 85% = 15%)   Hence Total eligible candidates belonged to other categories   = total eligible candidates × (15/100) = (95x/100) × (15/100)   = (95x × 15)/(100 × 100)   Given that Total eligible candidates belonged to other categories = 4275   ⇒ (95x × 15)/(100 × 100) = 4275   ⇒ (19x × 15)/(100 × 100) = 855   ⇒ (19x × 3)/(100 × 100) = 171   ⇒ (x × 3)/(100 × 100) = 9   ⇒ x/(100 × 100) = 3   ⇒ x = 3 × 100 × 100 = 30000   Answer : Option 30000
Answer: B
P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 5), the remainder is also D. If P/Q = 1020.75 and P/(Q + 5) = 816.6, then which of the following gives the correct set of {D, Q}?  Select the correct option:
A) {6, 12}	B) {6, 15}	C) {15,20}	D) {9, 15}	E) {15, 24}

Solution: p/q= d=p/q+5   d= .75 q   d= .6(q+5)   we get d = 15 and q = 20. Answer = {15,20}.
Answer: C
When a is divided by b, the quotient is c with remainder 6. What is a in terms of 6, b, and c?
Choose the correct choice:
A) bc+6  B) bc/6  C) bc-6  D) b/c  E) b-c

Solution: a/b =c with remainder 6   i.e, a-6 = bc   a= bc+6   bc+6nswer : bc+6
Answer: A
How many prime numbers exist between 1 and 20?
Pick one
A) 7  B) 6  C) 5  D) 8  E) 9

Solution: 9)
Answer: E
All of the positive integers are written in a triangular pattern, beginning with the following
four lines and continuing in the same way:
1
2 3 4
5 6 7 8 9
10 11 12 13 14 15 16
Which number appears directly below 2012?
Choose the correct choice:
A) 2100 B) 2102 C) 2104 D) 2106 E) 2108

Solution: Observe that the nth row has 2n- 1 numbers, that each number on the 2nth row is   equal to 2n-2 plus the one above it, and that the last number in the nth row is n2. (The latter   fact may be proved by observing that n2- (n- 1)2 = 2n- 1, the length of the nth row.)   442 = 1936 and 452 = 2025, so that 2012 is on the 45th row. The number below it will be   larger by (2 * 46- 2), so it will be 2102.   correct answer 2102
Answer: B
The product of all the prime numbers less than 20 is closest to which of the following powers of 10 ?  Choose the correct choice from the following
A) 10^9	B) 10^8	C) 10^7	D) 10^6	E) 10^5

Solution: We should find the approximate value of 2*3*5*7*11*13*17*19 to some power of 10.   # of different approximations are possible.   Approach #1:    2*5= 
 2*5 = 10
10;   3*7=~20 (actually more than 20);   11*19=~200 (actually more than 200);   13*17=~200 (actually more than 200);   2∗3∗5∗7∗11∗13∗17∗19≈10∗20∗200∗200=8∗106≈107   Answer: C.   Approach #2:    2*5= 
 2*5 = 10
10   3*17=~50 (actually more than 50);   7*13=~100 (actually less than 100);   11*19=~200 (actually more than 200)   2∗3∗5∗7∗11∗13∗17∗19≈10∗50∗100∗200=107.   Answer: 10^7.
Answer: C
There are 6 identical pens and 9 identical books. In how many different ways can a person select at least one object from this set?	Choose the correct choice from the following answers:
A) 15 B) 30 C) 69 D) 78 E) 90

Solution: We can select from 0 to 6 pens and from 0 to 9 books.   Thus the total possible ways to select objects is   7*10= 
  7*10 = 70
70   We must subtract 1 for the case with 0 pens and 0 books.   The answer is 69.
Answer: C
For all even integers n, h(n) is defined to be the sum of the even integers between 2 and n, inclusive. What is the value of h(20)/h(10) ?  Choose one:  A) 1.8  B) 60  C) 6  D) 18  E) 3

Solution: CONCEPT: When terms are in Arithmetic Progression (A.P.) i.e. terms are equally spaced then   Mean = Median =(First+Last)/2   and Sum = Mean*Number of terms   h(20) = [(2+20)/2]*9 = 99   h(10) (2+20)/2 *9= 
(2+20)/2 *9 = 99
99   h(10)= (2+10)/2]*5 = 30   h(18)/h(10) (2+10)/2 *5= 
(2+10)/2 *5 = 30
30   h(18)/h(10)= (99) / (30) ~ 3   Answer : 3
Answer: E
Two pipes can fill the cistern in 10hr and 12 hr respectively, while the third empty it in 15hr. If all pipes are opened simultaneously, then the cistern will be filled in Choose the correct choice from the following choices: A) 7.5 hr B) 8 hr C) 8.57 hr D) 10 hr E) None of these

Solution: Solution:   Work done by all the tanks working together in 1 hour.   1/10+1/12−1/15=7/60   Hence, tank will be filled in 60/7=8.57 hour   Option(8.57 hr)
Answer: C
The population of a town increased from 1,34,800 to 2,42,500 in a decade. The average percent increase of population per year is:  Select.
A) 4.37%	B) 7.9%	C) 6.8%	D) 8.75%	E) None

Solution: Explanation: Increase in 10 years = (242500 - 134800)= 
(242500 - 134800) = 107_700
107700   Increase%= (107700/134800 x 100)% = 79%.   Required average = (79/10)= 
(79/10) = 79/10 = around 7.9
7.9%.   Answer: Option 7.9%
Answer: B
In a company of 160 employees, 90 are females. A total of 80 employees have advanced degrees and the rest have a college degree only. If 40 employees are males with college degree only, how many employees are females with advanced degrees?  Choose the most appropriate option: A) 40 B) 45 C) 50 D) 55 E) 60

Solution: The number of males is 160-90= 
160-90 = 70
70.   The number of males with advanced degrees is 70-40= 
70-40 = 30
30.   The number of females with advanced degrees is   80-30= 
  80-30 = 50
50.   The answer is 50.
Answer: C
A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1400. The difference between the profit shares of A and C is?
Options:
A) 288
B) 560
C) 155
D) 600
E) 441

Solution: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6   And also given that, profit share of B is Rs. 1400   => 5 parts out of 15 parts is Rs. 1400   Now, required difference is 6 - 4= 
6 - 4 = 2
2 parts   Required difference= 2/5 (1400) = Rs. 560   Answer:560
Answer: B
Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 49 hours and 25 hours respectively. The ratio of their speeds is?
Choose one:
A) 4:9  B) 5:7  C) 4:5  D) 4:1  E) 4:2

Solution: Let us name the trains A and B.   Then, (A's speed) : (5:7's speed)   = √b : √a = √25 : √49   = 5:7   Answer:5:7
Answer: B
A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 42 years now, the son's age 5 years back was: Select the correct option.
A) 12 years. B) 14 years. C) 16 years. D) 17 years. E) 19 years.

Solution: Let the son's present age be x years. Then, (42 - x) = x   2x = 42.   x = 21   Son's age 5 years back (21- 5)= 
(21- 5) = 16
16 years.   ANSWER :16 years.
Answer: C
Simplify 3/4 of 6 0 – 8/5 of 60 + ? = 12  Select the correct option.
A) 48	B) 24	C) 56	D) 63	E) 14

Solution: 60 × 3/4 = 45, 60 × 8/5 = 96   45 – 96 + ? = 12 => 96 + 12= 
96 + 12 = 108
108 – 45= 63   [ 63 + 45= 
 63 + 45 = 108
108 – 96= 12]   Option 63
Answer: D
Find out the C.I on Rs.5000 at 4% p.a. compound half-yearly for 1 1/2 years.	Choices:
A) 306.09
B) 306.05
C) 306.04
D) 306.02
E) 306.01

Solution: A = 5000(51/50)3   = 5306.04   5000   -----------   306.04   Answer:306.04
Answer: C
A person spends 1/5th of his income on the education of his children, and 20% of the remaining on food. If he is left with Rs.576 find his income?  Choose the correct choice from the following answers
A) 800
B) 900
C) 700
D) 750
E) 650

Solution: X * 4/5 * 80/100 = 576   X = 14400/16= 
14400/16 = 900
900   ANSWER 900
Answer: B