MU-NLPC/Calc-aqua_rat huggingface dataset:
A bottle contains a certain solution. In the bottled solution, the ratio of water to soap is 3:2, and the ratio of soap to salt is six times this ratio. The solution is poured into an open container, and after some time, the ratio of water to soap in the open container is halved by water evaporation. At that time, what is the ratio of water to salt in the solution?  Choose the correct choice from the following answers
A) 1:1  B) 2:3  C) 3:2  D) 9:4  E) 54:8

Solution: Water:soap = 3:2   Soap:Salt=18:2   => For 18 soap, salt = 2   => For 2 Soap, salt = (2/18)*2 = 2/9   So, water:soap:salt = 3:2:2/9 = 54:36:4   After open container, water:soap:salt = 27:36:4   So, water:salt = 27:4 = 54:8   54:8
Answer: E
In case R is the only individual sewing on committee B, which among the following shouldserve on committee A?  Choose the correct choice:
A) V and U	B) V and T	C) U and S	D) T and S	E) T and U

Solution: T and S should serve on A   ANSWER:T and S
Answer: D
An unbiased die is tossed. Find the probability of getting a multiple of 6 Pick
A) A)1/6	B) B)2/5	C) C)1/4	D) D)2/3	E) E)3/7

Solution: Here S = {1,2,3,4,5,6}   E = event of getting a multiple of 3   E = {6}   P(E) = 1/6   1/6nswer is 1/6
Answer: A
Ravish has to secure 40% marks to clear his board exam of class 10th.
He got 40 marks and failed by 40 marks.
What is the maximum marks ?
Pick:
A) 150 B) 135 C) 160 D) 200 E) 155

Solution: D   200   To pass the exam ravish needs 40 + 40= 
40 + 40 = 80
80 marks.=> (80/40) *100= 
(80/40) *100 = 200
200
Answer: D
At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 4/7 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? Choose the correct choice:
A) 7/10  B) 2/5  C) 3/5  D) 4/5  E) 5/8

Solution: Method: X = No. of boxes loaded by day crew.   Boxes by night crew = 3/4 * 4/7 X = 3/7 X   % loaded by day crew = X/(X + 3/7X) = 7/10   7/10nswer 7/10
Answer: A
In the new budget, the price of rice rose by 20%. By how much percent must a common man reduce his consumption so that his expenditure on it does not increase?	Choices:	A) 16.66%	B) 17%	C) 15.8%	D) 12%	E) None of these

Solution: Explanation :   Solution: reduction in consumption = [r/(100+r) * 100]% = (20/120 * 100) = 16.66%   16.66%nswer : 16.66%
Answer: A
A tank contains 8,000 gallons of a solution that is 4 percent sodium chloride by volume. If 3,000 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Choose the most appropriate option:
A) 3.40%
B) 4.40%
C) 5.40%
D) 6.40%
E) 7.40%

Solution: We start with 8,000 gallons of a solution that is 4% sodium chloride by volume. This means that there are 0.04 x 8,000 = 320 gallons of sodium chloride.   When 3,000 gallons of water evaporate we are left with 5,000 gallons of solution. From here we can determine what percent of the 5,000 gallon solution is sodium chloride.   (sodium chloride/total solution) x 100 = ?   (320/5,000) x 100 = ?   0.064 x 100 = ?   = 6.4%   Answer is 6.40%.
Answer: D
A and B start a business with Rs.3000 and Rs.9000 respectively. Hoe should they share their profits at the end of one year? Choose the correct choice from the following options:	A) 3:5	B) 1:5	C) 1:3	D) 3:1	E) 3:2

Solution: They should share the profits in the ratio of their investments.   The ratio of the investments made by A and B =   3000 : 9000 => 1:3,Answer: 1:3
Answer: C
Car A runs at the speed of 65km/hr & reaches its destination in 5hr. Car B runs at the speed of 70 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?	Choose the correct option
A) 11 : 6 B) 12 : 7 C) 13 : 7 D) 15 : 6 E) 65 : 56

Solution: Sol. Distance travelled by Car A = 65 Ã— 5 = 325 km   Distance travelled by Car B = 70 Ã— 4 = 280 km   Ratio = 325/280 = 65 : 56   65 : 56
Answer: E
What is the ratio between perimeters of two squares one having 7 times the diagonal then the other?
Choose the correct choice: A) 3: 8 B) 3: 6 C) 3: 7 D) 7: 1 E) 3: 3

Solution: d = 7d d = d   a√2 = 7d a√2 = d   a = 7d/√2 a = d/√2 => 7: 1   Answer:7: 1
Answer: D
Its a very poor village so sahara group organized a beneficiary cricket match for these people.
The event raised Rs300000.
Tickets were priced as follows:
Rs 748 for males
Rs 712 for ladies
Rs 45 for kids
How many males,ladies and kids were there ? Choose the most appropriate option:  A) 100 males , 209 ladies & 52 kids  B) 120 males , 359 ladies & 72 kids  C) 149 males , 259 ladies & 92 kids  D) 150 males , 256 ladies & 92 kids  E) 135 males , 259 ladies & 50 kids

Solution: 149 males , 259 ladies & 92 kids   149 males , 259 ladies & 92 kids
Answer: C
At what rate percent on simple interest will Rs.750 amount to Rs.1200 in 5 years?  Answers.
A) 12	B) 3	C) 14	D) 5	E) 6

Solution: 450 = (750*5*R)/100   R = 12%.12nswer: 12
Answer: A
If each term in the sum a1+a2+a3+.....+an is either 7 or 77 and the sum equals 350, which of the following could be equal to n? Select:
A) 38	B) 39	C) 40	D) 41	E) 42

Solution: For example: as units digit of 350 is zero then # of terms must be multiple of 10. Only answer choice which is multiple of 10 is C (40).   To illustrate consider adding:   *7   *7   ...   77   77   ----   =350   So, several 7's and several 77's, note that the # of rows equals to the # of terms. Now, to get 0 for the units digit of the sum the # of rows (# of terms) must be multiple of 10. Only answer choice which is multiple of 10 is C (40).   Answer: 40.
Answer: C
Best friends Sprite and Icey have are playing a game of marbles. They invite 4 of their friends to play with them. There are 36 marbles in the bag. If all 6 people are playing, how many marbles does each person get?  Choose the correct choice from the following answers
A) 3
B) 4
C) 5
D) 6
E) 7

Solution: Answer= 6   36 / 6= 
36 / 6 = 6
6   Answer= 6
Answer: D
Two pipes can fill a tank in 18 minutes and 15 minutes. An outlet pipe can empty the tank in 45 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank? Select:
A) 12	B) 13	C) 11	D) 10	E) None of these

Solution: Explanation:   Part of the filled by all the three pipes in one minute   = 1/18 + 1/15 - 1/45 = (5 + 6 - 2)/90 = 9/90 = 1/10   So, the tank becomes full in 10 minutes.   ANSWER IS 10
Answer: D
The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is: Answers:
A) 57.5 km/hr.
B) 77.5 km/hr.
C) 87.5 km/hr.
D) 97.5 km/hr.
E) 37.5 km/hr.

Solution: C   87.5 km/hr.   Let the speed of two trains be 7x and 8x km/hr.   Then, 8x = 400/4= 
400/4 = 100
100   Let the speed of two trains be 7x and 8x km/hr.   --> x= 100/8= 
100/8 = 25/2 = around 12.5
12.5   --> Speed of first train= (7 x 12.5) km/hr = 87.5 km/hr.
Answer: C
Arya starts cycling along the boundaries of the squares. She starts from a point A and after 90 minutes she reached to point C diagonally opposite to A. If she is travelling with 24km/hr, then find the area of square field. Choose the correct choice from the following answers:  A) 125  B) 225  C) 256  D) 425  E) None of these

Solution: Explanation :   D = 24*3/2= 
24*3/2 = 36
36 km. So side of square is 16km, so area – 256km^2   Answer – 256
Answer: C
Jill has 7 gallons of water stored in quart, half-gallon, and one gallon jars. She has equal numbers of each size jar holding the liquid. What is the total number of water filled jars?	Choose the correct answer.
A) 3
B) 6
C) 9
D) 12
E) 14

Solution: Let the number of each size of jar = wthen 1/4w + 1/2w + w = 7 1 3/4w = 7w=4The total number of jars = 3w =12Answer: 12
Answer: D
When a certain number X is divided by 95, the remainder is 31. What is the remainder when X is divided by 19?	Answers.
A) 10  B) 11  C) 12  D) 15  E) 17

Solution: Let possible value of x is 126   least possible value of x/19 is 126/19 =>6 quotient with remainder 12   Thus answer is (12) 12
Answer: C
The lowest number which should be added to 5915 so that the sum is exactly divisible by 3, 5, 8 and 7 is:  Select the correct option:	A) 705	B) 825	C) 805	D) 905	E) 810

Solution: L.C.M. of 3, 5, 8 and 7= 840.   On dividing 5915 by 840, the remainder is 35.   Number to be added = (840 - 35)= 
(840 - 35) = 805
805. Answer: Option '805'
Answer: C
(166)^2 - (167)^2 =	Choose the correct option:
A) 1	B) 100	C) 229	D) 329	E) 335

Solution: Using the formula:   (a+1)^2 - a^2 = 2a+1   So, Answer = 167*2 + 1   = 334+1= 
334+1 = 335
335= Answer = 335
Answer: E
Ajay spends 20 per cent of his salary on house rent, 5 percent on food, 15 percent travel, 10 percent on clothes and the remaining amount of Rs.27000 is saved. What is Ajayâ€™s income? Choices:
A) Rs.60000 B) Rs.80500 C) Rs.54000 D) Rs.70500 E) None of these

Solution: Explanation:   Savings = Income â€“ expenditure   100 â€“   (20+5+15+10)= 
  (20+5+15+10) = 50
50%   50% of income= Rs.27000   :. Income = 27000 x 100/50 = Rs. 54000.   Answer: Option Rs.54000
Answer: C
In a certain lottery drawing, two balls are selected at random from a container with 30 balls, numbered from 1 to 30, inclusive. If the winner of the lottery is awarded a cash prize in the amount of $1,000 times the product of the numbers on the two selected balls, which of the following is a possible amount of the cash prize given to the winner? Answers:
A) $9.85 x 10^6
B) $9.90 x 10^6
C) $1.00 x 10^7
D) $1.05 x 10^7
E) $2.9*10^5

Solution: The max product of any two balls can be 29 * 100 = 9900 = 2.9 * 10^3   If you multiply it by $1000 the max amount will be 2.9 * 10^5.   $2.9*10^5
Answer: E
Of the 350 people attending a conference, 150 have signed up for the Marketing workshop and 320 have signed up for the Accounting workshop. If 60 of the people attending did not sign up for either workshop, then the number of people who signed up for both the Marketing and the Accounting workshops is:	Choose the correct choice from the following options
A) 180
B) 220
C) 245
D) 260
E) 275

Solution: Since the information in the prompt refers to the 'standard' 5 groups, you can use the Overlapping Sets Formula to get to the solution:   Total = Gp.1 + Gp.2 - Both + Neither   350 = 150 + 320 - Both + 60   350 = 530 - Both   Both = 180   Final 180nswer:   180
Answer: A
Average of 10 matches is 34, How many runs one should should score to increase his average by 4 runs. Pick one:  A) A)70  B) B)76  C) C)78  D) D)80  E) E)88

Solution: Explanation:   Average after 11 innings should be 38   So, Required score = (11 * 38) - (10 * 34)   = 418 - 340= 
418 - 340 = 78
78   Answer: Option 78
Answer: C
John makes $65 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase?	Select the correct option:
A) 7.69% B) 16.66% C) 17.8% D) 19% E) 21%

Solution: Increase = (5/65)*100 = (1/13)*100 = 7.69%.   7.69%
Answer: A
Zachary is helping his younger brother, Sterling, learn his multiplication tables. For every question that Sterling answers correctly, Zachary gives him 3 pieces of candy. For every question that Sterling answers incorrectly, Zachary takes away two pieces of candy. After 6 questions, if Sterling had answered 2 more questions correctly, he would have earned 31 pieces of candy. How many of the 6 questions did Zachary answer correctly?	Choices:
A) 6
B) 7
C) 8
D) 9
E) 10

Solution: i got two equations:   3x-2y=25   x+y=6   3x-2(6-x)=25   3x-12+2x=25   5x=37   x=7.4 or between 7 and 8. (ANS 7)
Answer: B
How many cubes of 8cm edge can be cut out of a cube of 16cm edge Choose the correct choice:  A) 36  B) 2  C) 8  D) 48  E) None of these

Solution: Explanation:   number of cubes=(16 x 16 x 16) / (8 x 8 x 8) = 8   Answer: 8
Answer: C
If Y < X and XM > YM, what must be true? Choose the correct choice from the following options
A) M < X.	B) M >0.	C) X < 0.	D) M < 0.	E) Y < 0.

Solution: X>Y, bus as soon as M is multiplied to both sides inequality sign changes.   This is only possible when ve is multiplied on both sides. That means M is ve   M >0. is the answer
Answer: B
A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 12 : 1 ? Select:
A) 6 months B) 3 months C) 2 months D) 8 months E) 9 months

Solution: Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 12. or x = (85000 * 12) / (42500 * 12)= 
(85000 * 12) / (42500 * 12) = 2
2.   So, B joined for 2 months.   Answer: 2 months
Answer: C
The average age of boys in a class is 16 years and that of the girls is 15 years. What is the average age for the whole class? Choose one:
A) 15  B) 16  C) 17  D) Insufficient Data  E) 15.5

Solution: We do not have the number of boys and girls. Hence we cannot find out the answer.   Answer is Insufficient Data.
Answer: D
A copy machine, working at a constant rate, makes 35 copies per minute. A second copy machine, working at a constant rate, makes 75 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
Choose the correct answer
A) 90	B) 2,700	C) 3,300	D) 5,400	E) 324,000

Solution: Together the two machines make 35+75= 
35+75 = 110
110 copies per minute. So, in half an hour they will make 110*30=3,300 copies.   Answer: 3,300.
Answer: C
What is the sum of the integers from -90 to 95, inclusive? Choose the correct choice from the following options.
A) 450  B) 550  C) 650  D) 750  E) 465

Solution: In an arithmetic progression,   the nth term is given by tn=a+(n-1)d   here tn=95, a=-90, d=1   hence, 95=-90+(n-1)   or n=186   Sum of n terms can be calculated by sn=n/2(a+l)   a=first term, l=last term, n=no. of terms   sn=186*(-90+95)/2   sn=186*5/2= 
186*5/2 = 465
465   Answer : 465
Answer: E
If 96 is divided into four parts proportional to 5, 7, 4, 8 then the smallest part is : Choose the correct choice from the following answers:
A) 16  B) 14  C) 20  D) 18  E) 22

Solution: Given ratio = 5 : 7 : 4 : 8 , sum of ratio = 24   :. The smallest part = (96 *4/24)= 
(96 *4/24) = 16
16   16NSWER:16
Answer: A
Find the lowest common multiple of 10, 14 and 20. Options
A) 360  B) 420  C) 510  D) 320  E) 140

Solution: LCM=2*2*5*7= 
2*2*5*7 = 140
140.   Answer is 140
Answer: E
The ratio 4:20 expressed as percent equals to
Choose the correct answer.
A) 20 %	B) 25 %	C) 55 %	D) 65 %	E) None of above

Solution: Explanation:   20 %ctually it means 4 is what percent of 20, which can be calculated as,   (4/20)*100 = 4*5= 
4*5 = 20
20   20 %nswer: Option 20 %
Answer: A
What do you get if you add 3 to 300 five times?  Options:
A) 305	B) 310	C) 320	D) 303	E) 309

Solution: 303   303 , 303 , 303 , 303 , 303
Answer: D
Three days ago, yesterday was the day before Sunday. What day will it be tomorrow?
Choose the correct choice from the following choices
A) monday  B) thursday  C) sunday  D) tuesday  E) wendesday

Solution: Three days ago, yesterday was the day before Sunday, so three days ago was itself Sunday.   That means today is Wednesday, so tomorrow is Thursday
Answer: B
Which one of the following can't be the square of natural number ? Choose the correct option.
A) 465456  B) 656565  C) 521213  D) 143642  E) 643212

Solution: The square of a natural number nerver ends in 2.   143642 is not the square of natural number.   Correct Option is 143642
Answer: D
Car A runs at the speed of 65km/hr & reaches its destination in 8hr. Car B runs at the speed of 75 km/h & reaches its destination in 4h. What is the respective ratio of distances covered by Car A & Car B?	Choose the correct choice from the following answers:
A) 26 : 15  B) 12 : 7  C) 13 : 7  D) 15 : 6  E) 13 : 6

Solution: Sol. Distance travelled by Car 26 : 15 = 65 Ã— 8 = 520 km   Distance travelled by Car B = 75 Ã— 4 = 300 km   Ratio = 520/300 = 26 : 15   26 : 15
Answer: A
The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is ?
Choose the correct choice from the following answers.
A) 118  B) 290  C) 119  D) 139  E) 132

Solution: Number of words which can be formed   = 5! - 1 = 120 - 1= 
120 - 1 = 119
119.   Answer:119
Answer: C
A farmer has 100337 seeds to plant throughout 9 acres. To evenly distribute the seeds, how many would he need to remove? Options:
A) 9  B) 3  C) 4  D) 0  E) 1

Solution: For this solution you need to add the digits of the total seeds and find the closest number divisible by 9. 100337=14. 9 is divisible by 9. 14-5=9 Therefore the farmer would need to remove 4 seeds to divide the seeds evenly between the acres. 4orrecr answer 4.
Answer: C
Which of the following integers is a divisor of(15!+15)? Choices:	A) 15	B) 14	C) 13	D) 7	E) 2

Solution: When we say 15!, it just means 1*2*3*4*5*...*13*14*15   So you need to find the integer which is a divisor of   (1*2*3*4*5*...*13*14*15 + 15) = 15 (1*2*3*4*5*...*12*13*14 + 1) We obtain this by taking 15 common.   Hence 15 is definitely a divisor of (15! + 15).   15
Answer: A
At a certain university, 7 students from the 10-student history department and 5 students from the 7-student English department will be selected to form a 12-student committee. At a neighboring university, 2 students from a 10-person math department and 3 students from a 7-student science department will be selected to form a 5-student focus group. What is the ratio of the number of ways in which the 12-student committee can be formed to the number of ways in which the 5-student focus group can be formed? Options
A) 25/16	B) 8/5	C) 12/5	D) 16/5	E) 144/25

Solution: Number of ways of selecting a 12 member student committee = 10C7 * 7C5   Number of ways of selecting a focus group of 5 students = 10C2 * 7C3   Ratio of 12 member student committee to 5 member focus group = 10C7∗7C5/10C2∗7C3= 8585   Answer: 8/5
Answer: B
The speed of a boat in upstream is 45 kmph and the speed of the boat downstream is 95 kmph. Find the speed of the boat in still water and the speed of the stream?
Answers
A) 10 kmph B) 11 kmph C) 25 kmph D) 18 kmph E) 19 kmph

Solution: Speed of the boat in still water = (45+95)/2= 
(45+95)/2 = 70
70 kmph. Speed of the stream= (95-45)/2= 
(95-45)/2 = 25
25 kmph.Answer: 25 kmph
Answer: C
How many four digit even numbers can be formed using the digits {2, 3, 5, 1, 7, 9}	Select the correct option.
A) 38	B) 77	C) 66	D) 28	E) 60

Solution: Explanation:   The given digits are 1, 2, 3, 5, 7, 9   A number is even when its units digit is even. Of the given digits, two is the only even digit.   Units place is filled with only '2' and the remaining three places can be filled in âµPâ‚ƒ ways.   Number of even numbers = âµPâ‚ƒ = 60.   Answer: 60
Answer: E
A, B and C enter into partnership. A invests some money at the beginning, B invests double the amount after 6 months, and C invests thrice the amount after 8 months. If the annual gain be Rs.18000. A's share is? Answers
A) 2999	B) 2778	C) 6000	D) 2889	E) 6612

Solution: x* 12 : 2x* 6: 3x* 4   1:1:1   1/3 * 18000= 
1/3 * 18000 = 6_000
6000   Answer:6000
Answer: C
Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 48 people bought tickets to the concert, what was the total revenue from ticket sales?	Choose the correct choice from the following answers.
A) $600 B) $820 C) $850 D) $980 E) $1,140

Solution: Price of 1 ticket = 20$   Revenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )   = 10 * 12= 
10 * 12 = 120
120   Revenue generated from sales of next 20 tickets= 20 *(85/100 * 20 )   =20*17= 
20*17 = 340
340   Revenue generated from sales of last 18 tickets= 20 * 18= 
20 * 18 = 360
360   Revenue generated from sales of 48 tickets= 120 + 340 + 360= 
120 + 340 + 360 = 820
820 $   Answer $820
Answer: B
The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is ? Choose the correct choice from the following answers.
A) 0.5987 B) 0.5904 C) 0.5978 D) 0.5928 E) 0.5917

Solution: P(winning prize atleast on one ticket)   = 1 - P("Losing on all tickets")   = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2)   = (1.64)(0.36)   = 0.5904   Answer: 0.5904
Answer: B
Rakesh invested an amount of Rs.12000 at the rate of 10% simple interest and another amount at the rate of 20% simple interest. The total interest earned at the end of one year on the amount invested became 14 p.c.p.a. Find the total amount invested .	Choose the correct answer
A) Rs.20000	B) Rs.22000	C) Rs.24000	D) Rs.25000	E) Rs.27000

Solution: Let the second amount be Rs.x. then,   (12000* 10 * 1)/100 + (x*20 *1)/100 = ((12000 +x)* 14*1)/100   = 1200 +x/5 = (168000 +14x)/100   600000 + 100x = 840000 +70 x   30x = 240000; X = 8000   Total investment = 12000 +8000 = Rs.20000   Rs.20000NSWER:Rs.20000
Answer: A
Today is 70 days before Mariah's graduation. If she graduates on a Sunday, what day of the week is it today?	Choose the correct choice from the following options.
A) Wednesday	B) Thursday	C) Friday	D) Saturday	E) Sunday

Solution: Each weekday is repeated every 7 days. 70 divided by 7 is 10, with no remainder. Therefore, 70 days before the graduation occurs on the same weekday as the graduation, meaning today is a Sunday. Answer: Sunday
Answer: E
A cargo ship carrying four kinds of items, doohickies, geegaws, widgets, and yamyams, arrives at the port. Each item weighs 2, 11, 5, and 7 pounds, respectively, and each item is weighed as it is unloaded. If, in the middle of the unloading process, the product of the individual weights of the unloaded items equals 149,072,000 pounds, how many widgets have been unloaded?	Choices.
A) 2
B) 3
C) 4
D) 5
E) 6

Solution: We need to know the number of widgets (which weigh 5 pounds each). The number of times that 5 divides the number is related to the number of times that 10 divides the number.   When we divide 149,072,000 by 1000, we get 149,072,000 = 149,072 * 5^3 *2^3.   149,072 is not divisible by 5, thus there are 3 widgets.   The answer is 3.
Answer: B
A survey of employers found that during 1993 employment costs rose 3.5 percent, where employment costs consist of salary costs and fringe-benefit costs. If salary costs rose 3 percent and fringe-benefit costs rose 7.5 percent during 1993, then fringe-benefit costs represented what percent of employment costs at the beginning of 1993 ?	Choose the correct choice: A) 16.5% B) 10% C) 35% D) 55% E) 65%

Solution: The amount by which employment costs rose is equal to 0.035(salary costs + fringe benefit costs);   On the other hand the amount by which employment costs rose is equal to 0.03*salary costs + 0.075*fringe benefit costs;   So, 35(S+F) = 30S+75F --> S = 9F --> F/S = 1/9 --> F/(S+F) = 1/(1+9) = 1/10 = 0.1.   Answer: 10%.
Answer: B
The respective ages of father and his son are 44 and 16 years. In how many years will the father be twice as old as his son ?
Choose the correct choice from the following: A) 19 years B) 9 years C) 10 years D) 15 years E) 12 years

Solution: Suppose x years later the father will be twice as old as his son.   x + 44 = 2 (x + 16)   x = 44 - 32= 
44 - 32 = 12
12 years   answer : 12 years
Answer: E
There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle.
Choose the correct choice from the following answers.
A) 10 B) 11 C) 12 D) 13 E) 14

Solution: Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm.   a2 = 784 = (4)(196) = (22).(142)   a = (2)(14) = 28   a = 2l, l = a/2 = 14   l = (7/3)s   Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12 cm.   Answer: Option 12
Answer: C