MU-NLPC/Calc-aqua_rat huggingface dataset:
Jim takes a seconds to swim S meters at a constant rate from point P to point Q in a pool. Roger, who is faster than Jim, can swim the same distance in b seconds at a constant rate. If Jim leaves point P the same time that Roger leaves point Q, how many fewer meters will Jim have swum than Roger when the two swimmers pass each other?  Choices:
A) c(b-a)/ a+b  B) c(a-b)/a+b  C) S(a-b)/(a+b)  D) ab(a-b)/a+b  E) ab(b-a)/a+b

Solution: Both JimRoger are travelling at constant speedin opposite direction:   So, speed of Jim = S/a speed of Roger = S/b   Let say Jim travelled distance x from P where it met Roger, it means that Roger travelled (S-x) from point Q   [x would be less than (c-x) as Jim is travelling slow]   From above, time taken by Jim to travel x = xa/S....................... (1)   Also, time taken by Roger to travel (c-x) = (S-x)b/S.....................(2)   Time taken by both JimRoger is same, so (1) = (2)   xa/S = (S-x)b/S,   Solving further, x = bS/(a+b).................... (3)   We require to find how many fewer meters will Jim have swum i.e   additional distance travelled by Roger = (S - x) - x   = S-2x   Substituting value of x from (3)solving the equation further, we get Answer = S(a-b)/a+b   Answer = (S(a-b)/(a+b))
Answer: C
Insert the missing number. 34, 7, 37, 14, 40, 28, 43, (...) Choose one:	A) 31	B) 42	C) 46	D) 56	E) 68

Solution: Explanation :   We have two series here   34, 37, 40, 43, ... (Increase by 3)   7, 14, 28, ... (Multiply by 2)   Hence, next term is 28 × 2 = 56   Answer : Option 56
Answer: D
Find the average of all the numbers between 6 and 34 which is divisible by 5 Choose the most appropriate option
A) 15 B) 18 C) 13 D) 19 E) 20

Solution: avg = (10+15+20+25+30)/5 = 100/5= 
100/5 = 20
> 20   ANSW20R 20
Answer: E
Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 37 kmph. Of how many minutes does the train stop per hour?	Pick.
A) 73
B) 83
C) 12
D) 83
E) 11

Solution: 11xplanation:   T = 8/45 * 60 = 11   Answer: Option 11
Answer: E
Without stoppages, a train travels certain distance with an average speed of 300 km/h, and with stoppages, it covers the same distance with an average speed of 200 km/h. How many minutes per hour the train stops ?	Choose the correct answer.
A) 20 B) 21 C) 22 D) 23 E) 24

Solution: Due to stoppages, it covers 100 km less .   Time taken to cover 100 km = 100â„300h = 1â„3h   = 1â„3 Ã— 60 min = 20 min   20nswer 20
Answer: A
If a sum of Rs.17,100 is divided between, A and B in the ratio 4:5, how much amount would A get ?	Select:	A) 9500	B) 6700	C) 7600	D) 7900	E) 9700

Solution: 9500 = 17100 × 4 / 9 = Rs.7600   B = 17100 × 5 /9 = Rs.9500   Option 9500
Answer: A
The ratio of two numbers is 3 : 4 and their H.C.F. is 4. Their L.C.M. is Choose the correct choice from the following choices: A) 12 B) 16 C) 24 D) 48 E) 50

Solution: Solution   Let the numbers be 3x and 4x. Then, their H.C.F. = x. So, x = 4.   So, the numbers are 12 and 16.   L.C.M. of 12 and 16 = 48.   Answer 48
Answer: D
In expressing a length of 81.472 km as nearly as possible with the three significant digits, find the
percentage error	Choose the correct choice from the following answers:
A) 0.35%
B) 0.34%
C) 0.034%
D) 0.035%
E) None of these

Solution: Explanation:   Error = (81.5 - 81.472)= 
(81.5 - 81.472) = 0.028
0.028   Required percentage=   0.02881.472×100=0.034   Answer: Option 0.034%
Answer: C
A person saved $50 in buying an item on sale. If he spent $500 for the item, approximately how much percent he saved in the transaction?
Choices
A) 8%  B) 10%  C) 2%  D) 5%  E) 1.8%

Solution: Actual price = 500+50= 
500+50 = 550
$550   Saving= 10/550 * 100 = 100/55 = 1.8% approximately   Answer is 1.8%
Answer: E
A boat having a length 8 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:
Select the correct option.
A) 12 kg B) 60 kg C) 72 kg D) 160 kg E) None of these

Solution: Explanation:   Volume of water displaced = (8 x 2 x 0.01) m3   = 0.16 m3.   ∴ Mass of man = Volume of Water displaced x Density of water   = (0.16 x 1000)kg   = 160 kg.   Answer: 160 kg
Answer: D
The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? Select:
A) 16 2/3% loss  B) 11 2/3% loss  C) 66 2/3% loss  D) 12 2/3% loss  E) 17 2/3% loss

Solution: Explanation:   15 CP = 18 SP   18 --- 3 CP loss   100 --- ? => 16 2/3% loss   16 2/3% lossnswer: 16 2/3% loss
Answer: A
A courtyard is 21 meter long and 14 meter board is to be paved with bricks of dimensions 14 cm by 8 cm. The total number of bricks required is :
Choose the most appropriate option
A) 16000 B) 18000 C) 20000 D) 26250 E) None of these

Solution: Explanation:   Number of bricks =Courtyard area /1 brick area   =(2100Ã—1400 /14Ã—8)=26250   Option 26250
Answer: D
Company A imported 12,000 widgets made of either brass or aluminum. The widgets are painted blue, red or green. If 10 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported?	Select:	A) 420	B) 480	C) 1050	D) 1680	E) 2100

Solution: Answer A.   We are told that 10% of all imported widgets are made of brass and of those, 20% are green and 40% are red. Since we know that there are only three colors, the remaining 40% must be blue. 40% blue of 10% brass widgets leads to 4% blue brass widgets out of the total 10,550 widgets.   12,000 /100 * 4 = 480.   Answer 480.
Answer: B
There is a train and car. The ratio between the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 480 km in 8 hours. The speed of the bus is 3/4th of the speed of the train. How many kilometers will the car cover in 4 hours?  Choose the correct answer:
A) 200
B) 250
C) 300
D) 350
E) 400

Solution: The speed of the bus is 480/8= 
480/8 = 60
60 km/hr   The speed of the train is  (60*4)/3= 
 (60*4)/3 = 80
80 km/hr   The speed of the car is   80/16 * 15= 
  80/16 * 15 = 75
75 km/hr   The distance covered by the car in 4 hours is 75 × 4= 300 km   The answer is 300.
Answer: C
The ratio of investments of two partners P and Q is 7:5 and the ratio of their profits is 7:10. If P invested the money for 20 months, find for how much time did Q invest the money?  Answers:
A) 11 B) 40 C) 18 D) 16 E) 12

Solution: 7*5: 20*x = 7:10   x = 40   Answer:40
Answer: B
Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?  Choices
A) 8
B) 12
C) 18
D) 20
E) 24

Solution: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.   So out of 30 boxes, 6 are 10-pound boxes and 24 are 20-pound boxes.   If the average of 10 and 20-pound boxes is to be 15, the ratio of 10-pound boxes:20-pound boxes should be 1:1.   The number of 10 pound boxes remain the same so we still have 6 of them.   To get a ratio of 1:1, the number of 20-pound boxes must be 6.   We need to remove 18 of the 20-pound boxes.   The answer is 18.
Answer: C
How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word? Choose the correct choice from the following choices:
A) 4
B) 6
C) 7
D) 8
E) 9

Solution: E,I fixed. Consonants can be arrangements in 3P3 = 3! = 6 ways   Option '6'
Answer: B
The average salary of the employees in a office is Rs.120/month.The avg salary of officers is Rs.460 and of non officers is Rs 110. If the no.of officers is 15,then find the No of nonofficers in the office.
Choose the correct choice from the following answers.
A) 400 B) 420 C) 430 D) 450 E) 510

Solution: Let no. of non- officers be x   15 * 460 + x * 110 = (x + 15) 120   x = 510   510
Answer: E
Find the average of all numbers between 4 and 34 which are divisible by 5
Choose the most appropriate option: A) 20 B) 21 C) 25 D) 30 E) 55

Solution: Explanation:   Average=(5+10+15+20+25+30) / 5=105 / 5= 
105 / 5 = 21
21   Option 21
Answer: B
What approximate value should come in place of the question mark (?).
36.0001 ÷ 5.9998 × √? = 108.0005	Select the correct option
A) 325  B) 316  C) 256  D) 16  E) 18

Solution: Using approximation, we get 36⁄6 × √? = 108   or, √? = 108⁄6   or, √? = 18   or, ? = 324 ≈ 325   Answer 18
Answer: E
A merchant sells an item at a 20% discount, but still makes a gross profit of 40 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?	Pick one: A) 20% B) 40% C) 50% D) 60% E) 75%

Solution: original SP = X   Cost =C   current selling price = .8x ( 20% discount)   .8x = 1.4C (40% profit)   x= 1.4/.8 *C   x= 7/4 C   Original selling price is 1.75C which is 75% profit   Answer 75%
Answer: E
Find large number from below question
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder.
Choose the correct choice.
A) 535  B) 565  C) 1234  D) 1345  E) 1635

Solution: Let the smaller number be x. Then larger number = (x + 1365).   x + 1365 = 6x + 15   5x = 1350   x = 270   Large number = 270+1365= 
270+1365 = 1_635
1635   1635
Answer: E
Jane and Thomas are among the 7 people from which a committee of 4 people is to be selected. How many different possible committees of 4 people can be selected from these 7 people if at least one of either Jane or Thomas is to be selected?
Choose one
A) 30  B) 45  C) 55  D) 65  E) 70

Solution: The total number of ways to choose 4 people from 7 is 7C4 = 35.   The number of committees without Jane or Thomas is 5C4 = 5.   There are  35-5= 
 35-5 = 30
30 possible committees which include Jane and/or Thomas.   The answer is 30.
Answer: A
The difference between the compound interest compounded annually and simple interest for 2 years at 20% per annum is Rs.360. Find the principal?	Choose the correct choice:
A) 2277  B) 2667  C) 9000  D) 2766  E) 1811

Solution: P = 360(100/5)^2 => P = 9000   Answer: 9000
Answer: C
A man took a loan from a bank at the rate of 9% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was : Choose the correct option:
A) Rs. 2000	B) Rs. 10,000	C) Rs. 15,000	D) Rs. 20,000	E) None

Solution: Solution   Principal = Rs.(100x5400/9x3)= Rs. 20000.   Answer Rs. 20,000
Answer: D
There is a train and car. The ratio between the speed of a train & a car is 16:15 respectively. Also, a bus covered a distance of 480 km in 8 hours. The speed of the bus is 3/4th of the speed of the train. How much distance will the car cover in 5 hours? Choose the correct choice from the following answers:
A) 300 km B) 325 km C) 375 km D) 425 km E) 450 km

Solution: The speed of the bus is 480/8= 
480/8 = 60
60 km/hr   The speed of the train is  (60*4)/3= 
 (60*4)/3 = 80
80 km/hr   The speed of the car is   80/16 * 15= 
  80/16 * 15 = 75
75 km/hr   The distance covered by the car in 5 hours is 75 × 5= 375 km   The answer is 375 km.
Answer: C
If (c - a)/(c - b) = 1, then (5b - 3a)/(c - a) =
Choose the most appropriate option:
A) 0.5  B) 1  C) 1.5  D) 2  E) 2.5

Solution: Let's say c=2, b=1, a=1 so that our 1st expression holds true. Now, ibsert those numbers in the second expression and we'll get 2   Answer 2 (hopefully )))
Answer: D
If n is a positive integer, what is the remainder when (7^(4n+2))(6^n) is divided by 10? Select:
A) 1  B) 2  C) 4  D) 6  E) 8

Solution: This one took me bout 3 1/2 min. Just testin numbers and what not.   First notice that n is positive. Save time by noticing thatI worked out one solution where n=0 only to find that thats not an option :p.   1-7 stands for ^1 thru 7   1: 7*1=7   2: 7*7=9   3: 7*9=3   4: 7*3=1   5: 7*1=7   6: 7*7=9   7: 7*9=3   Pattern repeats every @ 5. Notice every ^4 or multiple of 4 is always going to be 1. This is just for future notice for similar problems.   so 7^4n+3 ---> if n=1 then its ((7^7)*6))/10 which can say is going to be 3*8--> 18/10 --> R=8   Now from here if id double check just to make sure.   7^4(2)+3*6= 
3*6 = 18
18/10 ---> R=4.   4 or J in this problem.
Answer: C
When m is divided by 9, the remainder is 2. When m is divided by 13, the remainder is 4. If 1 < m < 300, what is the greatest possible value of m?  Options
A) 210	B) 230	C) 250	D) 270	E) 290

Solution: 13*9= 
13*9 = 117
117   Let's start with 4, and keep adding 13 until we find a number with the form 9k+2.   4, 17, 30, 43, 56= 9*6+2   The next possible number is  56 + 117= 
 56 + 117 = 173
173   The next possible number is  173 + 117= 
 173 + 117 = 290
290   The next possible number would be greater than 300.   The answer is 290.
Answer: E
The function g(h) is defined for integers h such that if h is even, g(h) = h/2 and if h is odd, g(h) = h + 5. Given that g(g(g(g(g(h))))) = 19, how many possible values for h would satisfy this equation?  Choose the correct choice from the following:
A) 1 B) 5 C) 7 D) 8 E) 11

Solution: Let me define terms:   in g(h) = R   h is argument, R is result, g() is function,   in g(g(g(g(g(h))))), g1 is inner most, g5 is outermost for identification.   From definition of function g, we can deduce that:   If Result is even then two possibilities for argument = 1 Even 1 Odd   If Result is odd then one possibility for argument = 1 Even   Since final result = 19 = Odd   Possibilities:   g1:1 Even   g2: 1*(Even,Odd ) =1 Even 1 Odd   g3: 1*(Even,Odd) + 1 Even =2 Even 1 Odd   g4: 2*(Even, Odd) + 1 Even =3 Even 2 Odd   g5: 3*(Even, Odd) + 2 Even =5 Even 3 Odd = Total 8   Ans 8 it is!
Answer: D
The average temperature of Tuesday Wednesday and Thursday was 37 C. The average temperature of Wednesday and Thursday and Friday was 38 C. if the temperature on Friday was 39 C.
Find the temperature on Tuesday.  Choose the correct option
A) 22	B) 36	C) 88	D) 20	E) 27

Solution: Tues + Wed + Thurs)/3=37   Tues + Wed + Thurs=111...(1)   (Wed + Thurs + Fri)/3=38   (Wed + Thurs + Fri) =114...(2)   Given friday is 39.   Then, (2) - (1) Fri - Tues = 3   So 39 - Tues = 3   Tuesday =36   Answer:36
Answer: B
A 180m long train is running at 72 kmph.If it crossed the platform in 20 sec.then find the platform length?	Choose the correct choice from the following answers
A) 220m B) 110m C) 230m D) 100m E) 90m

Solution: Length=speed*time   Length=72km/hr*time   Length=[72*(5/18)]*20 {(ie)(x)km/hr)}   =x*(5/18)   =20*20= 
20*20 = 400
400m   Length of platform=Length-Length of the train   Length of platform=400-180= 
400-180 = 220
220m   Option 220m
Answer: A
A sum of money at simple interest amounts to Rs. 835 in 3 years and to Rs. 854 in 4 years. The sum is:	Choose the correct choice from the following options
A) 647
B) 698
C) 778
D) 847
E) 976

Solution: S.I. for 1 year = Rs. (854 - 835) = Rs. 19.   S.I. for 3 years = Rs.(19 x 3) = Rs. 57.   Principal = Rs. (835 - 57) = Rs. 778.   Answer:778
Answer: C
If w is an even integer and q is an odd integer, which of the following must be an odd integer?  Choose the most appropriate option:	A) w/q	B) wq	C) 2w+q	D) 2(w+q)	E) 3w/q

Solution: this is a must question:   A. w/q   can be a non-integer   B. wq   always even   C. 2w+q   2w = even -> even+odd = odd   D. 2(w+q)   always even - w+q = odd *2 -> even   E. 3w/q   might be a non integer.   2w+q
Answer: C
In how many ways a committee of 4 members can be selected from 7men and 6ladies, consisting of 2 men and 2 ladies?
Choose the correct option.
A) 250
B) 315
C) 412
D) 256
E) 362

Solution: (2 men out 7) and (2 ladies out of 6) are to be chosen   Required number of ways = 7C2 * 6C2 = (7*6*6*5)/(2*1*2*1)= 
(7*6*6*5)/(2*1*2*1) = 315
315   Answer is 315
Answer: B
A salt manufacturing company produced a total of 5000 tonnes of salt in January of a particular year. Starting from February its production increased by 170 tonnes every month over the previous months until the end of the year. Find its average monthly production for that year?
Pick one
A) 2989 B) 2765 C) 5950 D) 2989 E) 9772

Solution: Total production of salt by the company in that year   = 5000 + 5170 + 5340 + .... + 6870 = 71390.   Average monthly production of salt for that year   = 71390/12   = 5950.   Answer:5950
Answer: C
A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 23 m * 2 m * 0.75 m?	Choices: A) 22377 B) 27782 C) 27891 D) 25000 E) 23000

Solution: 23 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x   23 = 1/100 * x => x = 23000   Answer: 23000
Answer: E
What is the smallest positive integer K such that the product of 3675 x K is a perfect square?  Choose the correct option
A) 3 B) 9 C) 15 D) 25 E) 63

Solution: A perfect square, is just an integer that can be written as the square of some other integer. For example 16=4^2, is a perfect square.   Now, 3675= 5^2 * 7^2 * 3, so if k=3 then 3675 k = (5 * 7 * 3)^2, which is a perfect square (basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even).   3nswer: 3.
Answer: A
The sale price of a trolley bag including the sale tax is Rs. 1120. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:  Choose the correct choice from the following answers.
A) Rs 1000
B) Rs 1515
C) Rs 800
D) Rs 900
E) None of these

Solution: Explanation :   112% of S.P. = 1120   S.P. = Rs.(1120x 100/112) = Rs.1000.   C.P. = Rs (100/125x 1000) = Rs 800.   Answer : Rs 800
Answer: C
The ages of two person , differ by 20 years. If 5 years ag , the elder one be 5 times as old as the younger one their present ages (in years) are respectively	Pick
A) 30, 10
B) 20,10
C) 35,15
D) 51,17
E) 20,17

Solution: Let their ages be x and (x + 20) years   (x - 5) * 5 = (x +20 - 5)   after solving this we get   x= 10 years   The age of elder one = 10 + 20= 
10 + 20 = 30
30 years   So the present ages are 30 and 10 years   30, 10NSWER : 30, 10
Answer: A
A van takes 5 hours to cover a distance of 495 km. What speed in kph should the van maintain to cover the same distance in 3/2 of the previous time?	Pick
A) 60
B) 63
C) 66
D) 69
E) 72

Solution: (3/2)*5= 
(3/2)*5 = 15/2 = around 7.5
7.5 hours   495 / 7.5= 
495 / 7.5 = 66
66 kph   The answer is 66.
Answer: C
SP of a book is Rs. 450 he gets a loss of 10%, find CP of the book?  Select the correct option:
A) Rs.300
B) Rs.450
C) Rs.500
D) Rs.600
E) Rs.640

Solution: Find cost price   Let C.P. of book = x and S.P. = Rs. 450   S.P. of book = C.P. – (10% of C.P.)   S.P. = x – (0.10x)   450 = 0.9 x   x i.e cost price = Rs.500   Rs.500
Answer: C
Complete the sequence:
E G K Q ?	Options.
A) M	B) D	C) Y	D) F	E) Z

Solution: E+2=G   G+4=K   K+6=Q   Q+8=Y   Y
Answer: C
What is the smallest of six consecutive odd integers whose average (arithmetic mean) is y + 2?	Choose the correct choice from the following choices:
A) y - 3  B) y-57  C) y - 1  D) y  E) x + 1

Solution: Since the numbers are consecutive odd integers, mean = median = 3rd integer + 4th integer /2   y - 3nd 1st integer= 3rd integer- 4   let's say 3rd integer = n and 4th integer = n+2   2n+2/2= y+2   n= y+1   1st integer= y+1-4= y-3   y - 3 is the answer
Answer: A
Right triangle PQR is the base of the prism in the figure above. If PQ=PR=âˆš14 and the height of the prism is 8, what is the volume of the prism?
Pick one
A) 12 B) 45 C) 87 D) 56 E) 23

Solution: Volume of prism = Area of base * height = 1/2* (square root of 14) * (square root of 14)*8 =56   Answer: 56
Answer: D
Two pipes P and Q can fill a cistern in 12 and 16 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
Choose the correct choice from the following options.
A) 11 1/2 min
B) 11 1/4 min
C) 11 2/4 min
D) 12 min
E) 11 7/4 min

Solution: 3/12 + x/16 = 1   x= 12   Answer: 12 min
Answer: D
The total of the ages of Amar, Akbar and Anthony is 30 years. What was the total of their ages three years ago ? Choose the correct answer:	A) 20 years	B) 28 years	C) 71 years	D) 21 years	E) 31 years

Solution: Explanation:   Required sum = (30 - 3 x 3) years = (30 - 9)= 
(30 - 9) = 21
21 years.   Answer: Option 21 years
Answer: D
At a certain college, 80 percent of the total number of students are freshmen. If 60 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 50 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?	Choose the correct choice from the following answers:
A) 25%  B) 20%  C) 22%  D) 21%  E) 24%

Solution: Let's say there is a TOTAL of100students at this college.   80 percent of the total number of students are freshmen.   # of freshmen = 80% of 100 =80   60 percent of the fresh-men are enrolled in the school of liberal arts...   Number of liberal arts freshmen = 60% of 80 = 48   ...and, of these, 50 percent are psychology majors...   Number of liberal arts freshmen who are psychology majors = 50% of 48=24   What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?   24/100= 24%   Answer:24%
Answer: E
The salaries of a,b,c are in the ratio 2:3:5.If the increment of 15%, 10% and 20% are allowed respectively in their salaries, then what will be the new ratio of their salaries?
Choose the correct choice from the following choices
A) 23:33:60 B) 24:33:60 C) 23:33:66 D) 23:38:60 E) 28:33:60

Solution: a:b:c = 2 :3 :5   200:300:500   15% 10% 20%   +30 +30 +100   230:330:600 = 23:33:60   23:33:60NSWER:23:33:60
Answer: A
6+2+2^2+2^3+2^4+2^5=？  Choices.
A) (2^3-1)(2^3+1)  B) 2^5-1  C) 2^6+4  D) 2^5+1  E) 2^5-2

Solution: From 6+2+2^2+2^3+2^4+2^5=68,   2^6+4=68   the correct answer is 2^6+4.
Answer: C
The sum of the present ages of A, B, C is 45 yrs. Three years ago their ages were in the ratio 1:2:3. What
is the present age of A
Choose the correct choice from the following options:
A) 10yrs	B) 6yrs	C) 8yrs	D) 9yrs	E) 7yrs

Solution: a:b:c=1:2:3   a=1x;b=2x;c=3x;   after three years   (x+3)+(2x+3)+(3x+3)=45;   x=6;   so present age of a will be x+3=6+3= 
6+3 = 9
9   ANSWER:9yrs
Answer: D
The ratio of the length and the width of a rectangle is 4 : 3 and the area of the rectangle is 5808 sq cm. What is the ratio of the width and the area of the rectangle?	Select the correct option.
A) 1:76  B) 1:80  C) 1:84  D) 1:88  E) 1:92

Solution: Let the length and the width be 4x and 3x respectively.   Area = (4x)(3x) = 5808   12x^2 = 5808   x^2 = 484   x = 22   The ratio of the width and the area is 3x : 12x^2 = 1 : 4x = 1 : 88   The answer is 1:88.
Answer: D
Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).  Options:
A) 31 minutes  B) 37 minutes  C) 32 minutes  D) 30 minutes  E) 33 minutes

Solution: 30 minutes   Distance travelled by Ramu = 45 * 4= 
45 * 4 = 180
180 km   Somu travelled the same distance in 6 hours.   His speed= 180/6= 
180/6 = 30
30 km/hr   Hence in the conditional case, Ramu's speed= 45 - 9= 
45 - 9 = 36
36 km/hr and Somu's speed= 30 + 10= 
30 + 10 = 40
40km/hr.   Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken= 0.5 hours = 30 minutes.
Answer: D
I bought a car with a peculiar 5 digit numbered licence plate which on reversing could still be read. On reversing value is increased by 78633.Whats the original number if all digits were different? Options:  A) 10968  B) 10969  C) 10868  D) 11968  E) 12968

Solution: Only 0 1 6 8 and 9 can be read upside down. So on rearranging these digits we get the answer as 10968.   10968NSWER:10968
Answer: A