Maths Book All new maths .. Kazy Tanjilus Salekeen 1/16/2015

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1. A man had traveled 1/3rd of the total distance of his trip when his car broke

down. He finished the journey on foot, spending twenty times as long

walking as he had spent driving. How many times faster was his driving

speed than his walking speed?

2. A train leaves station X for station Y. At 8:20 am, when the train has crossed

one fifth of the way to station Y, it passes station A at 8:30 am, when the

train has crossed one third of the way to station Y, it passes station B. At

what time does the train leave station X?

3. A man had traveled 1/4th of the total distance of his trip when his car broke

down. He finished the journey on foot. The ratio of his walking time to

driving time was 15:1. Calculate the ratio of his driving speed to his walking

speed.

4. A train left Dhaka to Chitagong at 62 km per hour and at the same time

another train left Chitagong for Dhaka at 48 km per hour on the same

route. How far apart were the two trains one hour before they met?

5. One third, one fourth, one fifth and one seventh of the human population of Island X, which has fewer than 5000 human inhabitants, are all whole

numbers and their sum is exactly the population of Island Y. what is the

population of Island Y?

6. A rope, x feet long, is cut into two pieces such that the length of one piece

is 1 foot more than twice the length of the other piece. Which of the

following is the length, in feet, of the larger piece? A) (x+2)/2 B) (2x+1)/2

C) (2x+3)/3 D) (2x+3)/4 E) (2x+1)/3

7. If you buy x apples at a cost of (y+1.5) taka per piece and y oranges at a cost

of Tk (x+1.5) per piece, and you spend higher amount of money on buying

apples, then which of the following is true? A. x>y B. yy+3 E. cannot be determined

8. If 1.4 is halfway between two point x and y, what are the possible values of

x and y?

a. -1.4 and 2.4 b. -1 and 2 c. -0.3 and 3.1 d. 0.15 and 1.55 e. none of these

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9. At a school teacher-student ratio is 1:9. If 2/3rd of the students are female

and one-quarter of the teachers are female, what fraction of the total

students and teachers are female?

10. Two varieties of sugar are mixed in a certain ratio. The cost of the mixture

per kg is Tk 0.50 less than that of the superior variety and Tk 0.75 more

than that of the inferior variety. What was the ratio of superior variety to

inferior variety in the mixture?

11. Arif wished to use his VCR to record a 60 minute documentary scheduled to

be aired at 10:30 PM. At 8:00 that morning, he set the timer to begin

recording at 10:30 PM the same day and to stop recording exactly 60

minutes later. If the timer on the VCR slows down by 30 seconds every hour

and the documentary was aired on schedule, then how much of the

program after the documentary did the VCR record?

12. The average of a set of 12 numbers which includes 34 is N. If 34 is removed

from the set and 38 is added to the set, what is the average of the new set

of numbers in terms of N?

a. (N+1)/3 b. (N+19)/6 C. N+4 D. N+6 E. None

13. A cashier reversed the digits of one customers correct amount of change

and thus gave the customer an incorrect amount of change. If the cash

register contained Taka 45 more than it should have as a result of this error,

which of the following could have been the correct amount of change in

Taka?

14. Find the volume of a triangular solid cylinder with the following

dimensions: 4 feet base, 3 feet height of triangle, and 10 feet height of the

cylinder

15. There are 8 job applicants sitting in a waiting room- 4 women and 4 men.

Two of the applicants are selected one after another at random. What is

the probability that both will be women?

16. Two similar triangles have areas of 18 cm square and 32 cm square. If the

base of the smaller triangle is 6 cm, find the base of the larger triangle.

17. If an integer is selected randomly and is divided by 7, what is the probability

that the remainder is greater than 0 and NOT an even number?

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18. A colony of 15000 ants increased by 50% after being fed. Then after 4

weeks without food, the number of the ants dropped by 60%. What

percentage decline did the original population undergo?

19. At college X, the faculty-to-student ratio is 1:9. If two-third of the students

are female and one-quarter of the faculty is female, what fraction of the

combined students and faculty is female?

20. Arman wanted to have Tk. 39200 as interest after 5 years. He has invested an amount in an account for 1 year at 8% interest rate. From the second

year, he invested the principal amount in another account offering 10%

interest for 3 years. At the beginning of the fifth year he invested the

principal amount in another account at the rate of 11%. What was the

principal amount? (assume simple interest)

21. Mr. jamil, a renowned engineer, designed a ball so that when it was

dropped, it rose with each bounce exactly one-half as high as it had fallen.

The engineer dropped the ball from a 24-foot platform and caught it after it

had traveled 23.25 yards. How many times did the ball bounce?

22. In a nationwide poll, P people were asked 2 questions. If 2/5 of them

answered yes to question 1, and of those 1/3 also answered yes to

question 2, which of the following represents the number of people polled

who did not answer yes to both questions?

A. 11/13 b. 3/16 c. 13/15 d. 2/15 e. None 23. Rahim and Sohail live in the same house and work in the same place. Rahim

takes 20 minutes and Sohail takes 30 minutes to reach workplace. Sohail

starts from the house 5 minutes earlier than Rahim starts. How many

minutes would Rahim take to meet sohail?

24. The price of sugar increases by 32%. A family reduces its consumption so

that the expenditure of the sugar is up by 10% only. If the total

consumption of sugar before the price rise was 10 kg per month, then the

consumption of sugar per month is approximately?

25. A maximum of 25 grams of salt dissolves in 100 grams of water and any more salt, if added, remain undissolved and a sediment falls at the bottom.

Now, water is evaporated from 1 kilogram of a 4% solution at the rate of 28

grams per hour. After how long would the salt start sedimenting?

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26. In a class, the average score of boys in an examination is 64 and that of girls

is 61. If the average score of the whole class is 62.2, then what percent of

the class are the boys?

27. A bag contains 25-p,10-p and 5-p coins in the ratio 1:2:3. If the total value

is Tk 30, the number of 5-p coins is:

28. Last year the ratio between the salaries of A and B was 3:4. But the ratio of

their individual salaries between last year and this year were 4:5 and 2:3

respectively. If the sum of their present salaries is Tk 4160, then how much

is the salary of A now?

29. A & B have incomes in the ratio 5:3. The expenses of A, B &C are in the ratio

8:5:2. If C spends Tk 2000 and B saves Tk 700, As saving is:

30. A ,B & C enter into partnership by investing in the ratio 3:5:7. After a year, C invests another Tk. 337600 while A withdraw Tk. 45600. The ratio of

investments then changes to 24:69:167. How much did A invest initially?

31. Two different schools, A and B, have the same number of students. Then

ratio of the boys in schools A & the boys in school B is 2:1 and the ratio of

the girls in schools A &n the girls of school B is 4: 5. What is the ratio of the

boys & girls in school A & the girls of school A ?

32. Let A,B & C shares profit at the ratio of 2:3:7 and A & B together get Tk.500

less than C gets. How much A will get:

33. Two different companies, X & Y, have the same number of workers. The ratio of the male workers in company X & the male workers in company Y is

2:1 and the ratio of the female workers in company X and the female

workers in company Y is 4:5. What is the ratio of the male workers to the

female workers in company X?

34. The ratio of marbles collected by Amir, Babu and Enam is 1:2:5. If Babu

gives 3 marbles to Amir and receives 6 marbles from Enam the ratio

becomes 3:5:8. How many marbles did Enam have?

35. A recipe for egg nog calls for 2 eggs for every 3 cups of milk. If there are 4

cups in a quart, how many eggs will be needed to mix with 6 quarts of milk?

36. A students grade in a course is determined by 4 quizzes and 1 exam. If the

exam counts twice as much as each of the quizzes, what fraction of the final

grade is determined by the exam?

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37. If cement, gravel and sand are to be mixed in the ratio 3:5:7 respectively

and 5 tones of cement are available, how many tons of the mixture can be

made?

38. Bucky leaves Amity for Truro, which is 8 miles away, at the same time that

Robin leaves Truro for Amity. If neither of them stops along the way and

they meet along the road 2 miles from Amity, what is the ratio of Buckys

average speed to Robins average speed?

39. For every Christian person in a representative committee there are two

Hindus and for each Hindu person there are seven Muslims. This policy

represents the ratio of different religions in a population. Express the ratio

of Muslims to Hindus to Christians in that population?

40. Two cars race around a circular track in opposite directions at constant rates. They start at the same point and meet every 30 seconds. If they

move in the same direction, they meet every 120 seconds. If the track is

1800 meter long, what is the speed of each car?